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qaws [65]
3 years ago
15

Will is 34​% taller than​ Wanda, so​ Will's height is​ ____% of​ Wanda's height.

Mathematics
2 answers:
Andre45 [30]3 years ago
5 0

Answer:

Will is 34% taller than Wanda, so Will's height is 134% of Wanda's height.

Step-by-step explanation:

If Will is 34% of Wanda's height, we can conclude that he has all of Wanda's height plus 34% of that height. All the height of Wanda represents 100% as it is referring to a complete system. From this we can conclude that Will is 100% more 34% of Wanda's height. Thus we can conclude that if Will is 34% higher than Wanda, then Will's height is 134% (100% + 34%) of Wanda's height.

insens350 [35]3 years ago
4 0
The easiest way for me to do this is too set their heights to actual numbers. Say Wanda is 100 feet tall (which I know isn’t a thing, but 100 is always an easy number for percentages.) If will is 34% taller than 100 feet, 1% is 1 foot, so Will is 134 feet tall. 134 / 100 is 134%, so will’s height is 134% of Wanda/s height. Hope this helps!
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\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

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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

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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}}

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