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
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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.
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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
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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
4. because it is reduced and the simplest to understand
This can be solved using the system of equations:
5500 = 1000c + 1500s
5 = c + s
As the first equation can have different combinations, it is the second equation that defines just how much acres or corn or strawberries(or mathematically, it defines the values of c or s in the first equation) there are. Therefore, the equation " 5 = c + s" is the constraint.
Hey there! :)
Answer:
C.
Step-by-step explanation:
For a graph to have a change in amplitude, there must be a coefficient in front of the equation, or the 'a' value.
Recall that the transformation form of a trigonometric graph is:
y = ±a(cos(b(x-h))+k
Where 'a' is the amplitude
'b' changes the period
'h' is a horizontal shift
'k' is a vertical shift
We can look at each choice and eliminate:
A. There is only a coefficient of -1 in front of the equation, which simply results in a reflection over the x-axis. This is incorrect.
B. This equation contains a b value of 2. This changes the period of the graph, not the amplitude. This is incorrect.
C. This equation contains a coefficient, or 'a' value of -2. The amplitude is changed by a factor of 2. This is correct.
D. This graph only contains a vertical shift of 1 unit up. This is incorrect.
Therefore, C is the correct answer.
Answer:
A Hope this helps
Step-by-step explanation:
