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3 years ago

Please help thank you.

Mathematics

1 answer:

sveta [45]3 years ago

5 0

Look at Arc DE

DE = 124°

∠A is 1/2 of Arc DE

124/2 = 62°

B.62 Degrees is your answer

hope this helps

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kakasveta [241]

Answer:

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2 years ago

MY NOTES

jeka57 [31]

<h3>Answers:</h3>

Part 1) $\displaystyle \frac{1}{n^2}$ or 1/(n^2) goes in the box.

Part 2) The series <u>converges</u>

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

Work Shown:

$\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\$

$\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\$

Because L is finite and positive, i.e. $0 < L < \infty$ , this means that the original series given and the series

$\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}$

either converge together or diverge together due to the Limit Comparison Test.

But the simpler series is known to converge (p-series test).

Therefore, the original series converges as well.

The two series likely don't converge to the same value, but they both converge nonetheless.

7 0

2 years ago

Please help. I keep getting a negative distance when doing the formula

jenyasd209 [6]

Answer:

EF ≥ 4

Step-by-step explanation:

EF is the midline of the trapezoid so its length is the average of the two base lengths:

(AD +BC)/2 = EF

AD +BC = 2·EF . . . . multiply by 2

8 +2x -4 = 2(x+2) . . . substitute the expressions for the segment lengths

2x +4 = 2x +4 . . . . . . true for any value of x

We only require that segment BC is non-negative in length, so ...

BC ≥ 0

2x -4 ≥ 0 . . . . substitute the expression for BC

x -2 ≥ 0 . . . . . divide by 2

x ≥ 2

Then segment EF will be ...

x +2 ≥ 4 . . . . add 2 to both sides of the inequality for x

The only restriction the figure puts on the length of EF is ...

EF ≥ 4

_____

We suggest you talk to your teacher about this problem. The figure shown does not require that EF have any particular value.

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olga55 [171]

Answer:

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Step-by-step explanation:

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