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Morgarella [4.7K]

4 years ago

5

The surface area of a rectangular prism is 170 ft. and both the length and width are 5 ft. Find the height of this prism.

1 answer:

soldi70 [24.7K]4 years ago

7 0

850ft. I think that is the answer to your question

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The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular.

vfiekz [6]

Answer:

Minimum surface area = $70.77 cm^2$

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container= $54 cm^3$

We have to find the minimum surface areas that this container will have.

Volume of container= $l\times b\times h$

$x\times 2x\times h=54$

$2x^2h=54$

$h=\frac{54}{2x^2}=\frac{27}{x^2}$

Surface area of container= $2(b+l)h+lb$

Because the container does not have lid

Surface area of container= $S=2(2x+x)\times \frac{27}{x^2}+2x\times x$

$S=\frac{162}{x}+2x^2$

Differentiate w.r.t x

$\frac{dS}{dx}=-\frac{162}{x^2}+4x$

$\frac{dx^n}{dx}=nx^{n-1}$

Substitute $\frac{dS}{dx}=0$

$-\frac{162}{x^2}+4x=0$

$4x=\frac{162}{x^2}$

$x^3=\frac{162}{4}=40.5$

$x^3=40.5$

$x=(40.5)^{\frac{1}{3}}$

$x=3.4$

Again differentiate w.r.t x

$\frac{d^2S}{dx^2}=\frac{324}{x^3}+4$

Substitute x=3.4

$\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0$

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area = $\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2$

8 0

3 years ago

7(2+2x)+(x+2)⋅6 what is the answer

Rzqust [24]

Answer:

20x+26

Step-by-step explanation:

hope this helped :)

5 0

3 years ago

Im timed! What is the slope of the line represented by the equation f(t)=2t−6?

givi [52]

Answer:

B

Step-by-step explanation:

Same thing but with t instead of x

8 0

3 years ago

48 – (−12) = A) -60 B) -36 C) 36 D) 60

34kurt

48 - (-12)

48 + 12 simplify brackets. (because two negatives equals a positive)

60 << answer

hope this helps, God bless!

6 0

4 years ago

Read 2 more answers

For working 3 hours, Sofia earns $30.60. For working 5 hours, she earns $51. For working 6 hours, she earns $61.20

Iteru [2.4K]

(3,30.6)
(5,51)
(6,61.2)

$\sf Slope = \frac{y_2-y_1}{x_2-x_1} = \frac{51-30.6}{5-3} = \frac{20.4}{2} =\boxed{10.2}$

The slope of the line that passes through points (3,30.6) and (5,51) is 10.2

The slope of the line represents how much she earns per hour.

4 0

4 years ago

Read 2 more answers