<img src="https://tex.z-dn.net/?f=%20%5Csin%2875%29%20" id="TexFormula1" title=" \sin(75) " alt=" \sin(75) " align="absmiddle" c

Since we know we only have 640 feet of fence available, we know that L + W + L = 640, $\implies$ 2L + W = 640. This allows us to represent the width, W, in terms of L: W = 640 – 2L

Remember, the area of a rectangle is equal to the product of its width and length, therefore,

$A_{\rm pigpen}=L(640-2L)\implies 640L-2L^2$

Notice that, quadratic has been vertically reflected, since the coefficient on the squared term is negative, so the graph will open downwards, and the vertex will be a maximum value for the area.

recall,

$x_{max}=-b/2a$
$f(x)_{max}=f(x_{max})$

Since our function is A(L)=640L-2L², we get

a=-2
b=640

plug in the value of a and b into the first formula:

$L_{max}=-(640)/2(-2)\implies 160$

$A(L)_{max}=640(160)-2(160)^2\implies 76800$

hence,the dimensions of the pen that will maximize the area are L=160m and W=76800/160=480m

and we're done!

3 0

2 years ago

PLEASE HELP EASY WORK GIVING BRAINLIEST REPORTING FALSE ANSWERS

LuckyWell [14K]

It is 70 because common sense people

7 0

3 years ago

A ladder leaning against a building makes an angle of 65 degrees with the ground and reaches a point on the building 20 feet abo

lesya692 [45]

22 feet. Using the sine rule theory: 20/sin(65)=x/sin(90). You know that it's 90 degrees because you assume the ground and the building make a 90 degree angle. So, you cross multiply and get 20sin(90)/xsin(65) and solve for x.

5 0

3 years ago