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4 years ago

Is the square root of 101 a rational number?

1 answer:

4 0

No because 101 is prime. Square roots of primes are always irrational. If they weren't, you could write sqrt(101) as some a/b and a²/b² would be 101. Then b² would be a divisor of 101 and 101 wouldn't be prime. That contradicts.

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If cos(θ)= -2/3 and θ lies in quadrant II, find the value of cotθ

Lera25 [3.4K]

$\text{Given that,}\\\\\cos \theta = - \dfrac 23\\\\\implies \cos^2 \theta = \dfrac 49\\\\\implies 1- \sin^2 \theta = \dfrac 49\\\\\implies \sin^2 \theta =1-\dfrac 49\\\\\implies \sin^2 \theta =\dfrac 59\\\\\\\text{Now,}\\\\\cot^2 \theta = \dfrac{\cos^2 \theta}{\sin^2 \theta} \\\\\\\implies \cot^2 \theta = \dfrac{\tfrac 49}{\tfrac 59}\\\\\\\implies \cot^2 \theta = \dfrac 49 \times \dfrac 95\\\\\\\implies \cot^2 \theta = \dfrac 45\\\\\\$

$\implies \cot \theta = \pm\sqrt{\dfrac 45} = \pm \dfrac 2{\sqrt 5}\\\\\\\text{Since}~ \theta ~ \text{lies in the second quadrant,} \cot \theta ~\text{will be negative.}\\\\\text{Hence,}~ \cot \theta = - \dfrac{2}{\sqrt 5}$

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2 years ago

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What is the range of possible

olya-2409 [2.1K]

Answer:

4<C <10

Step-by-step explanation:

Theorem: Given a triangle with sides A, B and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

1. A+B>C

2. B +C >A

3. A+C>B

Thus given two sides of A=3 and B=7 C can be:

7 −3<C < 7+3

C range

4<C <10

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3 years ago

How do u graph an inequality without graphing calculator?

Jet001 [13]

This video may help

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:inequalities-systems-graphs/x2f8bb11595b61c86:graphing-two-variable-inequalities/v/graphing-systems-of-inequalities-2

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3 years ago

What is 21ax + 10by - 35ay - 6bx?

lara [203]

Answer:

That is it's simplest form

Step-by-step explanation:

There is no coefficients that are the same

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3 years ago

PLEASE HELP AND EXPLAIN <br><br> Solve the following equation by factoring 2x^2 - x = 2-4x

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Answer:

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3 years ago

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