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nekit [7.7K]
3 years ago
7

Kristin says that the square root of 0.01 is irrational, because 0.01 is not a perfect square. Do you agree? Explain.

Mathematics
1 answer:
Rasek [7]3 years ago
4 0

Her assumption is incorrect. While it is not of the perfect squares we typically think about, the same rules do not hold for numbers under 1. The square root of .01 is .1 and therefore is not irrational. This is true of many fractions between 0 and 1.

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Answer:

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Step-by-step explanation:

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Given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)
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<u>Your question: </u>given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

The correct answer would be D \sqrt{3}

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3 years ago
Prove Euler's identity using Euler's formula.<br> e^ix = cos x + i sin x
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First list all the terms out.

e^ix = 1 + ix/1! + (ix)^2/2! + (ix)^3/3! ...

Then, we can expand them.

e^ix = 1 + ix/1! + i^2x^2/2! + i^3x^3/3!...

Then, we can use the rules of raising i to a power.

e^ix = 1 + ix - x^2/2! - ix^3/3!...

Then, we can sort all the real and imaginary terms.

e^ix = (1 - x^2/2!...) + i(x - x^3/3!...)

We can simplify this.

e^ix = cos x + i sin x

This is Euler's Formula.

What happens if we put in pi?

x = pi

e^i*pi = cos(pi) + i sin(pi)

cos(pi) = -1

i sin(pi) = 0

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That is Euler's identity.

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7 is the range of this function
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