We are given the first term and the common ratio, this means they belong to a geometric series.
For the given series:
Each term of the geometric series is obtained by multiplying the previous term by common ratio.
So the next terms will be:
-4.5, -6.75, -10.125, -15.1875, -22.78125
The general formula for the G.P would be:
On plotting the series, the result will be like this:
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
Answer:
Jiri is 12 years old
Step-by-step explanation:
To start off we need to make an equation. Since we know both of their ages add up to 48 and that Pamela's age is 3 times Jiri's age we can say x(Jiri's Age) + 3x(Pamela's age) =48 --> x+3x=48
Now we have the equation x+3x=48, and we need to solve it.
First combine like terms
4x=48
Now divide both sides by 4
x=12
And now since we are using Jiri's age as x we know Jiri is 12 years old.
Answer:
infinite solutions :)
Step-by-step explanation:
infinity solutions, there is infininte possibilitys.
Answer:
Corson had a better performance at the skills competition.
Step-by-step explanation:
In order to determine which player had a better performance at the skills competition, we need to find the percentage performance of both the players.
Therefore,
Corson's percentage performance
Charleigh's percentage performance
Corson's percentage performance > Charleigh's percentage performance
So, Corson had a better performance at the skills competition.
