millie has a box of 1 hundresds cubes she also has a bag of 70 cubes how many trains of 10 cubes can she make

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

Simplify -2 1/9 -(-4 1/3)

vesna_86 [32]

Answer:

$\frac{20}{9}$ or $2 \frac{2}{9}$

3 0

2 years ago

Read 2 more answers

What is the volume of the sphere that has a diameter of 3? use 3.14 for pie

aev [14]

Hey ! there

Answer:

113.04 unit cube

Step-by-step explanation:

In this question we are provided with a sphere having radius 3 units and value of π is 3.14 . And we're asked to find the volume of sphere .

For finding volume of sphere , we need to know its formula . So ,

$\qquad \qquad \: \underline{\boxed{ \frak{Volume_{(Sphere)} = \dfrac{4}{3} \pi r {}^{3} }}}$

Where ,

π refers to 3.14

r refers to radius of sphere

Solution : -

Now , we are substituting value of π and radius in the formula ,

$\quad \longrightarrow \qquad \: \dfrac{4}{3} \times 3.14 \times (3) {}^{3}$

Simplifying it ,

$\quad \longrightarrow \qquad \: \dfrac{4}{3} \times 3.14 \times 3 \times 3 \times 3$

Cancelling 3 with 3 :

$\quad \longrightarrow \qquad \: \dfrac{4}{ \cancel{3}} \times 3.14 \times 3 \times 3 \times \cancel{3}$

We get ,

$\quad \longrightarrow \qquad \:4 \times 3.14 \times 9$

Multiplying 4 and 3.14 :

$\quad \longrightarrow \qquad \:12.56 \times 9$

Multiplying 12.56 and 9 :

$\quad \longrightarrow \qquad \: \pink{\underline{\boxed{\frak{113.04 \: unit \: cube}}}} \quad \bigstar$

Henceforth , volume of sphere having radius 3 units is 113 .04 units cube .

<h2>#Keep Learning</h2>

5 0

1 year ago

Find the area of a circle with radius, r = 88cm. Give your answer rounded to 3 SF.

rusak2 [61]

Answer:

find using calculator yourself:))

Step-by-step explanation:

pi x r x r = pi x 88 x 88 = answer

7 0

2 years ago

Read 2 more answers

The ratio of boys to girls in Ella’s grade is 3 to 4. The ratio of boys to girls in Minh’s grade is 4 to 5. Each grade has a tot

Alex_Xolod [135]

Answer:

12 boys

Step-by-step explanation:

I believe the answer is 12 boys. I hope this helps!

8 0

2 years ago