What is the value of x? X= in

Mathematics

2 answers:

IrinaVladis [17]3 years ago

7 0

X = 24 inches because the ratio between the larger triangle and smaller triangle is 3 to 1

dsp733 years ago

4 0

From the small triangle to the larger triangle, there is a scale factor of 3...because 5 * 3 = 15.

so because of this scale factor, x would be : 8 * 3 = 24 <==

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Please help me with this question!!

Mama L [17]

Answer:

$=\pi$

Step-by-step explanation:

$\int _0^{2\pi }\sin ^2\left(x\right)-\cos ^3\left(x\right)dx$

compute the indefinite integral

$\int \sin ^2\left(x\right)-\cos ^3\left(x\right)dx=\frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)+C\\\int \sin ^2\left(x\right)-\cos ^3\left(x\right)dx\\\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\int \sin ^2\left(x\right)dx=\frac{1}{2}\left(x-\frac{1}{2}\sin \left(2x\right)\right)\\\int \cos ^3\left(x\right)dx=\sin \left(x\right)-\frac{\sin ^3\left(x\right)}{3}$

$=\frac{1}{2}\left(x-\frac{1}{2}\sin \left(2x\right)\right)-\left(\sin \left(x\right)-\frac{\sin ^3\left(x\right)}{3}\right)\\\mathrm{Simplify\:}\frac{1}{2}\left(x-\frac{1}{2}\sin \left(2x\right)\right)-\left(\sin \left(x\right)-\frac{\sin ^3\left(x\right)}{3}\right):\quad \frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)\\=\frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)\\Add\:a\:constant\:to\:the\:solution$

$=\frac{1}{2}x-\frac{1}{4}\sin \left(2x\right)-\sin \left(x\right)+\frac{1}{3}\sin ^3\left(x\right)+C\\\mathrm{Compute\:the\:boundaries}:\quad \int _0^{2\pi }\sin ^2\left(x\right)-\cos ^3\left(x\right)dx=\pi -0\\=\pi -0\\\mathrm{Simplify}\\=\pi$