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3 years ago

10

Determine the solution set of (x - 4)2 = 12.

1 answer:

galben [10]3 years ago

3 0

(x-4)2=12
First, you want to divide both sides by 2 to eliminate the 2 outside of the parenthesis. That leaves you with:
(x-4)=6
Then add four to both sides to eliminate the four inside the parenthesis:
x=10

To check work, substitute ten in for x in the original equation:
(10-4)2=12
(6)2=12
12=12, so this is correct :)

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Answer:

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Step-by-step explanation:

Given that,

The given curve between the specified points is

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Using formula of arc length

$L=\int_{a}^{b}{\sqrt{1+(\dfrac{dx}{dy})^2}dy}$

Put the value into the formula

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4}-y^{-3})^2}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-2\times\dfrac{y^3}{4}\times y^{-3}}dy}$

$L=\int_{1}^{2}{\sqrt{1+(\dfrac{y^3}{4})^2+(y^{-3})^2-\dfrac{1}{2}}dy}$

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$L=(\dfrac{y^4}{16}+\dfrac{y^{-2}}{-2})_{1}^{2}$

Put the limits

$L=(\dfrac{2^4}{16}+\dfrac{2^{-2}}{-2}-\dfrac{1^4}{16}-\dfrac{(1)^{-2}}{-2})$

$L=\dfrac{21}{16}$

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