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Elden [556K]
3 years ago
9

I miss the equation, point D.

Mathematics
1 answer:
Maru [420]3 years ago
7 0
The answer is : Sn = S(n-1) + n
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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
What is 17+95 i do not know and i need the help
zubka84 [21]
I got you fam it's 112! : )
8 0
3 years ago
Read 2 more answers
PLEASE HELP ITS DUE IN 20 MINUTES
anastassius [24]

Answer:14

Step-by-step explanation: it's says x= the sign at the end meaning whatever x is it's greater than 2 and 14 is the only one greater than 2

8 0
3 years ago
Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they
inysia [295]
You have two unknown rates, so we need to develop two equations to solve for these unknowns (based on the information given on the problem statement):

5x + 10y = 725
x + y = 100

By substitution, we get:

5x + 10(100 - x) = 725
5x + 1000 - 10x = 725
-5x = 725 - 1000
-5x = -275
x = -275/-5 = 55

100 - 55 = 45

Thus:
The mechanic who worked for 5 hours charged his time at $55/hr, and the mechanic who worked for 10 hours charged his time at $45/hr.

To verify, plug and chug the results back into the original equations:

5(55) + 10(45) = 725
275 + 450 = 725
725 = 725 [OK]

55 + 45 = 100 [OK]
4 0
3 years ago
WILL MARK YOU BRAINLIEST ASAP
34kurt

Answer:

(-0.5, -1)

Step-by-step explanation:

To find the midpoint add the coordinates then divide by 2

x = (2 + -1)/2

x = 1/2 = 0.5

y = (3 + -5)/2

y = -1

(-0.5, -1)

5 0
3 years ago
Read 2 more answers
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