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3 years ago

I did this problem and I was told I did it wrong how do I fix it??

Mathematics

1 answer:

Ksivusya [100]3 years ago

5 0

Answer:

(1/8)(cos(4x) -4cos(2x) +3)

Step-by-step explanation:

Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...

cos(x)² = (1/2)(1 +cos(2x))

In the context of this problem, using this formula gives you ...

sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))

sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)

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True or false when the x intercept of a graph occurs when the x=0

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True, hope this helps you.

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1 year ago

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.

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2 years ago

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3 years ago

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Marta_Voda [28]

Answer:

273.7

Step-by-step explanation:

first fine the sides that isn't the base.

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(14*9)/2 = 63

since there are 3 sides you multiply this by three.

63*3=189

then find the base.

same formula since its a triangle.

(12.1*14)/2 = 84.7

now add them both up:

84.7+189 = 273.7

hope this helps!

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3 years ago

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3 years ago

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