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Harman [31]
2 years ago
5

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function

h = −16t2 + 36t + 5. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
A. 2.25 s; 5 ft


B. 1.13 s; 25.25 ft


C. 1.13 s; 27.5 ft


D. 1.13 s; 65.75 ft
Mathematics
1 answer:
Ivenika [448]2 years ago
7 0
<span>A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 36t + 5. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?


A. 2.25 s; 5 ft


B. 1.13 s; 25.25 ft


C. 1.13 s; 27.5 ft


D. 1.13 s; 65.75 ft <====

</span>
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Among all rectangles that have a perimeter of 182, find the dimensions of the one whose area is largest.
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<em>The largest rectangle of perimeter 182 is a square of side 45.5</em>

Step-by-step explanation:

<u>Maximization Using Derivatives</u>

The procedure consists in finding an appropriate function that depends on only one variable. Then, the first derivative of the function will be found, equated to 0 and find the maximum or minimum values.

Suppose we have a rectangle of dimensions x and y. The area of that rectangle is:

A=x.y

And the perimeter is

P=2x+2y

We know the perimeter is 182, thus

2x+2y=182

Simplifying

x+y=91

Solving for y

y=91-x

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A=x.(91-x)=91x-x^2

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91-2x=0

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The largest rectangle of perimeter 182 is a square of side 45.5

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