What is the surface area of the given figure? and how did you find the answer?

A school wishes to enclose its rectangular playground using 480 meters of fencing.

Harlamova29_29 [7]

Answer:

Part a) $A(x)=(-x^2+240x)\ m^2$

Part b) The side length x that give the maximum area is 120 meters

Part c) The maximum area is 14,400 square meters

Step-by-step explanation:

The picture of the question in the attached figure

Part a) Find a function that gives the area A(x) of the playground (in square meters) in terms of x

we know that

The perimeter of the rectangular playground is given by

$P=2(L+W)$

we have

$P=480\ m\\L=x\ m$

substitute

$480=2(x+W)$

solve for W

$240=x+W\\W=(240-x)\ m$

<u><em>Find the area of the rectangular playground</em></u>

The area is given by

$A=LW$

we have

$L=x\ m\\W=(240-x)\ m$

substitute

$A=x(240-x)\\A=-x^2+240x$

Convert to function notation

$A(x)=(-x^2+240x)\ m^2$

Part b) What side length x gives the maximum area that the playground can have?

we have

$A(x)=-x^2+240x$

This function represent a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The x-coordinate of the vertex represent the length that give the maximum area that the playground can have

Convert the quadratic equation into vertex form

$A(x)=-x^2+240x$

Factor -1

$A(x)=-(x^2-240x)$

Complete the square

$A(x)=-(x^2-240x+120^2)+120^2$

$A(x)=-(x^2-240x+14,400)+14,400$

$A(x)=-(x-120)^2+14,400$

The vertex is the point (120,14,400)

therefore

The side length x that give the maximum area is 120 meters

Part c) What is the maximum area that the playground can have?

we know that

The y-coordinate of the vertex represent the maximum area

The vertex is the point (120,14,400) -----> see part b)

therefore

The maximum area is 14,400 square meters

Verify

$x=120\ m$

$W=(240-120)=120\ m$

The playground is a square

$A=120^2=14,400\ m^2$

8 0

3 years ago

Can someone plz help me?

ivann1987 [24]

Answer: The correct answer is Choice C.

Step-by-step explanation: In order to solve this problem you need to look at the equation’s parts.

The first part is multiplying 5 by the contents of the parenthesis. So, 5(2x-2) equals 10x - 10. Now, but the equation together and simplify it:

10x - 10 + 10x =

20x - 10

3 0

3 years ago

ANSWER ASAP IM BEING TIMED

Vsevolod [243]

Answer:

Standard form means that you write the terms by descending degree.

x^4y^2 + 4x^3y + 10x^2

The degree of the first term x^4y^2 is 4+2=6

The degree of the second term 4x^3y is 3+1=4

The degree of the third term 10x^2 is 2

The terms are written by descending degree. Therefore, polynomial x^4y^2 + 4x^3y + 10x^2 is written in standard form.

Step-by-step explanation: I hope this helps <3

5 0

3 years ago

A number split evenly into 6 groups. in expression symbol.

deff fn [24]

Answered already okay. GFY.

7 0

3 years ago

rhombus has sides of length 10 cm. and the angle between two adjacent sides is 76 degrees. Find the lengths of the other diagona

lisabon 2012 [21]

Let the length of one of the diagonals be 2x and the other be 2y, then
cos (76/2) = x/10
x = 10 cos 38 = 7.88 cm

sin (76/2) = y/10
y = 10 sin 38 = 6.16 cm

3 0

3 years ago