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2 years ago

6n + 4p -2n + 9= What’s the awnser?

Mathematics

1 answer:

jeka57 [31]2 years ago

8 0

The answer is 4n+4p+9

This is because you can’t simplify past this! There are no remaining like terms

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Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

3 years ago

the Olympic record for the men's 100m freestyle is 47 seconds. the Olympic record for the women's 50m freestyle is 24 seconds. w

Nikolay [14]

Answer:

Step-by-step explanation:

The unit rate of the 100m race is 2.12... m/s which you get by dividing the 100 meters by the 47 seconds. The unit rate for the 50m race is 2.08... m/s which you get by dividing the 50 meters by the 24 seconds. This means that the record for the 100m race is faster.

5 0

3 years ago

A number is 6 times another number and their difference is 30. What are the numbers?

Alenkasestr [34]

Answer:

x=36

y=6

Step-by-step explanation:

Let the numbers be x and y

Condition 1

x=6y ----------(1)

Condition 2

x-y=30 ------------(2)

Putting 1 in 2

6y-y=30

5y=30

Dividing both sides by 5

y=6

Now

Putting y=6 in 1

We get

x=6(6)

x=36

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3 years ago

What is the difference in place value between 2 in 324 and the 2 in 0.324

icang [17]

Answer: the decimal should still be there but you don’t want to have a zero so 3.42 would be correcr

Step-by-step explanation:

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3 years ago

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oksano4ka [1.4K]

Answer:

Step-by-step explanation:

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2 years ago