Answer:
300
Step-by-step explanation:
50 and above is rounded up
49 and below is rounded down
Answer:
Step-by-step explanation:
False
Answer:
D. none of these
Step-by-step explanation:
The image only shows two congruent angles/sides. In order for one of the given postulates to work, 3 congruent parts of the triangles must be applicable.
It would be 2/3 because u add the one yellow and three purple to make 4 (put that on the numerator) and the 6 would go on the denominator to make 4/6 then u divide each by two to reduce to get 2/3
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)
