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JulijaS [17]
3 years ago
6

Please help!! 11 points!!

Mathematics
1 answer:
MariettaO [177]3 years ago
5 0

Answer:3x < 8x - 3

Step-by-step explanation:

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I don’t see the it the picture
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Find the angle of least nonnegative​ measure, θC​, that is coterminal with θ=<br> 9π/4.
Lostsunrise [7]

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Answer:

  θC = π/4

Step-by-step explanation:

To find the desired angle, subtract multiplies of 2π until the angle is in the desired range.

  9π/4 -2π = (9-8)π/4 = π/4

The angle θC = π/4 is coterminal with θ = 9π/4.

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What is the square root of m^6?
Nastasia [14]
Answer:
If m is nonnegative (ie not allowed to be negative), then the answer is m^3
If m is allowed to be negative, then the answer is either |m^3| or |m|^3

==============================

Explanation:

There are two ways to get this answer. The quickest is to simply divide the exponent 6 by 2 to get 6/2 = 3. This value of 3 is the final exponent over the base m. Why do we divide by 2? Because the square root is the same as having an exponent of 1/2 = 0.5, so
sqrt(m^6) = (m^6)^(1/2) = m^(6*1/2) = m^(6/2) = m^3
This assumes that m is nonnegative. 

---------------------------

A slightly longer method is to break up the square root into factors of m^2 each and then apply the rule that sqrt(x^2) = x, where x is nonnegative

sqrt(m^6) = sqrt(m^2*m^2*m^2)
sqrt(m^6) = sqrt(m^2)*sqrt(m^2)*sqrt(m^2)
sqrt(m^6) = m*m*m
sqrt(m^6) = m^3
where m is nonnegative

------------------------------

If we allow m to be negative, then the final result would be either |m^3| or |m|^3. 

The reason for the absolute value is to ensure that the expression m^3 is nonnegative. Keep in mind that m^6 is always nonnegative, so sqrt(m^6) is also always nonnegative. In order for sqrt(m^6) = m^3 to be true, the right side must be nonnegative.

Example: Let's say m = -2
m^6 = (-2)^6 = 64
sqrt(m^6) = sqrt(64) = 8
m^3 = (-2)^3 = -8
Without the absolute value, sqrt(m^6) = m^3 is false when m = -2

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Bad idea.. because the cloth will get hot and then make your water inside warm
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