Temperatures on Mars The air temperature one chilly spring morning at your time-share condominium at the base of Olympus Mons, t hours after 6:00 a.m., was given by the function f(t) = −7t2 + 50t − 80 degrees Fahrenheit (0 ≤ t ≤ 4). † What was the temperature at 7:00 a.m.? °F How fast was it rising? (Round your answer to three decimal places.) °F per hour

Temperatures on Mars The air temperature one chilly spring morning at your time-share condominium at the base of Olympus Mons, t hours after 6:00 a.m., was given by the function f(t) = −7t2 + 50t − 80 degrees Fahrenheit (0 ≤ t ≤ 4). † What was the temperature at 7:00 a.m.? °F How fast was it rising? (Round your answer to three decimal places.) °F per hour

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.2: Domain And Range

Problem 60SE: The height h of a projectile is a function of the time t it is in die air. The height in feet for t...

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Field Trip A class of fourth graders walks to a park on a field trip. The function y=f(t) graphed below gives their distance from school in ft t minutes after they left school. What is the average speed going to the park? How long was the class at the park? How far away is the park? Graph the function y=0.5f(t). How is the graph of the new function related to the graph of the original function? What is the average speed going to the new park? How far is the new park? Graph the function y=f(t10). How is the graph of the new function related to the graph of the original function? How does the field trip described by this function differ from the original trip?
Titanic At 2:00 p.m. on April 11, 1912, the Titanic left Cobh, Ireland, on her voyage to New York City. At 11:40 p.m. on April 14, the Titanic struck an iceberg and sank, having covered only about 2100 miles of the approximately 3400-mile trip. (a) What was the total duration of the voyage in hours? (b) What was the average speed in miles per hour? (c) Write a function relating the distance of the Titanic from New York City and the number of hours traveled. Find the domain and range of the function. (d) Graph the function in part (c).
The height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?
Air Temperature As dry air moves upward, it expand and, in so doing, cools at a rate of about 1°C for each 100-meter rise, up to about 12 km. (a) If the ground temperature is 20°C, write a formula for the temperature at height h. (b) What range of temperatures can be expected if an air plane lakes off and reaches a maximum height of 5 km?
Running Ants A scientist observed that the speed S at which certain ants ran was a function of T, the ambient temperature. He discovered the formula S=0.2T-2.7, Where S is measured in centimetres per second and T is in degrees Celsius. a. Using functional notation, express the speed of the ants when the ambient temperature is 30 degrees Celsius, and calculate that speed using the formula above. b. Solve for T in the formula above to obtain a formula expressing the ambient temperature T as a function of the speed S at which the ants run. c. If the ants are running at a speed of 3 centimeters per second, what is the ambient temperature?
Temperature Conversions In everyday experience, the measure of temperature most often used are Fahrenheit F and Celsius C. Recall that the relationship between them is given by F=1.8C+32. Physicists and chemists often use the Kelvin temperature scale. You can get kelvinsK from degrees Celsius by using K=C+273.15. a. Explain in practical terms what K30 means, and then calculate that value. b. Find a formula expressing the temperature C in degrees Celsius as a function of the temperature K in kelvins. c. Find a formula expressing the temperature F in degrees Fahrenheit as a function of the temperature K in kelvins. d. What is the temperature in degrees Fahrenheit of an object that is 310 kelvins?
Swimming Laps Miyuki practices swimming laps with her team. The function y=f(t) graphed below gives her distance in meters from the starting edge of the pool t seconds after she starts her laps. Describe in words Miyukis swim practice. What is her average speed for the first 30 s? Graph the function y=1.2f(t). How is the graph of the new function related to the graph of the original function? What is Miyukis new average speed for the first 30 s?
Growth in Weight and Height Between the ages of 7 and 11 years, the weight w, in pounds, of a certain girl is given by the formula w=8t. Here t represents her age in years. a. Use a formula to express the age t of the girl as a function of her weight w. b. At what age does she attain a weight of 68 pounds? c. The height h, in inches, of this girl during the same period is given by the formula h=1.8t+40. i. Use you answer to part b to determine how tall she is when she weighs 68 pounds. ii. Use a formula to express the height h of the girl as a function of her weight w. iii. Answer the question in part i again, this time using your answer to part ii.