Concept explainers
Heights of a Plant The length of a certain weed, in centimeters, after
Answer the following questions by reading the graph in Fig. 3.
a. How fast is the weed growing after
b. When is the weed
c. When is the weed growing at the rate of
d. What is the maximum rate of growth ?
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Calculus & Its Applications (14th Edition)
- 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?arrow_forwardHeight of a Ball If a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is given by y=40t16t2 . What is the maximum height attained bythe ball?arrow_forwardA forest fire leaves behind an area of grass burned in an expanding circular pattern. If the radius of the circle of burning grass is increasing with time according to the formula r(t)=2t+1 , express the area burned as a function of time, t (minutes).arrow_forward
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- Builders Old Measurement The Builders Old Measurement was instituted by law in England in 1773 as the way to estimate the total tonnage T of a wooden ship from its beam width W and length L, both measured in feet. The formula is T=(L0.6W)W2188 In this exercise, we consider wooden ships of length 150 feet. a.Make a graph of T versus W, including beam widths up to 250 feet. b. What is the maximum tonnage for a ship of this length? c.Comment on the dimensions of the ship from part b. d. What is the maximum tonnage of a ship whose width is no more than half its length? That is, we assume that the beam width is at most 75 feet.arrow_forwardFluid Flow The intake pipe of a 100-gallon tank has a flow rate of 10 gallons per minute, and two drainpipes have flow rates of 5 gallons per minute each. The figure shows the volume V of fluid in the tank as a function of time t. Determine whether the input pipe and each drainpipe are open or closed in specific subintervals of the 1 hour of time shown in the graph. (There are many correct answers.)arrow_forward
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