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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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Barry also looks into the cost of repaying an easy access loan for $1000. The up-front cost of the loan is $3 for every $20 borr
natta225 [31]

Answer:

Barry has to pay back $1150

Step-by-step explanation:

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Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the followin
svp [43]

Answer:

a) 1+2+3+4+...+396+397+398+399=79800

b) 1+2+3+4+...+546+547+548+549=150975

c) 2+4+6+8+...+72+74+76+78=1560

Step-by-step explanation:

We know that a summation formula for the first n natural numbers:

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We use the formula, we get

a) 1+2+3+4+...+396+397+398+399=\frac{399·(399+1)}{2}=\frac{399· 400}{2}=399· 200=79800

b) 1+2+3+4+...+546+547+548+549=\frac{549·(549+1)}{2}=\frac{549· 550}{2}=549· 275=150975

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1+2+3+4+...+36+37+38+39=S/2

\frac{39·(39+1)}{2}=S/2

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39·40=S

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Therefore, we get

2+4+6+8+...+72+74+76+78=1560

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2 years ago
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