Solve by completing the square and graphing. 1. Find the dimensions of the recta

Question

Solve by completing the square and graphing.

1. Find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing.

2. Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3 pens of the same size given 500 feet of fencing.

3. Among all of the pairs of numbers whose sum is 6, find the pair with the largest product. What is the product?

4. A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) = 4.9t2 + 229t + 234. Find the maximum height the rocket attains.

Explanation / Answer

1) corral split into 2 pens

let length = l

width = w

setting up the equation

2 l + 3w = 300

2l = 300 - 3w

l = 150 - 3/2 w

area = length * width

= ( 150 - 3/2 w ) w

area = 150w - 3/2 w^2

width that will maximize area = -150/2 (-3/2)

w = 50 feet

length = 75 feet

so, dimensions are

length = 75 feet , width = 50 feet

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