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3 years ago

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Mathematics

1 answer:

bonufazy [111]3 years ago

5 0

Answer:

pick B trust me trust me trust me

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Write the next three multiples of 9 <br> 36,

GrogVix [38]

Answer:

45,54,63

Step-by-step explanation:

The multiples of 9 are

9,19,27,36,45,54,63,72,81

The three multiples are 36 are

45,54,63

3 0

3 years ago

Read 2 more answers

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

3 years ago

Find a polynomial f(x) of degree 5 that has the following zeros.

lara [203]

Answer:

Step-by-step explanation:

F(x) = (x - 2)(x - 9)(x + 4)²(x + 5)

4 0

2 years ago

A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the ins

Viefleur [7K]

Answer: $\frac{253}{44}$

Step-by-step explanation:

ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.

Similar triangles so we can do $\frac{50}{x+y} = \frac{6}{y}$ .

Solve for it we get 44y = 6x

Differentiate relative to time t, we get 44y' = 6x'.

change in x (x') is equal to 5. And we get the answer y' = $\frac{33}{44}$ .

the $\frac{33}{44}$ ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.

7 0

2 years ago

A diver went 25.65 feet below the surface of the ocean and then 16.5 feet further down he then rose 12.45 feet write and solve a

Anastaziya [24]

So a diver went 25.65 ft BELOW so it's negative.
then he went 16.5 ft further down, so that's negative also.
he then rose 12.45 ft, so that's positive.
so the expression is: -25.65+-16.5+12.45, the answer is 23.7

8 0

3 years ago