The square of a number decreased by the square of one half the number is 108. What is the number?

1 answer:

6 0

Let the number be n. Then

n^2 - (n/2)^2 = 108.
n
From this we get n^2 - (---- )^2 = 108.
2

Mult. both terms by 4, with the result 4n^2 - n^2 = 432

Then 3n^2 = 432, and n^2 = 144. n could be either 12 or -12. You must check both answers by subst. them into the original equation.

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inysia [295]

10 1/2x +2

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exis [7]

Answer: No.

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3 years ago

(Fog) (x) f(x)=6x-5 <br> g(x) =6x^2-3x

algol [13]

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see below

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put g(x) in for the x in f(x)

$f(x)= 6x-5\\g(x)= 6x^{2} -3x\\f(g(x)= 6(6x^{2} -3x)-5$

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3 years ago

Implicit differentiation of 1/x +1/y=5 y(4)= 4/19<br> y'(4)=?

Aneli [31]

$\frac{1}{x} +\frac{1}{y} = 5\\\\x^{-1}+y^{-1}=5\\$

Above, I changed the fraction form of x and y into exponential form so it is easier to see the differentiation. Now, we can differentiate:

$-1x^{-2}+-1y^{-2}\frac{dy}{dx}=5\\\\\frac{-1}{x^2}-\frac{1}{y^2}\frac{dy}{dx}=5\\\\-\frac{1}{y^2}\frac{dy}{dx}=5+\frac{1}{x^2}\\\\\frac{dy}{dx}=-5y^2-\frac{y^2}{x^2}$

Now that we have dy/dx, we can plug in the x, which is 4, and the y, which is 4/19. We know these values of x and y because your question stated y(4) = 4/19.

$\frac{dy}{dx}=-5(\frac{4}{19})^2-\frac{(\frac{4}{19})^2}{(4)^2}\\\\\frac{dy}{dx}=-5(\frac{16}{361})-\frac{(\frac{16}{361})}{16}\\\\\frac{dy}{dx}=\frac{-80}{361}-\frac{1}{361}\\\\\frac{dy}{dx}=\frac{-81}{361}$

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3 years ago