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LenKa [72]
3 years ago
9

Can you Please Help ASAP!

Mathematics
1 answer:
marin [14]3 years ago
4 0
THE ANSWER IS 70 !!

When you add up all the sides to get 290 and the total amount of the angles is 360 so you subtract 290-360 and you get 70
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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
Write the equation of the line, in slope-intercept form, that passes through the point (-8,-1) and that is parallel to x-3=0
nataly862011 [7]
Y=-5X which is the equation you use to figure out the answer
5 0
3 years ago
The price of a toy usually costing £50 to £65 work out the percentage increase FAST!!
VLD [36.1K]

Answer:

50 * 1.3 = 65

130% increase

6 0
2 years ago
Read 2 more answers
Please Evaluate 1/6 + 2/3
weeeeeb [17]

Answer:

Step-by-step explanation:

4/6

5 0
2 years ago
Read 2 more answers
FIND THE area of the shaded figure
bezimeni [28]

Answer:

12

3 x 4

if its one unit then you just multiply the sides in this case 3 x 4

3 0
3 years ago
Read 2 more answers
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