-x^2+5x-3 What point lies on the graph (0, 3) (1,4) (-2, 2) or (2,)

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

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

Find the area of the rectangular playground

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

What is (5.2 × 102) × (1.2 × 104)?

Maksim231197 [3]

(5.2 × 10^2) × (1.2 × 10^4)
= (5.2 × 1.2) × 10^6
= 6.24 x 10^6

answer D.
6.24 × 10^6

7 0

3 years ago

How many vertices does a sphere have?

Vinvika [58]

Hello, a sphere has zero vertices.

5 0

3 years ago

Festus bought a computer at $736.34, Apple iPad at $249.99, and a printer at 381.23. The sales tax rate is %6. What is the total

tatuchka [14]

The total purchase price including sales tax will be $1449.6136

Explanation

Festus bought a computer at $736.34, Apple iPad at $249.99 and a printer at $381.23

So, the total price of all three items $=(736.34+249.99+381.23) dollar = 1367.56$ dollar.

The sales tax rate is 6%. So, the amount of sales tax $=(1367.56*0.06) dollar= 82.0536$ dollar.

Thus, the total purchase price including sales tax will be: (1367.56 + 82.0536) dollar = 1449.6136 dollar

6 0

3 years ago

james wants to find out the favorite movie of students in his school. Which method would give James the BEST results? A)survey e

kolezko [41]

Answer:

D) Survey 100 randomly selected students from the school

Step-by-step explanation:

This gives an equal chance to everybody, so it's not biased and it is of everybody that goes to his school. A is only the people on the football team so its not students in his school. Walking to school has nothing to do with the survey topic and so thats also definitely not it. C again doesn't give a fair chance to everybody, so it would be possible to get an accurate, unbiased answer. D is definitely your answer!

I hope that helps!!

Have an awesome day! :)

8 0

3 years ago

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