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jonny [76]
3 years ago
8

Which is the rationalized form of the expression sqrtx/sqrtx+sqrt7

Mathematics
1 answer:
ArbitrLikvidat [17]3 years ago
5 0

Answer:

(x - √7*√x) / (x - 7)

Step-by-step explanation:

I suppose your expression is √x / (√x + √7)

(√x * (√x - √7)) / ((√x + √7) * √x - √7)) = (√x * √x - √7 * √x) / (x - 7)

= (x - √7*√x) / (x - 7)

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Can someone solve this?
ladessa [460]
  • First question:

Recall that \cos^2x+\sin^2x=1 and \sqrt{x^2}=|x| for all x. So

\sqrt{1-\cos^2x}=\sqrt{\sin^2x}=|\sin x|

\sqrt{1-\sin^2x}=\sqrt{\cos^2x}=|\cos x|

For 0, we expect both \cos x>0 and \sin x>0 (i.e. the sine and cosine of any angle that lies in the first quadrant must be positive). By definition of absolute value, |x|=x if x>0.

So we have

\dfrac{\sqrt{1-\cos^2x}}{\sin x}+\dfrac{\sqrt{1-\sin^2x}}{\cos x}=\dfrac{\sin x}{\sin x}+\dfrac{\cos x}{\cos x}=1+1=\boxed{2}

making H the answer.

  • Second question:

C is always true, because the inequality reduces to x > y.

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4 years ago
When given an inverse variation, how do you find k?
atroni [7]

Considering an inverse proportional relationship, you find k taking a point (x,y), and multiplying the values of x and y.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For an inverse relationship, the function is:

y = \frac{k}{x}.

Then:

k = xy.

Which means that to find k, you take a point (x,y), and multiply the values of x and y.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

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2 years ago
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Step-by-step explanation:

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S_A_V [24]

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