When I think of temperature, I usually think of two things. I think of temperature as it relates to weather and I think of temperature as it relates to my health. I'm sure I'm not alone in those thoughts. We look at temperature measurements everyday. Anytime you turn on the TV or radio to find figure out how to dress appropriately, I would assume the air temperature has a big affect on your decision. The importance of knowing what temperature is, what it measures, and how it affects us isn't limited to our daily fashion decisions.
First, what are we measuring when we measure temperature? Temperature really is a measurement of energy. Heat is a result of the amount of energy that is in the particles of a substance. Does that make sense? In other words, in a particular substance, like air, there are tiny particles that are moving and bouncing off each other. The more energy that is in the substance, the more these particles move and bounce, giving off heat. When you think of the term "cold" don't think of it as the opposite of heat, think of it as a lack of heat, or lack of energy in a substance. A piece of ice has a lot less heat energy stored in the particles than boiling water does. After all, to boil water, don't you add energy to it?
So, now that we barely scratched the surface of what temperature is measuring ( energy ), we can look at what methods are used to measure it. In the U.S. we typically use Fahrenheit as the standard temperature measurement system. We also use the Metric standard of Celsius, or Centigrade. Most of the world uses the Metric standard. In science, the use of Kelvin as a temperature standard is sometimes used, but is used typically for very cold measurements.
Sometimes, we will adjust our view of temperature from what the measurement actually is, to what it "feels" like. When we use temperature to estimate our comfort level for outdoor activities, we often times will adjust for other factors that can affect how the temperature feels. An example of one of these adjustments is the wind chill factor. When the wind is blowing across our bodies, it can make the outside air temperature seem much cooler than the actual temperature. In fact, the air movement helps to dissipate heat from our body, aiding in the cooling affect. Another example on the opposite side of the spectrum is the heat index. When there are high levels of moisture in the atmosphere the air surrounding our body isn't able to absorb as much of the heat energy within our bodies and we tend to feel warmer than the actual outdoor temperature readings may show.
It is important to know some of the math behind these temperature readings and how the wind chill and heat indices work. For more information on how to convert temperatures and how we adjust these measurements to determine our comfort levels, try some of these online calculators.
Celsius to Fahrenheit Conversion Calculator
Fahrenheit to Celsius Conversion Calculator
Heat Index Calculator
Wind Chill Calculator
Temperature Calculator Menu
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Friday, September 30, 2011
Thursday, September 29, 2011
Time. The Most Important Measurement Since the Beginning of...Itself
Time is referred to so many times in a day. Think about how many moments you take to look at a clock, a watch, or your cellphone. We use time to judge where we are in our daily routine, or to coordinate a certain event. But, we also use time as a measurement. We think about how much time has lapsed from one event, to the next.
When looking at time as a comparing measurement between two events, rather than a reference to where we are in our daily routine, it is easy to look at sports as an example. In most sports, there is an element of time. You can have a set amount of time that you have to perform the best you can, such as the 4 quarters of a basketball game. There can also be a measurement of time as a comparison of the sport. In track, the competitor with the quickest time to run a set distance is the winner.
Because time is so important with our lives, it is important to be able to measure time and understand the math of time to accurately compare. Luckily, time is not measured differently in Metric, or U.S. Standard measurements.
Over the centuries, our time units have been derived from how the Earth rotates and revolves around the sun. This results in our seasons, years and days. From there we break down our measurements further to hours, minutes, and seconds.
Sometimes it can get confusing if you are looking at other planets and how they are arranged around the Sun. Because a year is how long it takes the Earth to revolve around the Sun, it does not work the same for other planets. It takes much longer for some planets to make a full revolution around the sun, therefore one year for that planet would be multiple Earth years. The same can be said for days. One Earth day is how long it takes the Earth to turn one full rotation. On other planets it may take longer to make a full rotation. That planet's day, would be multiple Earth days.
Enough with some of the basics of time. I could spend a lot of time discussing this. It is important to know how to convert from years, to days, hours, minutes, and seconds. For more on time and how to convert between these units, try using this online calculator:
Time Conversion Calculator
To see how time can be used in conjunction with other mathematical concepts like speed, flow rate, and navigation, browse through some of these other online calculators: (But only if you have enough time)
Online Calculator Categories
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
When looking at time as a comparing measurement between two events, rather than a reference to where we are in our daily routine, it is easy to look at sports as an example. In most sports, there is an element of time. You can have a set amount of time that you have to perform the best you can, such as the 4 quarters of a basketball game. There can also be a measurement of time as a comparison of the sport. In track, the competitor with the quickest time to run a set distance is the winner.
Because time is so important with our lives, it is important to be able to measure time and understand the math of time to accurately compare. Luckily, time is not measured differently in Metric, or U.S. Standard measurements.
Over the centuries, our time units have been derived from how the Earth rotates and revolves around the sun. This results in our seasons, years and days. From there we break down our measurements further to hours, minutes, and seconds.
Sometimes it can get confusing if you are looking at other planets and how they are arranged around the Sun. Because a year is how long it takes the Earth to revolve around the Sun, it does not work the same for other planets. It takes much longer for some planets to make a full revolution around the sun, therefore one year for that planet would be multiple Earth years. The same can be said for days. One Earth day is how long it takes the Earth to turn one full rotation. On other planets it may take longer to make a full rotation. That planet's day, would be multiple Earth days.
Enough with some of the basics of time. I could spend a lot of time discussing this. It is important to know how to convert from years, to days, hours, minutes, and seconds. For more on time and how to convert between these units, try using this online calculator:
Time Conversion Calculator
To see how time can be used in conjunction with other mathematical concepts like speed, flow rate, and navigation, browse through some of these other online calculators: (But only if you have enough time)
Online Calculator Categories
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Wednesday, September 28, 2011
A Quick Blog About Speed Conversions and Rates
Speed is one of the most common forms of measurement. Just think about how many times you reference speed in a day. Just driving, how many times do you think about how fast you are going? Just like other measurements there are different systems of measurement for speed.
First, to understand speed, you need to understand how it is calculated. Speed is a rate measurement. It is the amount of distance travelled in a set amount of time. In the U.S. we often times look at speed in miles per hour. It's fairly self-explanatory. If you are travelling at a speed that allows you to cover a distance of 5 miles in one hour, your speed is 5 miles per hour. If you travel 10 miles in 2 hours, your rate of speed is still 5 miles per hour.
Many times in navigation, you may hear of a speed term called Knots. This term is similar to our traditional miles per hour (MPH) speed rate. The difference is the length of the mile. In our traditional MPH rate, the mile is called a statute mile. A knot is another way of saying nautical mile per hour. A nautical mile length is slightly different that the statute mile length we normally associate with in the U.S. The reason that the two different mile measurements have been used is that the statute mile was evolved from surveying land, and nautical miles were evolved from seafaring navigation.
In addition to these forms of speed measurement, there is also the Metric system speed measurements. Luckily, there is a universal standard measurement for time, so length is the main concern when comparing speed measurements. Metric speed is found from using a metric form of length for the distance travelled per set amount of time. Some examples of metric system speed rates could be kilometers per hour, or even meters per second.
It is important to have a basic understanding of how speed is calculated, as well as how to convert between different standards. In addition to converting the length from US Standards to Metric Standards, it is also important to be cognizant of the time referenced in each speed rate. If a speed is measured in length per second, you should be able to convert that to it's equivalent in length per hour.
For more practice on converting speeds and lengths, try some of the calculators below:
Miles per Hour to Kilometers per Hour Conversion Calculator
Knots to Statute Miles per Hour Conversion Calculator
Miles per Hour to Knots Conversion Calculator
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
First, to understand speed, you need to understand how it is calculated. Speed is a rate measurement. It is the amount of distance travelled in a set amount of time. In the U.S. we often times look at speed in miles per hour. It's fairly self-explanatory. If you are travelling at a speed that allows you to cover a distance of 5 miles in one hour, your speed is 5 miles per hour. If you travel 10 miles in 2 hours, your rate of speed is still 5 miles per hour.
Many times in navigation, you may hear of a speed term called Knots. This term is similar to our traditional miles per hour (MPH) speed rate. The difference is the length of the mile. In our traditional MPH rate, the mile is called a statute mile. A knot is another way of saying nautical mile per hour. A nautical mile length is slightly different that the statute mile length we normally associate with in the U.S. The reason that the two different mile measurements have been used is that the statute mile was evolved from surveying land, and nautical miles were evolved from seafaring navigation.
In addition to these forms of speed measurement, there is also the Metric system speed measurements. Luckily, there is a universal standard measurement for time, so length is the main concern when comparing speed measurements. Metric speed is found from using a metric form of length for the distance travelled per set amount of time. Some examples of metric system speed rates could be kilometers per hour, or even meters per second.
It is important to have a basic understanding of how speed is calculated, as well as how to convert between different standards. In addition to converting the length from US Standards to Metric Standards, it is also important to be cognizant of the time referenced in each speed rate. If a speed is measured in length per second, you should be able to convert that to it's equivalent in length per hour.
For more practice on converting speeds and lengths, try some of the calculators below:
Miles per Hour to Kilometers per Hour Conversion Calculator
Knots to Statute Miles per Hour Conversion Calculator
Miles per Hour to Knots Conversion Calculator
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Tuesday, September 27, 2011
Don't Wait to Learn More About Weight Conversion Math
Weight is one of the most common measurements used in our society. Weight is commonly used as a measurement of mass. But, it is also used to measure the gravitational force on an object. Because of the two uses, it can often become confusing on how it is measured and mistakes can be commonplace when you misinterpret measurements.
When it comes to mass, weight is a measurement of comparison. Mass is one of the measurements used to calculate density. When you visit the doctor, they may have you stand on a set of scales that uses small weights to balance an arm that measures your weight. This scale is not affected by changes in gravity and measures your weight, or mass, in comparison with the known mass of a small weight. This type of scale is not affected by changes in gravitational pull.
Many times, an electonic scale may be used. This scale measures the amount of pressure that your weight applies to a surface. Because it is measuring the amount of gravitational force the Earth is applying to your body, it will change with how far you are from the center of the Earth, or it could even change if the moon is directly above and the moon's gravity is counteracting the gravity of the Earth.
I know this can be confusing. Just remember to think about what you are actually measuring. Are you comparing weight to a known mass like on a counterbalance scale, or are you measuring how much force the Earth's gravity is pulling down on an object.
To add to the confusion is the separate standards for measuring weight. There is the U.S. Standard and their is the Metric System. The metric system uses a base unit of weight/mass called the gram and then larger and smaller units are derived from the gram in powers of 10. For example, a milligram is 1/1000th of a gram and a kilogram is 1000 grams.
The U.S. Standard is a little more difficult to calculate. There are different weight units. For example, you have the ounce, pound, and ton. One ounce is 1/16th of a pound and one ton is 2,000 pounds.
Not only is it important to be able to convert within one system of measurement, like calculating how many ounces are in a ton, but also to be able to convert from U.S. Standard measurements to Metric.
For some practice on converting weight and mass measurements, try using these calculators:
Grams to Metric and US Standard Weight Conversion Calculator
Pounds to Metric and US Standard Weight Conversion Calculator
A Menu of Weight Conversion Calculators
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
When it comes to mass, weight is a measurement of comparison. Mass is one of the measurements used to calculate density. When you visit the doctor, they may have you stand on a set of scales that uses small weights to balance an arm that measures your weight. This scale is not affected by changes in gravity and measures your weight, or mass, in comparison with the known mass of a small weight. This type of scale is not affected by changes in gravitational pull.
Many times, an electonic scale may be used. This scale measures the amount of pressure that your weight applies to a surface. Because it is measuring the amount of gravitational force the Earth is applying to your body, it will change with how far you are from the center of the Earth, or it could even change if the moon is directly above and the moon's gravity is counteracting the gravity of the Earth.
I know this can be confusing. Just remember to think about what you are actually measuring. Are you comparing weight to a known mass like on a counterbalance scale, or are you measuring how much force the Earth's gravity is pulling down on an object.
To add to the confusion is the separate standards for measuring weight. There is the U.S. Standard and their is the Metric System. The metric system uses a base unit of weight/mass called the gram and then larger and smaller units are derived from the gram in powers of 10. For example, a milligram is 1/1000th of a gram and a kilogram is 1000 grams.
The U.S. Standard is a little more difficult to calculate. There are different weight units. For example, you have the ounce, pound, and ton. One ounce is 1/16th of a pound and one ton is 2,000 pounds.
Not only is it important to be able to convert within one system of measurement, like calculating how many ounces are in a ton, but also to be able to convert from U.S. Standard measurements to Metric.
For some practice on converting weight and mass measurements, try using these calculators:
Grams to Metric and US Standard Weight Conversion Calculator
Pounds to Metric and US Standard Weight Conversion Calculator
A Menu of Weight Conversion Calculators
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Monday, September 26, 2011
A Short Length Blog About Length and Converting Lengths.
I don't want to get into a lengthy discussion in a blog about length and converting lengths. Actually, I apologize for the pun. Length may seem like a pretty straight-forward measurement, but there have been so many ways that people have measured length through history. It is common to make mistakes when people don't reference the same standard of measurements. Because of the different ways to measure length, it's important to know the math behind converting from one system of measurement to another.
There are two basic systems of measurement currently used in the world. Probably the most widely used is the Metric System. This system is fairly simple to use. For length, the basic unit is the meter. For longer and shorter measurements, the meter is either multiplied, or divided, by powers of 10. For example, for measurements that would require thousands of meters to measure, you may use a decameter which is equal to 10 meters. A hectometer is equal to 100 meters. And for longer measurements, a kilometer is 1000 meters.
The same can be used for smaller measurements of length. A decimeter is 1/10th of a meter, a centimeter is 1/100th of a meter, and a millimeter is 1/1000th of a meter.
The United States has it's own customary measurement system that is derived from the British Imperial system. The basic lengths used in this system have been derived from centuries of different standards of measurements. This system is made up of various lengths like the inch, foot, yard and mile. Although this system is very widely used in the US, the metric system is still preferred as the standard for use in Science, Aviation and the Military.
Because of the difference between these two commonly used standards of length, it is important to know how to convert from one system to the other. Because measurements of length are necessary in designing buildings, machinery, or just for comparisons, it is easy to see how mistakes can be made when converting. For an example of a common length conversion, try using this Mile to Metric Length Conversion Calculator. Just the same, you can use this Kilometer to Mile Conversion Calculator. The next time you travel, try converting miles to kilometers, or look at the speedometer to see how many kilometers per hour is equal to 60 miles per hour.
For more length conversion calculators, try the link below.
Length Conversion Calculators
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
There are two basic systems of measurement currently used in the world. Probably the most widely used is the Metric System. This system is fairly simple to use. For length, the basic unit is the meter. For longer and shorter measurements, the meter is either multiplied, or divided, by powers of 10. For example, for measurements that would require thousands of meters to measure, you may use a decameter which is equal to 10 meters. A hectometer is equal to 100 meters. And for longer measurements, a kilometer is 1000 meters.
The same can be used for smaller measurements of length. A decimeter is 1/10th of a meter, a centimeter is 1/100th of a meter, and a millimeter is 1/1000th of a meter.
The United States has it's own customary measurement system that is derived from the British Imperial system. The basic lengths used in this system have been derived from centuries of different standards of measurements. This system is made up of various lengths like the inch, foot, yard and mile. Although this system is very widely used in the US, the metric system is still preferred as the standard for use in Science, Aviation and the Military.
Because of the difference between these two commonly used standards of length, it is important to know how to convert from one system to the other. Because measurements of length are necessary in designing buildings, machinery, or just for comparisons, it is easy to see how mistakes can be made when converting. For an example of a common length conversion, try using this Mile to Metric Length Conversion Calculator. Just the same, you can use this Kilometer to Mile Conversion Calculator. The next time you travel, try converting miles to kilometers, or look at the speedometer to see how many kilometers per hour is equal to 60 miles per hour.
For more length conversion calculators, try the link below.
Length Conversion Calculators
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Saturday, September 24, 2011
Lightning and Thunder Math. Calculating the Distance from a Strike.
I have been fascinated by storms all of my life. The unpredictability of lightning, thunder, winds and rain add to the aspects of apprehension and excitement to see what will happen. I know I'm not alone. If you ever sit to observe the surrounding animals when a storm is moving in, you'll notice a change in their behavior as well. Don't get me wrong, storms can be very dangerous, but if you are smart and safe, they are a very wondrous part of nature.
Enough of ranting about storms. Let's talk lightning and thunder. Lightning is the electrical discharge that can occur in nature. It is similar to the static electricity that sometimes will surprise you when you touch a doorknob, only on a much larger and dangerous scale. Lightning occurs when a buildup of static electricity is in the atmosphere. When there is a storm, the ability to build up this static is much more evident and a discharge will occur.
Thunder is the soundwave that is created by the lightning heating the surrounding air around the discharge of electricity. The drastic amount of heat that is created sends waves of vibrations through the air. Sometimes it's a low rumble, and sometimes it's a sharp crack.
Growing up, I was told you could approximate the distance you are from a lightning strike by counting the amount of seconds it took from the moment you saw the lightning to the moment you hear the thunder. I've learned over the years that everyone seems to have a different rule as to how many seconds and how far the lightning strike is. So, let's look at how to calculate this.
When you observe a lightning strike, what you see is the light generated by the electrical discharge. When you hear the thunder, you are hearing the sound vibration created by that electrical discharge. The speed of light and the speed of sound are very different. Because light travels at over 186,000 miles per second and the speed of sound travels at .21 miles per second, we can approximate the distance you are from the lightning strike.
Since light travels so fast, and we're looking for an estimated difference, we're only going to calculate the distance using the speed of sound. If you observe a lightning strike and start counting, every second you are able to count before you hear the thunder is about .21 miles. So, if you count to 5, you have about 1 mile between you and the lightning strike.
This is a very simple way of calculating the distance. If you want to learn more about the math behind this, calculating the speed of light, or calculating the speed of sound, follow the links below.
Speed of Sound Calculator
Light Year Distance Calculator
Lightning Strike Distance Calculator
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Enough of ranting about storms. Let's talk lightning and thunder. Lightning is the electrical discharge that can occur in nature. It is similar to the static electricity that sometimes will surprise you when you touch a doorknob, only on a much larger and dangerous scale. Lightning occurs when a buildup of static electricity is in the atmosphere. When there is a storm, the ability to build up this static is much more evident and a discharge will occur.
Thunder is the soundwave that is created by the lightning heating the surrounding air around the discharge of electricity. The drastic amount of heat that is created sends waves of vibrations through the air. Sometimes it's a low rumble, and sometimes it's a sharp crack.
Growing up, I was told you could approximate the distance you are from a lightning strike by counting the amount of seconds it took from the moment you saw the lightning to the moment you hear the thunder. I've learned over the years that everyone seems to have a different rule as to how many seconds and how far the lightning strike is. So, let's look at how to calculate this.
When you observe a lightning strike, what you see is the light generated by the electrical discharge. When you hear the thunder, you are hearing the sound vibration created by that electrical discharge. The speed of light and the speed of sound are very different. Because light travels at over 186,000 miles per second and the speed of sound travels at .21 miles per second, we can approximate the distance you are from the lightning strike.
Since light travels so fast, and we're looking for an estimated difference, we're only going to calculate the distance using the speed of sound. If you observe a lightning strike and start counting, every second you are able to count before you hear the thunder is about .21 miles. So, if you count to 5, you have about 1 mile between you and the lightning strike.
This is a very simple way of calculating the distance. If you want to learn more about the math behind this, calculating the speed of light, or calculating the speed of sound, follow the links below.
Speed of Sound Calculator
Light Year Distance Calculator
Lightning Strike Distance Calculator
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Sunday, September 18, 2011
Vehicle Cost, Are You Driving Yourself Into Debt?
It's a fact that owning a vehicle can be considered a necessity for your transportation needs. In many parts of the world, owning a car is almost considered to be a rite of passage. Some people even view car ownership as a way to display their higher social status. Many view vehicles as collectible items that are at, or near, museum quality artifacts. Regardless of your view on vehicle ownership, there are many who find themselves biting off more than they can financially chew. Mostly because they weren't prepared for the true cost of vehicle ownership. There is more to vehicle cost than just the purchase price.
Whether you're looking at purchasing a new car, or an used car, there are numerous costs to take into account other than just the initial purchase price. Even the initial purchase can have hidden taxes and fees that you may not be aware of. There is also the depreciation in value that occurs the moment you drive a new car off of the car lot. If you are looking at a used car, you may not have depreciation, in fact, in some cases an older car can appreciate in value if it is deemed collectable. But, the drawback to a used car is the lack of warranty and any mechanical costs are going to come out of your pocket.
For simplicity let's look at fuel mileage, and the yearly financial costs for insurance, taxes and the loan cost. These factors are going to be a large part of the total cost of ownership for a vehicle.
When shopping for a vehicle, most cars offer a measurement of fuel economy. If you don't see it listed on the car, you can usually find an average fuel economy statistic on the internet. Let's use an example. If you drive an average of 20 miles per work day, and you work 50 weeks per year, your yearly mileage needs would be 5000 miles per year. This isn't including any other mileage that you would use your vehicle for. If you purchased a car that averaged 20 miles per gallon of fuel, you would consume 250 gallons of fuel per year just driving for work. If fuel costs $4.00 per gallon, that is $1000 of fuel costs per year to drive to work.
For more on how to calculate fuel mileage of your car use this online calculator: Fuel Mileage Calculator
In addition to fuel, there is may also been a monthly loan payment if you financed the purchase of the vehicle. If you want to learn more on how to calculate the monthly payment of a vehicle loan, try this online
calculator: Vehicle Loan Monthly Payment Calculator
If you are looking at purchasing a vehicle, you may want to look beyond just the monthly required payment. How much money will you spend in the long run just to own the car? By the time you pay off the loan, how much will the vehicle be worth? These are important things to consider. To learn more about the total cost of a vehicle loan, use this online calculator:
Vehicle Loan Total Cost Calculator
Now you have just some of the costs of owning a vehicle. In addition to these there may be maintenance costs, taxes, and insurance to think about. Don't drive yourself crazy trying to own a car you may not be able to afford.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Whether you're looking at purchasing a new car, or an used car, there are numerous costs to take into account other than just the initial purchase price. Even the initial purchase can have hidden taxes and fees that you may not be aware of. There is also the depreciation in value that occurs the moment you drive a new car off of the car lot. If you are looking at a used car, you may not have depreciation, in fact, in some cases an older car can appreciate in value if it is deemed collectable. But, the drawback to a used car is the lack of warranty and any mechanical costs are going to come out of your pocket.
For simplicity let's look at fuel mileage, and the yearly financial costs for insurance, taxes and the loan cost. These factors are going to be a large part of the total cost of ownership for a vehicle.
When shopping for a vehicle, most cars offer a measurement of fuel economy. If you don't see it listed on the car, you can usually find an average fuel economy statistic on the internet. Let's use an example. If you drive an average of 20 miles per work day, and you work 50 weeks per year, your yearly mileage needs would be 5000 miles per year. This isn't including any other mileage that you would use your vehicle for. If you purchased a car that averaged 20 miles per gallon of fuel, you would consume 250 gallons of fuel per year just driving for work. If fuel costs $4.00 per gallon, that is $1000 of fuel costs per year to drive to work.
For more on how to calculate fuel mileage of your car use this online calculator: Fuel Mileage Calculator
In addition to fuel, there is may also been a monthly loan payment if you financed the purchase of the vehicle. If you want to learn more on how to calculate the monthly payment of a vehicle loan, try this online
calculator: Vehicle Loan Monthly Payment Calculator
If you are looking at purchasing a vehicle, you may want to look beyond just the monthly required payment. How much money will you spend in the long run just to own the car? By the time you pay off the loan, how much will the vehicle be worth? These are important things to consider. To learn more about the total cost of a vehicle loan, use this online calculator:
Vehicle Loan Total Cost Calculator
Now you have just some of the costs of owning a vehicle. In addition to these there may be maintenance costs, taxes, and insurance to think about. Don't drive yourself crazy trying to own a car you may not be able to afford.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Have You Heard About The Speed of Sound?
The speed of sound can be hard to grasp for some. After all, there are other speeds that we are more comfortable with that we use daily. Just about anyone can judge what rate of speed is in miles per hour, or kilometers per hour. We see those measurements all of the time driving down the road. Up until the last century, it was difficult for anyone to imagine travelling at the speed of sound, and most probably didn't understand just what that speed is.
Let's look at sound. Sound is a vibration that travels through a medium. For what we hear, it is a vibration through the air. Air is the medium. If you are under water, vibrations travel through the liquid and the water is the medium. The density of the medium has a large affect on how fast sound can travel through it. The more dense it is, the faster the sound will travel. Water is thicker than air and therefore a sound travelling through water will move faster than through the air.
When we are measuring the speed of a vehicle, like an airplane, we are normally looking at the speed of sound through air. When a jet plane creates a sonic boom, it has reached a speed greater than the speed of sound. As mentioned before, the density of the air will determine at what speed the jet will need to travel to break the sound barrier. Temperature can have a large affect on the density of the air. Hot air is going to be less dense than cold air. Air close to sea level is going to be more dense than air at higher altitudes. So the speed of sound on a hot day at high altitude will be slower than the speed of sound at low altitude on a cold day. The standard used for the speed of sound is the speed in dry air at 68 degrees Fahrenheit. This speed is 768 mile per hour.
To see how much affect the air temperature has on the speed of sound try looking at these calculators.
Speed of Sound Calculator (Fahrenheit)
Speed of Sound Calculator (Celsius)
Now that you have a better understanding of the speed of sound, you can look at other aspects of your life an understand why you may see something and hear it a moment later. For example, you may be at a football game and see the kicker kick the ball in the distance, but hear it a moment later. You can also see lightning and hear the thunder after a few moments. Using the speed of sound you can count how many seconds there is between seeing the lightning, and hearing the thunder to estimate the distance you are from the lightning strike.
Lightning Strike Distance Calculator
In the meantime, try to keep your daily commute at a safe speed and don't try to break any sound barriers on your daily commute.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Let's look at sound. Sound is a vibration that travels through a medium. For what we hear, it is a vibration through the air. Air is the medium. If you are under water, vibrations travel through the liquid and the water is the medium. The density of the medium has a large affect on how fast sound can travel through it. The more dense it is, the faster the sound will travel. Water is thicker than air and therefore a sound travelling through water will move faster than through the air.
When we are measuring the speed of a vehicle, like an airplane, we are normally looking at the speed of sound through air. When a jet plane creates a sonic boom, it has reached a speed greater than the speed of sound. As mentioned before, the density of the air will determine at what speed the jet will need to travel to break the sound barrier. Temperature can have a large affect on the density of the air. Hot air is going to be less dense than cold air. Air close to sea level is going to be more dense than air at higher altitudes. So the speed of sound on a hot day at high altitude will be slower than the speed of sound at low altitude on a cold day. The standard used for the speed of sound is the speed in dry air at 68 degrees Fahrenheit. This speed is 768 mile per hour.
To see how much affect the air temperature has on the speed of sound try looking at these calculators.
Speed of Sound Calculator (Fahrenheit)
Speed of Sound Calculator (Celsius)
Now that you have a better understanding of the speed of sound, you can look at other aspects of your life an understand why you may see something and hear it a moment later. For example, you may be at a football game and see the kicker kick the ball in the distance, but hear it a moment later. You can also see lightning and hear the thunder after a few moments. Using the speed of sound you can count how many seconds there is between seeing the lightning, and hearing the thunder to estimate the distance you are from the lightning strike.
Lightning Strike Distance Calculator
In the meantime, try to keep your daily commute at a safe speed and don't try to break any sound barriers on your daily commute.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
The Cylinder - Not a Round Rectangle...But, Kinda...
We depend so much on the shape of the cylinder. If you truly understand what a cylinder is, you will see that we use it everywhere. To help understand what a cylinder is, I think it is best to imagine one. I think of a can of food. A can is a cylinder. If you look at it from the side, it looks like a rectangle, if you look at it from the top, it's a square. That is the basics of a cylinder.
Now that I've pointed out one example of a cylinder, look around and see what other examples you can think of. How about an unsharpened pencil? A pizza is a very flat cylinder. Any pole or even the columns on old buildings can be cylinders. It's pretty obvious that this shape is important to us. This is why it's important to understand the basic math behind the cylinder.
First, we'll look at the volume of a cylinder. Since volume measures the 3-D aspect of the shape, we need to know the area of the base, then multiply that by the height. The base is a circle, so to find the area we multiply Pi x R2. Pi is a constant that is approximately 3.1416. R is the radius of the circle. Once we find the area of the base circle, we multiply that by the height to find the volume. The total equation is Pi x R2 x H.
Online Calculator for Cylinder Volume
Online Calculator for Circle Area
Surface area of a cylinder is also important to know. The surface area is the amount of area on the surface of the cylinder. This would include the area of the circle on the base, and the area of the circle on the top of the cylinder, as well as the rectangle that wraps around the body of the cylinder. So the total surface area of the two circles would be 2 x Pi x R2. The area of the rectangle that surrounds the body would be found by multiplying the height of the cylinder by the circumference of the base of one of the circles. The circumference is found from the equation 2 x Pi x R. So to find the total surface area of a cylinder the equation is: (2 x Pi x R2) + (2 x Pi x R)
Online Calculator for Cylinder Surface Area
Online Calculator for Circle Circumference
Now you have the basic math behind the cylinder. What other objects would you consider to be cylinders? What is the surface area or volume of those objects? I like to know the volume of the pizza I eat, try that next time you're at a restaurant.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Now that I've pointed out one example of a cylinder, look around and see what other examples you can think of. How about an unsharpened pencil? A pizza is a very flat cylinder. Any pole or even the columns on old buildings can be cylinders. It's pretty obvious that this shape is important to us. This is why it's important to understand the basic math behind the cylinder.
First, we'll look at the volume of a cylinder. Since volume measures the 3-D aspect of the shape, we need to know the area of the base, then multiply that by the height. The base is a circle, so to find the area we multiply Pi x R2. Pi is a constant that is approximately 3.1416. R is the radius of the circle. Once we find the area of the base circle, we multiply that by the height to find the volume. The total equation is Pi x R2 x H.
Online Calculator for Cylinder Volume
Online Calculator for Circle Area
Surface area of a cylinder is also important to know. The surface area is the amount of area on the surface of the cylinder. This would include the area of the circle on the base, and the area of the circle on the top of the cylinder, as well as the rectangle that wraps around the body of the cylinder. So the total surface area of the two circles would be 2 x Pi x R2. The area of the rectangle that surrounds the body would be found by multiplying the height of the cylinder by the circumference of the base of one of the circles. The circumference is found from the equation 2 x Pi x R. So to find the total surface area of a cylinder the equation is: (2 x Pi x R2) + (2 x Pi x R)Online Calculator for Cylinder Surface Area
Online Calculator for Circle Circumference
Now you have the basic math behind the cylinder. What other objects would you consider to be cylinders? What is the surface area or volume of those objects? I like to know the volume of the pizza I eat, try that next time you're at a restaurant.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
To The Point with Cone Math
Although the cone isn't as popular, or as common as other shapes, it is still a mainstay in our daily lives. Without the cone, there would be fewer options to hold your ice cream, it would be difficult to alter traffice around construction zones, and the funnel wouldn't even exist. How would we be able to pour fluids into a small space without a funnel? Because of the unique qualities of this shape, it's important to know the basic math behind the cone.
Let's look at what a cone is. It is a shape that is similar to a pyramid. Instead of the pyramid having a square, or triangular base, it has a circle for a base. The body of the cone extends from the circular base and meets at a point.
The volume of a cone can be calculated from a combination of two equations. First, we need to know the area of the circular base. This equation is Pi x R2. Pi is the constant estimated at 3.1416. R is the radius of the circle. Now that we have what we need to find the area of the cone base, we need to multiply that by 1/3 x Height to find the total volume. This gives us a final equation for volume of 1/3 x H x Pi x R2.
Circle Area Calculator Cone Volume Calculator
Another math function for cones is the surface area. Again, this is a two part equation with the first part finding the area of the base. Again, we use Pi x R2 for the area of the base, now we need to find the surface area of the body of the cone. To find the body surface area we use Pi x R x S. R is the radius of the base, and S is the length of the slant of the outside edge of the cone from the base to the point. The slant can either be measured on it's own, or you can use the Pythagorean theorem to find the slant length from the cone height and base radius. The total combination of these two parts forms the equation for cone surface area. Pi x R2 x Pi x R x S
Pythagorean Theorem Calculator Cone Surface Area Calculator
Now that you have the basic math behind the geometry of cones, you can effectively find out how much ice cream is left in the bottom of your ice cream cone. And we all know how important that is.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Let's look at what a cone is. It is a shape that is similar to a pyramid. Instead of the pyramid having a square, or triangular base, it has a circle for a base. The body of the cone extends from the circular base and meets at a point.
The volume of a cone can be calculated from a combination of two equations. First, we need to know the area of the circular base. This equation is Pi x R2. Pi is the constant estimated at 3.1416. R is the radius of the circle. Now that we have what we need to find the area of the cone base, we need to multiply that by 1/3 x Height to find the total volume. This gives us a final equation for volume of 1/3 x H x Pi x R2.
Circle Area Calculator Cone Volume Calculator
Another math function for cones is the surface area. Again, this is a two part equation with the first part finding the area of the base. Again, we use Pi x R2 for the area of the base, now we need to find the surface area of the body of the cone. To find the body surface area we use Pi x R x S. R is the radius of the base, and S is the length of the slant of the outside edge of the cone from the base to the point. The slant can either be measured on it's own, or you can use the Pythagorean theorem to find the slant length from the cone height and base radius. The total combination of these two parts forms the equation for cone surface area. Pi x R2 x Pi x R x S
Pythagorean Theorem Calculator Cone Surface Area Calculator
Now that you have the basic math behind the geometry of cones, you can effectively find out how much ice cream is left in the bottom of your ice cream cone. And we all know how important that is.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Fluid Power –How Hydraulics Can Move Mountains
Many people may not realize the potential power that they hold in a glass of water. If you really look closely at the power of fluids, like water, you’ll see how they have the ability to literally move mountains. Examples are everywhere in nature. One of the best examples of how powerful a fluid can be is the Grand Canyon. With enough time, water can carve out vast parts of our landscape. And it didn’t take long for humans to harness fluid power in the form of hydraulics.
Hydraulics is a term used for the application of fluid power in a liquid form. After all, gas is also a fluid. When you look at gas as a fluid power, it is referred to as pneumatic. Hydraulics is most commonly used in machinery. The advantage of using hydraulics in machinery is the ability to move, cut, carry, lift, dig, or mix a very large load. In machinery the hydraulics form a system made up of a pump to move the fluid, hoses or pipes for the fluid to move through, and a hydraulic actuator that performs work. The two most common types of actuators in hydraulics are cylinders and motors.
Before we can get into how the hydraulic motors and cylinders work, we need to understand two aspects of hydraulic power: pressure and flow. Pressure is the amount of force that is being transmitted through a fluid and can be calculated as pounds per square inch (PSI). If you apply 1000 pounds onto one square inch of area, you have 1000 PSI. Flow is the amount of volume and speed in which you are moving the fluid, and is many times calculated as Gallons per Minute (GPM). If you are pumping 20 gallons of fluid every minute, your flow is 20GPM. In hydraulics, horsepower is calculated from pressure and flow.
Calculate Hydraulic Horsepower
A hydraulic cylinder is basically a rod that is inside a sealed tube. As the tube is filled with fluid, it forces the rod out of the tube. Cylinders are everywhere in machinery and can push and pull very large loads of weight. Think of a fork truck and the cylinders used to lift the load. The force that the cylinder can exert depends on cylinder size and the amount of pressure being applied. The amount of speed that the rod moves out at is determined by cylinder size and the flow of the fluid.
Calculate Cylinder Force Calculate Cylinder Speed
A hydraulic motor is very similar to a pump. A pump is being turned by electrical, mechanical, or even human power to create pressure and flow in the fluid. A motor converts the pressure and flow back to a rotating output. Many times motors are mounted to wheels, augers, or mixers. Think of the drum on a cement truck. That is a heavy load being turned. The amount of torque the motor is able to produce depends on the motor displacement and the pressure of the fluid. The speed of the motor also depends on the motor displacement, but depends on fluid flow.
Calculate Hydraulic Motor Torque Calculate Hydraulic Motor Speed
Now you have the basics of how hydraulics work and why they are used on heavy machinery. The next time you drive by a construction site and see the large machinery, think about the river in the Grand Canyon and how powerful fluids really can be.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Hydraulics is a term used for the application of fluid power in a liquid form. After all, gas is also a fluid. When you look at gas as a fluid power, it is referred to as pneumatic. Hydraulics is most commonly used in machinery. The advantage of using hydraulics in machinery is the ability to move, cut, carry, lift, dig, or mix a very large load. In machinery the hydraulics form a system made up of a pump to move the fluid, hoses or pipes for the fluid to move through, and a hydraulic actuator that performs work. The two most common types of actuators in hydraulics are cylinders and motors.
Before we can get into how the hydraulic motors and cylinders work, we need to understand two aspects of hydraulic power: pressure and flow. Pressure is the amount of force that is being transmitted through a fluid and can be calculated as pounds per square inch (PSI). If you apply 1000 pounds onto one square inch of area, you have 1000 PSI. Flow is the amount of volume and speed in which you are moving the fluid, and is many times calculated as Gallons per Minute (GPM). If you are pumping 20 gallons of fluid every minute, your flow is 20GPM. In hydraulics, horsepower is calculated from pressure and flow.
Calculate Hydraulic Horsepower
A hydraulic cylinder is basically a rod that is inside a sealed tube. As the tube is filled with fluid, it forces the rod out of the tube. Cylinders are everywhere in machinery and can push and pull very large loads of weight. Think of a fork truck and the cylinders used to lift the load. The force that the cylinder can exert depends on cylinder size and the amount of pressure being applied. The amount of speed that the rod moves out at is determined by cylinder size and the flow of the fluid.
Calculate Cylinder Force Calculate Cylinder Speed
A hydraulic motor is very similar to a pump. A pump is being turned by electrical, mechanical, or even human power to create pressure and flow in the fluid. A motor converts the pressure and flow back to a rotating output. Many times motors are mounted to wheels, augers, or mixers. Think of the drum on a cement truck. That is a heavy load being turned. The amount of torque the motor is able to produce depends on the motor displacement and the pressure of the fluid. The speed of the motor also depends on the motor displacement, but depends on fluid flow.
Calculate Hydraulic Motor Torque Calculate Hydraulic Motor Speed
Now you have the basics of how hydraulics work and why they are used on heavy machinery. The next time you drive by a construction site and see the large machinery, think about the river in the Grand Canyon and how powerful fluids really can be.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Circle Math - A Well Rounded Education
There are a lot of clichés to choose from for a blog about circle math. What goes around comes around, a new spin on math, or it’s easy as PI. Regardless of the corny ways to describe the subject, there is no denying the importance of knowing the basic math associated with circles. We rely on circles heavily in our daily lives. Imagine a world without wheels, circular planets, and (most important to me) round food like pizza and hamburgers. There are so many aspects in our lives that we rely on circles and spheres that is why it is important to know the basic math associated with them.
The most important mathematical ingredient to understand on this subject is Pi. This is a constant number used when calculating different aspects of circles. The actual number of Pi is approximately 3.141592654….it actually has a never ending amount of numbers after the decimal. In most math classes it suffices to use 3.14 or 3.1416 for more specific answers.
In addition to PI, there is the radius and diameter. The radius is the amount of distance from the center of the circle to the outside of the circle. The diameter is the distance of a line that bisects the circle from one side to the other and crosses through the center. The diameter of a circle is always twice the distance as the radius.
There are no corners, or even sides to this shape. It is a continuous curve around a common point. The outside of a circle is called a circumference. It’s similar to the perimeter of other shapes, but since there isn’t a side, just a constant curve, it’s called a circumference. To calculate the circumference of a circle you need to know the radius length and Pi. The equation is: 2 x Pi x R where R is the radius. Sometimes you’ll also see this equation used with the diameter. Because the diameter is twice the distance as the radius, the equation would be: Pi x D where D is the Diameter.
The area of a circle is also important. ( I want to know how much pizza I’m eating ) To calculate the area of a circle, you can use Pi and the radius again. The equation to find the area is: Pi x R². If you take the square of the radius and multiply that by Pi you will have the area.
Since the sphere is the 3-D version of the circle, the math to calculate the surface area and volume only slightly more complex. You can use the following equation to calculate the surface area of a sphere: 4 x Pi x R². To calculate the volume of a sphere, use the equation: 4/3 x Pi x R³.
Now you have the basic math for circles and spheres. What you can do with this mathematical power is nearly limitless. You can calculate the volume of the Earth, you can calculate the surface area of a baseball, or like me, you can find out the area of a pizza.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
The most important mathematical ingredient to understand on this subject is Pi. This is a constant number used when calculating different aspects of circles. The actual number of Pi is approximately 3.141592654….it actually has a never ending amount of numbers after the decimal. In most math classes it suffices to use 3.14 or 3.1416 for more specific answers.
In addition to PI, there is the radius and diameter. The radius is the amount of distance from the center of the circle to the outside of the circle. The diameter is the distance of a line that bisects the circle from one side to the other and crosses through the center. The diameter of a circle is always twice the distance as the radius.
There are no corners, or even sides to this shape. It is a continuous curve around a common point. The outside of a circle is called a circumference. It’s similar to the perimeter of other shapes, but since there isn’t a side, just a constant curve, it’s called a circumference. To calculate the circumference of a circle you need to know the radius length and Pi. The equation is: 2 x Pi x R where R is the radius. Sometimes you’ll also see this equation used with the diameter. Because the diameter is twice the distance as the radius, the equation would be: Pi x D where D is the Diameter.
The area of a circle is also important. ( I want to know how much pizza I’m eating ) To calculate the area of a circle, you can use Pi and the radius again. The equation to find the area is: Pi x R². If you take the square of the radius and multiply that by Pi you will have the area.
Since the sphere is the 3-D version of the circle, the math to calculate the surface area and volume only slightly more complex. You can use the following equation to calculate the surface area of a sphere: 4 x Pi x R². To calculate the volume of a sphere, use the equation: 4/3 x Pi x R³.
Now you have the basic math for circles and spheres. What you can do with this mathematical power is nearly limitless. You can calculate the volume of the Earth, you can calculate the surface area of a baseball, or like me, you can find out the area of a pizza.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Thursday, September 8, 2011
Basic Math of Triangles
It's hard to imagine a world without the triangle. I'm not talking about the musical instrument version, the love version, or even the famous Bermuda version. If you really think about how many uses you see for triangles in every aspect of our lives, it would be scary to imagine a world without them. They are used in engineering, architecture, machinery, nature and decorations. Because there are so many uses, it is important to have a strong grasp of the basic math principles behind this shape.
A triangle is a 3 sided shape with 3 corners and can be described in 3 ways. There are three basic types: Isosceles, Scalene and Equilateral. An Equilateral triangle has equal lengths on all 3 sides. An Isosceles has 2 sides of equal length. And Scalene has 3 different lengths of all sides.
A unique triangle is the Right triangle. This triangle has one corner that is 90 degrees. No matter what version you have, you can add all 3 angles at the corners and the sum will be 180 degrees.
To find the perimeter you find the total sum of the lengths of all three sides. It's pretty simple. To calculate the triangle perimeter you add Length1 + Length2 + Length3.
The area of a triangle is a little more tricky. Think of a triangle as half of a parallelogram. To calculate the area of a parallelogram, you multiply the base length by the height. Don't confuse the height length as one of the side lengths. To calculate the area of triangle , you multiply 1/2 x base length x height.
Finally we get to the Pythagorean Theorem. On any triangle, the longest side is referred to as the hypotenuse. If you look at a Right triangle, the hypotenuse is directly across from the 90 degree angle. Using the Pythagorean Theorem, we can calculate the length of the hypotenuse of the Right Triangle from the lengths of the other two sides. To calculate the hypotenuse (c), use the equation: a2 + b2 = c2
These are some of the most basic math calculations for triangles. Try to spend a day and make a list of how many times you see a triangle in use.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
A triangle is a 3 sided shape with 3 corners and can be described in 3 ways. There are three basic types: Isosceles, Scalene and Equilateral. An Equilateral triangle has equal lengths on all 3 sides. An Isosceles has 2 sides of equal length. And Scalene has 3 different lengths of all sides.
A unique triangle is the Right triangle. This triangle has one corner that is 90 degrees. No matter what version you have, you can add all 3 angles at the corners and the sum will be 180 degrees.To find the perimeter you find the total sum of the lengths of all three sides. It's pretty simple. To calculate the triangle perimeter you add Length1 + Length2 + Length3.
The area of a triangle is a little more tricky. Think of a triangle as half of a parallelogram. To calculate the area of a parallelogram, you multiply the base length by the height. Don't confuse the height length as one of the side lengths. To calculate the area of triangle , you multiply 1/2 x base length x height.
Finally we get to the Pythagorean Theorem. On any triangle, the longest side is referred to as the hypotenuse. If you look at a Right triangle, the hypotenuse is directly across from the 90 degree angle. Using the Pythagorean Theorem, we can calculate the length of the hypotenuse of the Right Triangle from the lengths of the other two sides. To calculate the hypotenuse (c), use the equation: a2 + b2 = c2
These are some of the most basic math calculations for triangles. Try to spend a day and make a list of how many times you see a triangle in use.
CalcuNATION is a website featuring online calculators and educational resources for mathematics. Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)
Subscribe to:
Posts (Atom)