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Simplify this expression 4p plus 9 plus 7p plus 2 equals?

Updated: 4/28/2022

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11p+11

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A window consists of an open rectangle topped by a semicircle and is to have a perimeter of 288in. find the radius of the semicircle that will maximize the area of the window?

Let x be the width and y be the length of the rectangle. x/2 is the radius of the semicircle Perimeter of the Norman window is x+2y+(π x)/2 Let P be the perimeter --- 288 in this problem. P = x+2y+(π x)/2--------(1) Solving for y from equation (1) 2y = P-x-πx/2 y = P/2-x/2-πx/4--------(2) Area = xy + π x^2 / 8 A = x(P/2-x/2-π x/4) + π x^2/8 A= Px/2-x^2 /2 -πx^2/4 +πx^2/8 dA/dx = P/2 -2x/2-2πx /4 +2πx / 8 =0 (4p-8x-2πx)/8=0 4p-2x(π+4)=0 4p=2x(π+4) x= 2P / (4+π) The radius is x/2 = P/(4+PI) Substitute P with 288 radius = 288 / (4+PI) will maximize the area of the window. d^2A/dx^2 =-1-π/2+π/4 < 0, indicates that the area is maximized. You'll have to simplify x and y if you want them in numeric format.

Related questions

Simplify this expression 4p plus 9 plus minus 7p plus 2 equals?

4p + 9 - 7p + 2 4p - 7p + 9 + 2 p(4 - 7) + 9 + 2 -3p + 11

Simplify this expression 4p plus 9 plus-7pplus 2?

11-3p

Simplify this expression 4p plus 9 plus 7p plus 2?

It is: 11p+11 simplified

How do you simplify this expression 4p plus 9 plus 7p plus 2?

Collect like terms together: 4p + 9 + 7p + 2 = (4p + 7p) + (9 + 2) = (4 + 7)p + 11 = 11p + 11 = 11(p + 1)

How do you simplify the expression 4p 9-7 2?

23

Simplify 4p plus 9 plus -7p plus 2?

4p + 9 + (-7p) + 2 = 4p - 7p + 9 + 2 = -3p + 11

Simplify p plus p plus p plus p?

4 times p or 4p

How would you simplify this expression 5p times 2q divided by 4p?

5p x 2p = 10p, then 10p / 4p = 2 remainder 2

If 4p plus 1 equals 10 what is p?

4p+1 = 10 4p = 10-1 4p = 9 p = 2.25

What is 4p plus 72p-5?

It is an expression that can be simplified to: 76p-5

4p plus 9 plus -7p plus 2 equals?

4p+9-7p+2 -3p+11 p = 11/3

What is 4p plus 2 equals 3p-7?

4p+2 = 3p-7 4p-3p = -7-2 p = -9

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