Concept explainers
Reminder Round all the answers to two decimal places unless otherwise indicated.
A Leaking Can The side of a cylindrical can full of water springs a leak, and the water begins to stream out. (See Figure
Distance D, in inches |
Depth H, in inches |
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a. Use regression to find a formula for
b. When the depth is
c. When the water stream strikes the ground
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FUNCTIONS+CHANGE -WEBASSIGN
- Arctic Foxes The age-weight relationship of female Arctic foxes caught in Svalbard, Norway, can be estimated by the function Mt=3102e-e-0.022t-56, where t is the age of the fox in days and Mt is the weight of the fox in grams. Source: Journal of Mammalogy. a. Estimate the weight of a female fox that is 200 days old. b. Use Mt to estimate the largest size that a female fox can attain. Hint: Find limtMt. c. Estimate the age of a female fox when it has reached 80% of its maximum weight. d. Estimate the rate of change in weight of an Arctic fox that is 200 days old. Hint: Recall that Dteft=f'teft. e. Using a graphing calculator to graph Mt and then describe the growth pattern. f. Use the table function on a graphing calculator or a spreadsheet to develop a chart that shows the estimated weight and growth rate of female foxes for days 50,100,150,200,250, and 300.arrow_forwardRipples in a pond When a stone is thrown into the center of a pond, the ripples spread out in a circular pattern, moving at a rate of 3 feet per second. If the stone is dropped at a point (0,0) in the illustration, when will the ripple reach the seagull floating at the point (15,36)?arrow_forwardLIFE SCIENCE APPLICATIONS Length of a Pendulum Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the time T for one complete oscillation can be determined from the data in the table. Source: Gary Rockswold. L(ft) T(sec) 1.0 1.11 1.5 1.36 2.0 1.57 2.5 1.76 3.0 1.92 3.5 2.08 4.0 2.22 a. Plot the data from the table with L as the horizontal axis and T as the vertical axis. b. Find the least squares line equation and graph it simultaneously, if possible, with the data points. Does it seem to fit the data? c. Find the correlation coefficient and interpret it. Does it confirm your answer to part b?arrow_forward
- Stopping Distance The table below shows the average stopping distance D, in feet, for a car on dry pavement versus the speed S of the car, in miles per hour. S= speed mph 15 25 35 40 60 75 D = stopping distance feet 44 85 136 164 304 433 a Find a model of stopping distance as power function of speed. b If speed is doubled, how is stopping distance affected? c Plot the data and the power model on the same screen.arrow_forwardSkidding in a Curve A car is traveling on a curve that forms a circular arc. The force F needed to keep the car from skidding is jointly proportional to the weight w of the car and the square of its speed s and is inversely proportional to the radius r of the curve. a Write an equation that expresses this variation. b A car weighing 1600 lb travels around a curve at 60 mi/h. The next car to round this curve weighs 2500 lb and requires the same force as the first car to keep from skidding. How fast is the second car traveling?arrow_forwardOhms Law: says that when electric current is flowing across a resistor, the current i, measured in amperes, can be calculated from the voltage v, measured in volts, and the resistance R, measured in ohms. The relationship is given by i=vRamperes. a. A resistor in a radio circuit is rated at 4000 ohms. i. Find a formula for the current as a function of the voltage. ii. Plot the graph of i versus v. include values of the voltage up to 12 volts. iii. What happens to the current when the voltage increases? b. The lights on your car operate on a 12-volt battery. i. Find a formula for the current in your car lights as a function of the resistance. ii. Plot the graph of i versus R. We suggest a horizontal span here of 1 to 25. iii. What happens to the current when the resistance increases?arrow_forward
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