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3 years ago

Calculate the value of 3√216 by using prime factors

Mathematics

1 answer:

Trava [24]3 years ago

5 0

Answer: 43,2

Step-by-step explanation:

$\bf 3\sqrt{216 }=3\cdot 6\sqrt{6}=18\sqrt{6} \approx43.2 \\\\ \sqrt{216} =\sqrt{ 2^{3}\cdot 3^3}=\sqrt{2^2\cdot 3^2\cdot 3\cdot 2}=3\cdot 2\sqrt{3\cdot 2} =6\sqrt{6}$

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Answer is provided in the image attached.

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A cosmetic company makes three bottles of scented lotion using the recipe shown. Each bottle holds a different amount of lotion.

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Answer:

Part 1) Bottle 1 (vanilla=1,almond=3,pineapple=4)

Part 2) Bottle 2 (vanilla=2,almond=6,pineapple=8)

Part 3) Bottle 3 (vanilla=1 1/2,almond=4 1/2,pineapple=6)

Step-by-step explanation:

Let

x ----> the amount of vanilla sent

y ----> amount of almond sent

z ----> the amount of pineapple sent

we know that

$x:y:z=\frac{1}{8}:\frac{3}{8}:\frac{1}{2}$

$\frac{x}{y}=\frac{1}{8}:\frac{3}{8}$

$\frac{x}{y}=\frac{1}{3}$

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$\frac{x}{z}=\frac{1}{4}$

$x=\frac{1}{4}z$ -----> equation B

$\frac{y}{z}=\frac{3}{8}:\frac{1}{2}$

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Part 1) Bottle 1

vanilla=?

almond=?

pineapple=4

we have

$z=4$

Find the value of x

substitute the value of z in equation B

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Find the value of y

substitute the value of z in equation C

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vanilla=?

almond=6

pineapple=?

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substitute the value of y in equation A

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substitute the value of x in equation B

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solve for z

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therefore

Bottle 2

vanilla=2

almond=6

pineapple=8

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almond=?

pineapple=?

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convert to an improper fraction

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substitute the value of x in equation A

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convert to mixed number

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substitute the value of x in equation B

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Bottle 3

vanilla=1 1/2

almond=4 1/2

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