Step-by-step explanation:
take the right triangle
15^2 = 9^2 + x^2
225 = 81 + x^2
x = 12
area of square b = 144
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.
<h3>What is an area bounded by the curve?</h3>
When the two curves intersect then they bound the region is known as the area bounded by the curve.
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be
Then the intersection point will be given as
![\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214](https://tex.z-dn.net/?f=%5Crm%205%20%5Csin%20%5Ctheta%20%20%3D%204%5C%5C%5C%5C%5Ctheta%20%3D%200.927%20%2C%202.214)
Then by the integration, we have
![\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cint%20_%7B0.927%7D%5E%7B2.214%7D%5B%20%285%20%5Csin%20%5Ctheta%29%5E2%20-%204%5E2%5D%20d%5Ctheta%20%5C%5C%5C%5C%5C%5C%5Crightarrow%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cint%20_%7B0.927%7D%5E%7B2.214%7D%20%5B25%5Csin%20%5E2%20%5Ctheta%20-%2016%5D%20d%5Ctheta%20%5C%5C%5C%5C%5C%5C%5Crightarrow%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20%5Cint%20_%7B0.927%7D%5E%7B2.214%7D%20%5B%20%5Cdfrac%7B25%7D%7B2%7D%281%20-%20%5Ccos%202%5Ctheta%20%29%20-%2016%5D%20d%5Ctheta%20%5C%5C)
![\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cdfrac%7B1%7D%7B2%7D%20%5B%5Cdfrac%7B25%20%5Ctheta%20%7D%7B5%7D%20-%20%5Cdfrac%7B25%20%5Ccos%202%5Ctheta%20%7D%7B2%7D%20-%2016%5Ctheta%5D_%7B0.927%7D%5E%7B2.214%7D%20%5C%5C%5C%5C%5C%5C%5Crightarrow%20%5Cdfrac%7B1%7D%7B2%7D%20%5B%5Cdfrac%7B25%282.214%20-%200.927%29%20%7D%7B5%7D%20-%20%5Cdfrac%7B25%20%28%5Ccos%202%5Ctimes%202.214%20-%20%5Ccos%202%5Ctimes%200.927%29%20%7D%7B2%7D%20-%2016%282.214%20-%200.927%5D%5C%5C)
On solving, we have
![\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75](https://tex.z-dn.net/?f=%5Crightarrow%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%207.499%5C%5C%5C%5C%5Crightarrow%203.75)
Thus, the area of the region is 3.75 square units.
More about the area bounded by the curve link is given below.
brainly.com/question/24563834
#SPJ4
The answer is 523.6 and all you have to do is round it to the nearest hundredth
The answer is 17
This is because 1 + 2 must equal 180 as they are in a straight line.
So 4x + 2 + 110 = 180
Take away 110 from both sides
4x + 2 = 70
Take away 2 from both sides to get 4x = 68. Finally, divide both sides by 4 to get x = 17
Answer:
198
Step-by-step explanation:
If the ratio of adults to children is 6:11, then 6/17 of the people are adults and 11/17 of the people are children.
11/17 × 306 = 198
There are 198 children.