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Dropping Rocks on Mars The behavior of objects falling near Earth’s surface depends on the mass of Earth. On Mars, a much smaller planet than Earth, things are different. If Galileo had performed his experiment on Mars, he would have obtained the following table of data.
t
|
V
|
0 | 0 |
1 | 12.16 |
2 | 24.32 |
3 | 36.48 |
4 | 48.64 |
5 | 60.8 |
a. Show that these data can be modeled by a linear function, and find a formula for the function.
b. Calculate
c. Galileo found that the acceleration due to gravity of an object falling near Earth’s surface was 32 feet per second per second. Physicists normally denote this number by the letter g. If Galileo had lived on Mars, what value would he have found for g?
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- Energy ConsumptionThe monthly residential consumption of energy in the U.S. for 2012 is found in the following table. Source: Energy Information Administration. Month Energytrillion BTU January 990.527 February 833.163 March 560.826 April 412.426 May 297.500 June 253.015 July 240.486 August 248.035 September 249.354 October 378.094 Number 631.203 December 838.265 Plot the data, letting t=1 correspond to January, t=2 to February, and so on. Is it reasonable to assume that the monthly consumption of energy is periodic? Find the trigonometric function of the form C(t)=asin(bt+c)+d that models these data when t is the month of the year and C(t) is the energy consumption. Graph the function on the same calculator window as the data. Estimate the total energy consumption for the year for residential customers in the United States and compare it to the actual value. Calculate the period of the function found in part b. Is this period reasonable?arrow_forwardFocal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece see Figure 3.42. For a given magnification M of the telescope, the focal length F of the objective lens is a linear function of the focal length Fe of the eyepiece. For example, a telescope with magnification M=80 times can be constructed using various combinations of lenses. The following table gives some samples of focal length for telescopes with magnification M=80. Here focal lengths are in centimeters. Fe 0.3 0.5 0.7 0.9 F 24 40 56 72 a. Construct a linear model for the data. b. In this example, the magnification M is 80. In general, F is proportional to Fe, and the constant of proportionality is M. Use this relation to write a formula for F in terms of Fe and M. c. Solve the equation you obtained in part b for M and thus obtain a formula for magnification as a function of objective lens focal length and eyepiece focal length. d. To achieve a large magnification, how should the objective and eyepiece lenses be selected? FIGURE 3.42arrow_forwardDoes Table 1 represent a linear function? If so, finda linear equation that models the data.arrow_forward
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