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Planets The following table contains the average distance
Source: The Natural history of the Universe.
Planet | Distance
|
Period
|
Mercury |
|
|
Venus |
|
|
Earth |
|
|
Mars |
|
|
Jupiter |
|
|
Saturn |
|
|
Uranus |
|
|
Neptune |
|
|
The distances are given in astronomical units
a. Find functions of the form
b. Use a graphing calculator to plot the data in the table and to graph the three functions found in part a. Which function best fits the data?
c. Use the best-fitting function from part b to predict the period of Pluto (which was removed from the list of planets in 2006), which has a distance from the sun of
d. If you have a graphing calculator or computer program with a power regression feature, use it to find a power function (a function of the form
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Calculus For The Life Sciences
- Running Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner’s time at the each of each lap, obtaining the data in the following table. (a) What was the man’s average speed (rate) between 68 s and 152 s? (b) What was the man’s average speed between 263 s and 412 s? (c) Calculate the man’s speed for cadi lap, Is he slowing down, speeding up, or neither?arrow_forwardRunning Speed A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runners time at the end of each lap, obtaining the data in the following table. aWhat was the mans average speed rate between 68 s and 152 s? bWhat was the mans average speed between 263 s and 412 s? cCalculate the mans speed for each lap. Is he slowing down, speeding up or neither? Time s Distance m 32 200 68 400 108 600 152 800 203 1000 263 1200 335 1400 412 1600arrow_forwardThe Kelvin Temperature Scale Physicists and chemists often use the Kelvin temperature scale. In order to determine the relationship between the Fahrenheit and Kelvin temperature scales, a lab assistant put Fahrenheit and Kelvin thermometers side by side and took readings at various temperatures. The following data were recorded. K = kelvins F = degrees Fahrenheit 200 -99.67 220 -63.67 240 -27.67 260 8.33 280 44.33 300 80.33 a. Show that the temperature F in degrees Fahrenheit is a linear function of the temperature K in kelvins. b. What is the slope of this linear function? Note: Be sure to take into account that the table lists kelvins in jumps of 20 rather than in jumps of 1. c. Find a formula for the linear function. d. Normal body temperature is 98.6 degrees Fahrenheit. What is that temperature in kelvins? e. If temperature increases by 1 kelvin, by how many degrees Fahrenheit does it increase? If temperature increases by 1 degree Fahrenheit, by how many kelvins does it increase? f. The temperature of 0 kelvins is known as absolute zero. It is not quite accurate to say that all molecular motion ceases at absolute zero, but at that temperature the system has its minimum possible total energy. It is thought that absolute zero cannot be attained experimentally, although temperatures lower than 0.0000001 kelvin have been attained. Find the temperature of absolute zero in degrees Fahrenheit.arrow_forward
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