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mina [271]
2 years ago
12

There are many square prisms with volume 125 in. Let w represent the side length of the square base and h represent the height i

n
inches. Then the formula for the volume V, in cubic inches of these prisms is V = w2h and the equation for the surface area S, in
square inches, is S = 2w2 + 4wh.
Mathematics
1 answer:
iogann1982 [59]2 years ago
5 0

Answer:

5in by 5in by 5in

Step-by-step explanation:

We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.

Given

Volume = 125in³

Formula

V = w²h ..... 1

S = 2w²+4wh ..... 2

w is the side length of the square base

h is the height of the prism

125 = w²h

h = 125/w² ..... 3

Substitute eqn 3 into 2 as shown

S = 2w²+4wh

S = 2w²+4w(125/w²)

S = 2w²+500/w

To minimize the surface area, dS/dw = 0

dS/dw =4w-500/w²

0= 4w-500/w²

Multiply through by w²

0 = 4w³-500

-4w³ = -500

w³ = 500/4

w³ =125

w = cuberoot(125)

w = 5in

Get the height

125 =w²h

125 = 25h

h = 125/25

h = 5in

Hence the dimension of the prism is 5in by 5in by 5in

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mina [271]

Step-by-step explanation:

there is no mathematical problem to solve.

just follow the instructions as given.

this is an exercise for you to get a feeling about what is what. it is imperative that you do it.

there is really nothing to solve.

remember, that a positive slope means the line goes up (from left to right), and a negative slope means the line goes down (again from left to right).

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7 0
2 years ago
275 + 180 + 120=275 +_____=_____
Galina-37 [17]
275 + 180 + 120 = 275 + 300 = 575
not 100% that this is right but this is my best guess. Hope this helps!!
4 0
3 years ago
Read 2 more answers
X^2-8x+16 divided by ax-4x numerator
Vedmedyk [2.9K]

Answer:

Given:

1). x^2-8x+16 divided by x-4

⇒ \frac{x^2-8x+16}{x-4}

⇒ \frac{x^2-2\times x\times 4+4^2}{x-4}

By factorising numerator by using identity, (a-b)^2=a^2-2\times a \times b +b^2

⇒ \frac{(x-4)^2}{x-4}

⇒ \frac{(x-4)\times(x-4)}{x-4}

⇒ x-4  <u> {Answer}</u>

2). 3x^2y divided by 6xy^2

⇒ \frac{3x^2y}{6xy^2}

⇒\frac{3\times x\times x\times y}{6\times x\times y\times y}

⇒ <u>\frac{x}{2y}</u>  <u>{ Answer}</u>

4 0
3 years ago
Sean bought 1.8 pounds of gummy bears and 0.6 pounds of jelly beans and paid $10.26. He went back to the store the following wee
Ymorist [56]

Answer:

Gummy bears $3.20/lbs

Jelly beans $7.50/lbs

Step-by-step explanation:

For this we will substitute gummy bear price for "x" and jelly bean price for "y" which creates this system (also assuming there is no sales tax involved):

1.8x + 0.6y = 10.26

1.2x + 1.5y = 15.09

Then once solved, answers come out to be (x,y) = (16/5,15/2) which is (3.2,7.5)

7 0
2 years ago
Original Equation:8 - 7x^2 + 3 = 4x^2 - 1Frist step:11 - 7x^2 = -4x^2 - 1Which property justifies the first step?A. Division pro
Tpy6a [65]

8 - 7x^2 + 3 = 4x^2 - 1

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B. Commutative property of addition

We can swap numbers and obtain the same results.

In this case, we swapped 8+3 and added them.

7 0
1 year ago
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