Given:
All the edges of a cube are expanding at a rate of 4 in. per second.
To find:
The rate of change in volume when each edge is 10 in. long.
Solution:
Let a be the edge of the cube.
According to the question, we get
![\dfrac{da}{dt}=4\text{ in./sec}](https://tex.z-dn.net/?f=%5Cdfrac%7Bda%7D%7Bdt%7D%3D4%5Ctext%7B%20in.%2Fsec%7D)
![a=10\text{ in.}](https://tex.z-dn.net/?f=a%3D10%5Ctext%7B%20in.%7D)
We know that, volume of a cube is
![V=a^3](https://tex.z-dn.net/?f=V%3Da%5E3)
Differentiate with respect to t.
![\dfrac{dV}{dt}=\dfrac{d}{dt}a^3](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7Bd%7D%7Bdt%7Da%5E3)
![\dfrac{dV}{dt}=(3a^2)\times \dfrac{da}{dt}](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%283a%5E2%29%5Ctimes%20%5Cdfrac%7Bda%7D%7Bdt%7D)
Putting the given values, we get
![\dfrac{dV}{dt}=(3(10)^2)\times 4](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%283%2810%29%5E2%29%5Ctimes%204)
![\dfrac{dV}{dt}=3(100)\times 4](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D3%28100%29%5Ctimes%204)
![\dfrac{dV}{dt}=300\times 4](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D300%5Ctimes%204)
![\dfrac{dV}{dt}=1200\text{ in}^3\text{/sec}](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D1200%5Ctext%7B%20in%7D%5E3%5Ctext%7B%2Fsec%7D)
Therefore, the rate of change in volume 1200 cubic inches per second.
Answer: 6 tsp of baking powder.
Explanation: 1 pancake= 2 tsp of baking powder and 3c of flour. If there is 9c of flour you would assume that is 3 pancakes meaning 2 tsp times 3 is 6 tsp of baking powder. PLEASE MAKE ME THE BRAINLIEST.
Answer:
The definition of a bisector is something that cuts an object into two equal parts. This "something" is usually a line or a segment.
Step-by-step explanation:
An angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. to create similar triangles. ... An angle bisector is a ray in the interior of an angle forming two congruent angles.