For Exercises 39–42, use the model
with
or
. (See Example 3)
In a classic Seinfeld episode, Jerry tosses a loaf of bread (a marble rye) straight upward to his friend George who is leaning out of a third-story window.
a. If the loaf of bread leaves Jerry’s hand at a height of 1 m with an initial velocity of 18 m/sec, write an equation for the vertical position of the bread s (in meters) t seconds after release.
b. How long will it take the bread to reach George if he catches the bread on the way up at a height of 16 m? Round to the nearest tenth of a second.
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College Algebra (Collegiate Math)
- The formula V = kr4, discovered by the physiologist Jean Poiseuille (1797–1869), allows us to predict how much the radius of a partially clogged artery has to be expanded in order to restore normal blood flow. The formula says that the volume V of blood flowing through the artery in a unit of time at a fixed pressure is a constant k times the radius of the artery to the fourth power. How will a 10% increase in r affect V?arrow_forwardAnswer question 7(e)arrow_forwardFor Exercises 33–38, find the exact value of each expression without the use of a calculator. (See Example 5)arrow_forward
- America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?arrow_forwardIn cold weather, we feel colder when the wind blows. This is quantified by the wind chill index W, which is supposed to predict how cold we will feel for a given air temperature T, in degrees Fahrenheit, and wind speed V, in miles/hour. The National Weather Service uses the following formula: W=35.74+0.6215T−35.75V^0.16+0.4275TV^0.16, for T≤50 and V≥3. What is the wind chill index when the air temperature is 25 degrees and the wind speed is 18 miles/hour?Answer: Calculate the partial derivatives WT and WV when T=25 and V=18.WT= WV= Use your answer above to do the following question: When the air temperature is 25 degrees, estimate the change in the wind chill index if the wind speed increases by 2 miles/hour from 18 miles/hour.Answer:arrow_forwardConsider a sports car which accelerates from O ft/sec to 85 ft/sec in 5 seconds (85 ft/sec = 58 mph). The car's velocity is given in the following table. What is the lower bound (left sum) for the number of feet the car travels in 5 seconds? 1 2 3 t (sec) V(t) (ft/sec) 4 30 52 68 80 85arrow_forward
- Explain the value of t?arrow_forwardYou are on an airplane. The pilot announces the plane’s speed over the intercom. Which speed do you think is being reported: the speed of the plane in still air or the speed after the effect of the wind has been accounted for? Explain your answer.arrow_forwardWhat is the value of t ?arrow_forward
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