Given:
To find:
The rate of change in volume at 
Solution:
We know that, volume of a cone is
Differentiate with respect to t.
![\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%20%5Cleft%5B%28r%5E2%5Cdfrac%7Bdh%7D%7Bdt%7D%29%20%2B%20h%282r%5Cdfrac%7Bdr%7D%7Bdt%7D%29%5Cright%5D)
Substitute the given values.
![\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B1%7D%7B3%7D%5Ctimes%20%5Cdfrac%7B22%7D%7B7%7D%5Ctimes%20%5Cleft%5B%28120%29%5E2%28-2.1%29%20%2B175%282%29%28120%29%281.4%29%5Cright%5D)
![\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]](https://tex.z-dn.net/?f=%5Cdfrac%7BdV%7D%7Bdt%7D%3D%5Cdfrac%7B22%7D%7B21%7D%5Ctimes%20%5Cleft%5B-30240%2B58800%5Cright%5D)
Therefore, the volume of decreased by 29920 cubic inches per second.
Answer:
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
to find the first 4 terms, substitute n = 1, 2, 3, 4 into the expression
n = 1 → 1(1 - 1) - 4 = 0 - 4 = - 4
n = 2 → 2(2 - 1) - 4 = 2 - 4 = - 2
n = 3 → 3(3 - 1) - 4 = 6 - 4 = 2
n = 4 → 4(4 - 1) - 4 = 12 - 4 = 8
the first four terms are - 4, - 2, 2, 8 → C
<h3>
Answer:</h3>
x² -6x = -13 ⇒ x ∈ {3-2i, 2+2i}
<h3>
Step-by-step explanation:</h3>
To make a=1, divide the equation by the coefficient of x², which is 8.
... x² -6x = -13 . . . . . . your blanks are filled with -6 and -13
Now, to complete the square, add the square of half the x-coefficient:
... (-6/2)² = 9.
... x² -6x +9 = -4 . . . 9 added to both sides
... (x -3)² = -4 . . . . . rewrite as a square
... x -3 = ±2i . . . . . . take the square root
... x = 3 ±2i . . . . . . . add 3
The solutions are the complex numbers x = 3 ±2i.
Answer:
-1.25
Step-by-step explanation:
The change in position for x is -5, the change in position for y is 4, -5/4 = -1.25
