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murzikaleks [220]
3 years ago
15

Ben is 5 years less than 3 times Gracie's age. How can that be represented as an expression?  

Mathematics
1 answer:
Tanzania [10]3 years ago
7 0
You can write 5 times 3
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Part A: 3x + 15 = 5x - 25

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Pls answer with real answers only thank you
aev [14]
Answer: 32.35 cm^2

Step by step:

Find the area of the rectangle first.

A= L • W
A= 11 • 4.2
A= 46.2 cm^2

Then find the area of the circle. The formula is A= pi (r)^2. The diameter of the circle is 4.2 cm because looking at the width of the rectangle it fits into the circle as well.

Half of the diameter is 2.1 cm which is the radius.

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Then you would subtract 13.85 from 46.2 to find the shaded portion.

Hope this helps :))

4 0
3 years ago
Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1
defon
I'm guessing the series is supposed to be

\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}

By the ratio test, the series converges if the following limit is less than 1.

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|

The first n terms in the numerator's denominator cancel with the denominator's denominator:

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|

|x^n| also cancels out and the remaining factor of |x| can be pulled out of the limit (as it doesn't depend on n).

\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0

which means the series converges everywhere (independently of x), and so the radius of convergence is infinite.
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Whitepunk [10]
The animal is a bat.
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