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2 years ago

Helpp please… due at 12:00

Mathematics

2 answers:

zmey [24]2 years ago

4 0

Answer:alternate exterior angles

Step-by-step explanation:

Since they’re on the outside of the parallel lines that makes them exterior

Eddi Din [679]2 years ago

3 0

The correct answer is C. Alternate Exterior Angles

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Nikolay [14]

Replace x with π/2 - x to get the equivalent integral

$\displaystyle \int_{-\frac\pi2}^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

but the integrand is even, so this is really just

$\displaystyle 2 \int_0^{\frac\pi2} \cos(\cot(x) - \tan(x)) \, dx$

Substitute x = 1/2 arccot(u/2), which transforms the integral to

$\displaystyle 2 \int_{-\infty}^\infty \frac{\cos(u)}{u^2+4} \, du$

There are lots of ways to compute this. What I did was to consider the complex contour integral

$\displaystyle \int_\gamma \frac{e^{iz}}{z^2+4} \, dz$

where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be

$\displaystyle \left|\int_{z=Re^{i0}}^{z=Re^{i\pi}} f(z) \, dz\right| \le \frac{\pi R}{|R^2-4|}$

which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit

$\displaystyle \int_{-\infty}^\infty \frac{\cos(x)}{x^2+4} \, dx = 2\pi i {} \mathrm{Res}\left(\frac{e^{iz}}{z^2+4},z=2i\right) = \frac\pi{2e^2}$

and it follows that

$\displaystyle \int_0^\pi \cos(\cot(x)-\tan(x)) \, dx = \boxed{\frac\pi{e^2}}$

7 0

1 year ago

Determine the Probability: P(B^c)

Alona [7]

abcdefghijklmnopqrstuvwxyz

5 0

2 years ago

What’s the length of the missing leg?!

posledela

So the right answer is 12 m.

Look at the attached picture

Hope it will help you..

-Pragya~~

8 0

2 years ago

Does anyone know this :/ ?

choli [55]

Angles 7, 6, 3, 2 are all vertical angles, which mean they are congruent (equal)

so if angle 7 is 115° so are 6, 3, and 2

so the measure of angle 2 is 115°

7 0

2 years ago

Read 2 more answers

What is the solution to this inequality? -13x < 65

xeze [42]

Answer:

x > -5 or x = (-5, + oo)

Step-by-step explanation:

-13x < 65
x > - 65/13
x > -5
x = (-5, + oo)

4 0

2 years ago