Cross multiply the expression so that we can get
(1+sinx)(1-sinx) = cos^2 x
1 - sin^2 x = cos^2 x
cos^2 x + sin^2 x = 1
since
cos^2 x + sin^2 x = 1
therefore
1 = 1
the two expressions are identical in a trigonometric sense
Below are the choices that can be found elsewhere:
A.12 oz of gold and 20 oz of silver
B.10 oz of gold and 10 oz of silver
C.16 oz of gold and 30 oz of silver
<span>D.25 oz of gold and 20 oz of silver
</span>
The answer is <span>A because the points(12,20) are in the blue shaded area.
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.
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You want to find the volume inside the hemisphere
(i.e. inside the sphere but above the plane
) and outside the cylinder
. Call this region
.
In cylindrical coordinates, we have
![\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Ciiint_R%5Cmathrm%20dV%3D%5Cint_0%5E%7B2%5Cpi%7D%5Cint_1%5E2%5Cint_0%5E%7B%5Csqrt%7B4-r%5E2%7D%7Dr%5C%2C%5Cmathrm%20dz%5C%2C%5Cmathrm%20dr%5C%2C%5Cmathrm%20d%5Ctheta)
![\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D2%5Cpi%5Cint_1%5E2%20r%5Csqrt%7B4-r%5E2%7D%5C%2C%5Cmathrm%20dr)
![\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D-%5Cpi%5Cint_3%5E0%5Csqrt%20u%5C%2C%5Cmathrm%20du)
(where
)
![\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du](https://tex.z-dn.net/?f=%5Cdisplaystyle%3D%5Cpi%5Cint_0%5E3%5Csqrt%20u%5C%2C%5Cmathrm%20du)
![=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B2%5Cpi%7D3u%5E%7B3%2F2%7D%5Cbigg%7C_0%5E3%3D2%5Csqrt3%5C%2C%5Cpi)
5/g=n because the denominator is always the total amount and g is the total amount of granola bars in the box. And the 5 comes from the amount of kids that received the bars and the n is on the outside because your looking for that amount. I’m sorry if this doesn’t make sense, i tried my best to explain.