Question 33 with explanation please! 15 points

Mathematics

2 answers:

Dominik [7]3 years ago

7 0

1. do you realize you have Paul at the bottom of the paper, 2. Well, Its Paul, because it says “all the girls only have 1 pet and 1 brother or sibling,”

FrozenT [24]3 years ago

3 0

Well Jessica’s brothers is (Paul) because lakisha has a bulldog and Angela’s brothers are men and Stephan’ and all girls can have one pet and one brother,This means Angela and lakisha are sisters.

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Finn imagines 1 more row of nines to find the total area of 9 * 9 rectangle. explain how this could help him solve 9 * 9

Juliette [100K]

Im confused by the question.

but i would say imagining nine rows of nine

the area would be 81.

Hope this helps :)

6 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Crm%20%5Cint_%7B0%7D%5E%7B%20%20%5Cpi%20%7D%20%5Ccos%28%20%5Ccot%28x%29%20%20%20%20-%20%2

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

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