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2 years ago

ILL GIVE BRAINLIEST !! RANDOM ANSWERS WILL BE REPORTED!!

Mathematics

2 answers:

kap26 [50]2 years ago

3 0

Answer:

15. 1

16. 1

17. X

18. ?

19. 1

20. p

Step-by-step explanation:

Ira Lisetskai [31]2 years ago

3 0

15. 1
16. 1
17. x
18. 5x^-4 + 5y^-4
19. 1
20. p

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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

2 years ago

Help me please thanks

kow [346]

Correct answer:
First reflect across the y-axis, then rotate 90 degrees clockwise about point K, then shift 3 units down.

6 0

2 years ago

If LN = 12x + 16, what is the length of Line segment L N in units?

elena55 [62]

Answer:

LN = 64 units

Step-by-step explanation:

Given M lies on LN, so LN = LM + MN --------------(1)

LN = 12x + 16

LM = 10x + 8

MN = 5x - 4

Substituting the values in equation 1, we get:

12x + 16 = (10x + 8) + (5x - 4)

12x + 16 = 15x + 4

15x - 12x = 16 -4

3x=12

Therefore x=4

LN= 12(4) + 16 = 64 units

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1 year ago

What is the intersection of the three sets: A = {1,2,3,4,5),

Lubov Fominskaja [6]

Answer:

(2,3)

Step-by-step explanation:

The only two numbers all three share

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2 years ago

Find the unknown side length for the triangle. Area = 18 cm² A. 9 cm B. 14 cm C. 18 cm D. 36 cmFind the unknown side length for

Nataliya [291]

The answer would be A. 9cm

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2 years ago