B. Complete the missing factors of the following polynomials.

A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

If y varies inversely as the square root of x, what is the constant of proportionality if y = 16 when x = 4?

krek1111 [17]

The answer is D.64

Explain i have the test myself

5 0

3 years ago

For which intervals is the function positive? Select each correct answer.

lys-0071 [83]

Answer:

(-infinity, -2) and (0,4)

Step-by-step explanation:

4 0

4 years ago

Consider the linear function that is represented by the equation y=4x+5 and the linear function that is represented by the table

Serhud [2]

Answer:

The slope and y-intercept of the table are greater than the slope and y-intercept of the equation.

Step-by-step explanation:

The slope of y = 4x + 5 is 4 and the y-intercept is (0,5).

The slope of the table is found by subtracting two points from the table in the formula $m=\frac{y_2-y_1}{x_2-x_1}$ .

$m=\frac{26-16}{4-2}=\frac{10}{2}=5$

This means that the function increases by 5 for every x value that increases by 1. Knowing this, you can work backwards by subtracting 5 to find when x=0 (the y-intercept). When x=1 then y= 11. When x =0 then x =6. The table has the y-intercept (0, 6)

The slope and y-intercept of the table are greater than the slope and y-intercept of the equation.

This is true since 5 > 4 and 6>5.

4 0

3 years ago

Read 2 more answers

What is the area of a rectangle 15 feet by 2 feet's rectangle. The shape of a flag is a rectangle. The length is 15 ft. And the

Westkost [7]

Answer:

30 ft^2

Step-by-step explanation:

Area of rectangle is length x width

= 15ft x 2ft = 30 ft^2

6 0

3 years ago