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4 years ago

8

Which numbers will produce a rational number when multiplied by 1/5

1 answer:

labwork [276]4 years ago

3 0

A rational number times a rational number=rational numberan irrational number times a rational number=irrational number
remember, a rational number is a number that can be written as a/b where a and b are integers and b≠0

A is irrational because the pattern doesn't repeatb is irrational because it's a crazy square rootC is irrationalD is not irrational, it is a fraction

answer is D

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Proof that :<br><img src="https://tex.z-dn.net/?f=%20%7Bsin%7D%5E%7B2%7D%20%5Ctheta%20%2B%20%20%7Bcos%7D%5E%7B2%7D%20%5C%3A%5Cth

Arisa [49]

Answer:

Solution given:

Right angled triangle ABC is drawn where <C= $\theta$

we know that

$\displaystyle Sin\theta=\frac{opposite}{hypotenuse} =\frac{AB}{AC}$

$\displaystyle Cos\theta=\frac{adjacent}{hypotenuse}=\frac{BC}{AC}$

Now

left hand side

$\displaystyle {sin}^{2} \theta + {cos}^{2} \:\theta$

Substituting value

$(\frac{AB}{AC})²+(\frac{BC}{AC})²$

distributing power

$\frac{AB²}{AC²}+\frac{BC²}{AC²}$

Taking L.C.M

$\displaystyle \frac{AB²+BC²}{AC²}$ ....[I]

In ∆ABC By using Pythagoras law we get

$\boxed{\green{\bold{Opposite²+adjacent²=hypotenuse²}}}$

AB²+BC²=AC²

Substituting value of AB²+BC² in equation [I]

we get

$\displaystyle \frac{AC²}{AC²}$

=1

Right hand side

<h3><u>proved</u></h3>

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3 years ago

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Answer:

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