If you drive 8 miles in 30 minutes, how far will you drive in 2 1/2 hours?

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

A regular octagon has a radius of 6 ft and a side length of

Svetlanka [38]

Answer:

<h2>Area of the regular octagon is approximately 102ft²</h2>

Step-by-step explanation:

Given the radius and length of a side of regular octagon as shown;

radius = 6ft and length of side = 4.6ft

Area of a regular octagon is expressed as $A = 2(1+\sqrt{2} )a^{2}$ where a is the length of one side. Given a = 4.6ft

Area = $A = 2(1+\sqrt{2} )(4.6)^{2}\\$

$= 2(1+\sqrt{2} )*21.16\\= (2+2\sqrt{2})*21.16\\ = 4.83*21.16\\= 102.20ft^{2} \\$

Area of the regular octagon is approximately 102ft²

3 0

3 years ago

Can someone help me with this equation?

navik [9.2K]

Answer:

so far i think 9 but that's all I know for how

Step-by-step explanation:

image them turning into triangles

5 0

3 years ago

A math teacher noticed that her students always missed class when she gave a test. she was very confused by this, since a test i

IgorC [24]

Deductive reasoning!!!

3 0

4 years ago

A translation moves A(-3,2) to a'(0,0). find b', the image of b(5,4)) under the same translation

statuscvo [17]

The image of b, b', would be (8,2)

hope this helps!

7 0

3 years ago