Since a target is a circle and the bulls-eye is also a circle, the percent of the circle that is bulls-eye would be (Area of the bulls eye)/(Area of the target)
[tex] A = \pi r^{2} \\
d = 2r \\ r = \frac{d}{2} \\\\
\frac{ \pi ( \frac{d}{2})^{2}}{ \pi ( \frac{d}{2})^{2} }= \frac{ \pi ( \frac{3}{2})^{2}}{ \pi ( \frac{15}{2})^{2} }\\
\frac{ \pi ( \frac{3}{2})^{2} }{ \pi ( \frac{15}{2})^{2} } = \frac{ \pi (1.5)^{2} }{ \pi (7.5)^{2} } \\
\frac{ \pi (1.5)}{ \pi (7.5) } = \frac{ \pi (2.25)}{ \pi (56.25)}\\
\frac{ \pi (2.25)}{ \pi (56.25)}=\frac{2.25}{56.25}= 0.04 [tex]
So the bulls-eye takes up 4% of the target.
Answer:
-8
Step-by-step explanation:
3×3=9+
8×2=16=
(9+16_4×-3)+(×
Answer:
C
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given integral:
Solve by using <u>Integration by Substitution</u>
<u />
Substitute u for one of the functions of 
to give a function that's easier to integrate.
Find the derivative of u and rewrite it so that 
is on its own:
Use the substitution to change the limits of the integral from -values to u-values:
Substitute everything into the original integral and solve:
![\begin{aligned}\displaystyle \int^{\pi}_{\frac{\pi}{2}}\dfrac{\cos \theta}{\sqrt{1+ \sin \theta}}\:\:d\theta & =\int^{1}_2}\dfrac{\cos \theta}{\sqrt{u}}\:\cdot \dfrac{1}{\cos \theta}\:\:du\\\\& =\int^{1}_{2}\dfrac{1}{\sqrt{u}} \:\:du \\\\& =\int^{1}_{2} u^{-\frac{1}{2}}\:\:du \\\\& = \left[ 2u^{\frac{1}{2}} \right]^{1}_{2}\\\\& = \left(2(1)^{\frac{1}{2}}\right)-\left(2(2)^{\frac{1}{2}}\right)\\\\& = 2-2\sqrt{2}\\\\& = -2(\sqrt{2}-1)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cdisplaystyle%20%5Cint%5E%7B%5Cpi%7D_%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%5Cdfrac%7B%5Ccos%20%5Ctheta%7D%7B%5Csqrt%7B1%2B%20%5Csin%20%5Ctheta%7D%7D%5C%3A%5C%3Ad%5Ctheta%20%26%20%3D%5Cint%5E%7B1%7D_2%7D%5Cdfrac%7B%5Ccos%20%5Ctheta%7D%7B%5Csqrt%7Bu%7D%7D%5C%3A%5Ccdot%20%5Cdfrac%7B1%7D%7B%5Ccos%20%5Ctheta%7D%5C%3A%5C%3Adu%5C%5C%5C%5C%26%20%3D%5Cint%5E%7B1%7D_%7B2%7D%5Cdfrac%7B1%7D%7B%5Csqrt%7Bu%7D%7D%20%5C%3A%5C%3Adu%20%5C%5C%5C%5C%26%20%3D%5Cint%5E%7B1%7D_%7B2%7D%20u%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%5C%3A%5C%3Adu%20%5C%5C%5C%5C%26%20%3D%20%5Cleft%5B%202u%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%5Cright%5D%5E%7B1%7D_%7B2%7D%5C%5C%5C%5C%26%20%3D%20%5Cleft%282%281%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%29-%5Cleft%282%282%29%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5Cright%29%5C%5C%5C%5C%26%20%3D%202-2%5Csqrt%7B2%7D%5C%5C%5C%5C%26%20%3D%20-2%28%5Csqrt%7B2%7D-1%29%5Cend%7Baligned%7D)
