Answer:
v= 141.37
Step-by-step explanation:
π · 3^2 · 15/ 3
=141.37167
Answer:
y > 4
Step-by-step explanation:
2 (5y-4)>32
Divide each side by 2
2/2 (5y-4)>32/2
5y-4 > 16
Add 4 to each side
5y-4+4 > 16+4
5y > 20
Divide each side by 5
5y/5 > 20/5
y > 4
![\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}=\dfrac{2sec^2\theta}{tan^2\theta-1}](https://tex.z-dn.net/?f=%5Cdfrac%7Bsin%5Ctheta%20%2B%20cos%5Ctheta%7D%7Bsin%5Ctheta-cos%5Ctheta%7D%2B%5Cdfrac%7Bsin%5Ctheta-cos%5Ctheta%7D%7Bsin%5Ctheta%2Bcos%5Ctheta%7D%3D%5Cdfrac%7B2sec%5E2%5Ctheta%7D%7Btan%5E2%5Ctheta-1%7D)
From Left side:
![\dfrac{sin\theta + cos\theta}{sin\theta-cos\theta}\bigg(\dfrac{sin\theta+cos\theta}{sin\theta+cos\theta}\bigg)+\dfrac{sin\theta-cos\theta}{sin\theta+cos\theta}\bigg(\dfrac{sin\theta-cos\theta}{sin\theta-cos\theta}\bigg)](https://tex.z-dn.net/?f=%5Cdfrac%7Bsin%5Ctheta%20%2B%20cos%5Ctheta%7D%7Bsin%5Ctheta-cos%5Ctheta%7D%5Cbigg%28%5Cdfrac%7Bsin%5Ctheta%2Bcos%5Ctheta%7D%7Bsin%5Ctheta%2Bcos%5Ctheta%7D%5Cbigg%29%2B%5Cdfrac%7Bsin%5Ctheta-cos%5Ctheta%7D%7Bsin%5Ctheta%2Bcos%5Ctheta%7D%5Cbigg%28%5Cdfrac%7Bsin%5Ctheta-cos%5Ctheta%7D%7Bsin%5Ctheta-cos%5Ctheta%7D%5Cbigg%29)
![\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}](https://tex.z-dn.net/?f=%5Cdfrac%7Bsin%5E2%5Ctheta%2B2cos%5Cthetasin%5Ctheta%2Bcos%5E2%5Ctheta%7D%7Bsin%5E2%5Ctheta-cos%5E2%5Ctheta%7D%2B%5Cdfrac%7Bsin%5E2%5Ctheta-2cos%5Cthetasin%5Ctheta%2Bcos%5E2%5Ctheta%7D%7Bsin%5E2%5Ctheta-cos%5E2%5Ctheta%7D)
NOTE: sin²θ + cos²θ = 1
![\dfrac{1 + 2cos\theta sin\theta}{sin^2\theta-cos^2\theta}+\dfrac{1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%20%2B%202cos%5Ctheta%20sin%5Ctheta%7D%7Bsin%5E2%5Ctheta-cos%5E2%5Ctheta%7D%2B%5Cdfrac%7B1-2cos%5Ctheta%20sin%5Ctheta%7D%7Bsin%5E2%5Ctheta-cos%5E2%5Ctheta%7D)
![\dfrac{1 + 2cos\theta sin\theta+1-2cos\theta sin\theta}{sin^2\theta-cos^2\theta}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%20%2B%202cos%5Ctheta%20sin%5Ctheta%2B1-2cos%5Ctheta%20sin%5Ctheta%7D%7Bsin%5E2%5Ctheta-cos%5E2%5Ctheta%7D)
![\dfrac{2}{sin^2\theta-cos^2\theta}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7Bsin%5E2%5Ctheta-cos%5E2%5Ctheta%7D)
![\dfrac{2}{\bigg(sin^2\theta-cos^2\theta\bigg)\bigg(\dfrac{cos^2\theta}{cos^2\theta}\bigg)}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B%5Cbigg%28sin%5E2%5Ctheta-cos%5E2%5Ctheta%5Cbigg%29%5Cbigg%28%5Cdfrac%7Bcos%5E2%5Ctheta%7D%7Bcos%5E2%5Ctheta%7D%5Cbigg%29%7D)
![\dfrac{2sec^2\theta}{\dfrac{sin^2\theta}{cos^2\theta}-\dfrac{cos^2\theta}{cos^2\theta}}](https://tex.z-dn.net/?f=%5Cdfrac%7B2sec%5E2%5Ctheta%7D%7B%5Cdfrac%7Bsin%5E2%5Ctheta%7D%7Bcos%5E2%5Ctheta%7D-%5Cdfrac%7Bcos%5E2%5Ctheta%7D%7Bcos%5E2%5Ctheta%7D%7D)
![\dfrac{2sec^2\theta}{tan^2\theta-1}](https://tex.z-dn.net/?f=%5Cdfrac%7B2sec%5E2%5Ctheta%7D%7Btan%5E2%5Ctheta-1%7D)
Left side = Right side <em>so proof is complete</em>
Answer:
(B). A physical change takes place that causes molecules to move faster
Step-by-step explanation:
When a bar of chocolate melts its physical form is changed, there is no difference in its chemical composition as it is still same.
When the chocolate bar was frozen its molecules were held strongly, and they were barely moving, whereas when it melts the molecules are more free to move now.