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3 years ago

Perform the indicated operation 5(3x^3)^3-2(3x^3)

Mathematics

1 answer:

Pie3 years ago

5 0

5(3x^3)^3-2(3x^3)
=5(3^3 x^9) - 6x^3
= 135x^9 - 6x^3
= 3x^3 (45x^6 - 2)

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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

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

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

A number t is less than or equal to 5

Pavel [41]

It would be written as
T < 5, but there would be a line underneath the less then sign

4 0

2 years ago

3. How many gallons of ice-cream are produced each week?

andrezito [222]

Answer:

Each week 26,849,315 Gallons of ice cream is produced each week

Step-by-step explanation:

To find this we see how much is made in a year which is 1.4 billion gallons in the U.S.

To see how much is in a day we divide 1.4 billion by 365. Which is 3835616 Then we multiply it by 7 because there is 7 days in a week and the answer is 26849315

5 0

2 years ago

Phone Company A charges a monthly fee of $42.50, and $0.02 for each minute talk time. Phone company B charges a monthly fee of $

Y_Kistochka [10]

We need to call for x minute
+ Phone Company A charges a monthly fee of $42.50, and $0.02 for each minute talk time. So we have to spend: $42.50+ $0.02x
+ Phone company B charges a monthly fee of $25.00, and $0.09 for each minute of talk time. So we have to spend: $25.00+ $0.09x

We solve for x: $42.50+ $0.02x> $25.00+ $0.09x
or $42.50- $25.00 > $0.09x- $0.02x
and we have $0.07x<$27.50
or x< 27.50:0.07 and x< 393.86

The answer is:
If we have to call much time, at least 394 minutes, we should choose A
If not, choose B

8 0

2 years ago

Please help my with this!!!!!!!!!!!!!!!!!!!!!!!!

butalik [34]

Answer:

ummmmmmmm

Step-by-step explanation:

5 0

2 years ago