If n is directly proportional to the cube of mand n = 27 when m=
the value of n when m= 2.
(ii) the value of m
when n = 125​

Answers

Answer 1

Missing Part of the Question

If n is directly proportional to the cube of m and n = 27 when m =  4

Answer:

i. [tex]n = \frac{27}{64}[/tex]

ii. [tex]n = \frac{20}{3}[/tex]

Explanation:

Given

Direct proportion between n and cube of m

This is represented as:

[tex]n\ \alpha\ m^3[/tex]

Convert proportion to equation

[tex]n = km^3[/tex]

Where k is the constant of variation;

Substitute 27 for n and 4 for m

[tex]27 = k * 4^3[/tex]

[tex]27 = k * 64[/tex]

[tex]27 = 64k[/tex]

Divide both sides by 64

[tex]k = \frac{27}{64}[/tex]

Solving for n when m = 2.

Recall that [tex]n = km^3[/tex]

Substitute [tex]\frac{27}{64}[/tex] for k and  2 for m

[tex]n = \frac{27}{64} * 2^3[/tex]

[tex]n = \frac{27}{64} * 8[/tex]

[tex]n = \frac{27 * 8}{64}[/tex]

[tex]n = \frac{27}{64}[/tex]

Solving for the value of m  when n = 125​

Recall that [tex]n = km^3[/tex]

Substitute 125 for n and [tex]\frac{27}{64}[/tex] for k

[tex]125 = \frac{27}{64} * n^3[/tex]

[tex]125 = \frac{27 * n^3}{64}[/tex]

[tex]125 = \frac{27 n^3}{64}[/tex]

Multiply both sides by 64

[tex]64 * 125 = \frac{27 n^3}{64} * 64[/tex]

[tex]64 * 125 = 27 n^3[/tex]

Divide both sides by 27

[tex]\frac{64 * 125}{27} = \frac{27n^3}{27}[/tex]

[tex]\frac{64 * 125}{27} =n^3[/tex]

Take Cube root of both sides

[tex]\sqrt[3]{\frac{64 * 125}{27}} = \sqrt[3]{n^3}[/tex]

[tex]\sqrt[3]{\frac{64 * 125}{27}} = n[/tex]

[tex]\frac{4 * 5}{3} = n[/tex]

[tex]\frac{20}{3} = n[/tex]

[tex]n = \frac{20}{3}[/tex]


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Answers

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Answers

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Answers

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Answers

Answer:

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Answers

Answer:

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Answers

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Answer:

Hey There!! The answer to this is His radical political ideas and events such as the Paris uprising.

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ItsNobody~ ☆

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Answers

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