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2 years ago

Daniel wants to buy cookies for her friend. The radius of a cookie is 5 inches. What is the cookie's circumference?

1 answer:

4 0

31.4. circumference formula is pi x diameter, and the formula for diameter is radius x 2. so, 5x2= 10 and 10 x 3.14= 31.4

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$

note that any constant dividing infinity is equal to zero

$|\frac{1+2/\infty+1/\infty^2}{5}|\\\\$

$\frac{1+0+0}{5}\\ = 1/5$

$\rho = 1/5$

Since The limit of the sequence given is less than 1, hence the series converges.

5 0

2 years ago

Write a doubles fact to find the sum 3+2

valentina_108 [34]

Answer:

5 or -5

Step-by-step explanation:

3+2=5

-1(3+2)=-5

3 0

2 years ago

Can someone please tell me if this is correct if it’s not can u tell me what’s the correct answer

bearhunter [10]

Answer:

2. option D and 3. option A

Step-by-step explanation:

2. 7 + y = 30

7 - 7 + y = 30 - 7

y = 23

3. w - 32 = 55

w - 32 + 32 = 55 - 32

w = 87

Basically the answers you choose are right. Hope this helps, thank you :) !!

8 0

2 years ago

The sum of three numbers is 21. Three times the smallest is 3 less than the largest, while the sum of the largest and smallest i

Lynna [10]

3, 6, 12
I guessed and checked. So if 3 is the smallest number, I would, multiply it by 3, which is 9. 9 is 3 less than the largest number which would be 12. 12 + 3 is 15. To find the third number, subtract 21 and 15 which is 6

7 0

2 years ago

Read 2 more answers

What is the sum of the negative integers greater than -5

uranmaximum [27]

-10= ( -4)+(-3)+(-2)+(-1)

7 0

2 years ago