Answer:
x=-5 y=6
Step-by-step explanation:
Multiply the first by 3 and the second by -4
Then add them. Y will be 6
Put 6 for y in the first one and youll find x=-5

and yes, the restrictions are -4, -2 and 1.
the original expression has such restrictions because if ever "x" becomes one of those values, one of the denominators will turn to 0 making the fraction
undefined.
The x-coordinate of the vertex can be found by -b/2a where the equation is ax^2 + bx + c
3x^2 + 6x + 3
b is 6, and a is 3
-b/2a = -6/2(3) = -6/6 = -1
The x-coordinate of the vertex is -1. To find the y-coordinate plug the x-coordinate into the equation and solve for y.
f(-1) = 3(-1)^2 + 6(-1) + 3
= 3(1) - 6 + 3
= 3 - 6 + 3
= 0
The y-coordinate is 0
The vertex is (-1, 0)
Luke Castellan the son of hermes
Answer:
The volume is increasing at a rate of 16286 in³/min.
Step-by-step explanation:
a) The volume of a cone is given by:

Where:
r: is the radius
h: is the height
The rate of change of the volume can be calculated by using the chain rule:
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{dh}{dt}r^{2} + h\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5B%5Cfrac%7Bdh%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20h%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
Since h = 4/3 r we have:
![\frac{dV}{dt} = \frac{\pi}{3}[\frac{d(\frac{4r}{3})}{dt}r^{2} + \frac{4r}{3}\frac{d(r^{2})}{dt}]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%5B%5Cfrac%7Bd%28%5Cfrac%7B4r%7D%7B3%7D%29%7D%7Bdt%7Dr%5E%7B2%7D%20%2B%20%5Cfrac%7B4r%7D%7B3%7D%5Cfrac%7Bd%28r%5E%7B2%7D%29%7D%7Bdt%7D%5D%20)
(1)
With:
= 3 in/min

And by entering the above values into equation (1) we have:
![\frac{dV}{dt} = \frac{4\pi}{9}[(3 in/min)*(36 in)^{2} + 2*(36 in)^{2}*3 in/min]](https://tex.z-dn.net/?f=%20%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B9%7D%5B%283%20in%2Fmin%29%2A%2836%20in%29%5E%7B2%7D%20%2B%202%2A%2836%20in%29%5E%7B2%7D%2A3%20in%2Fmin%5D%20)

Therefore, the volume is increasing at a rate of 16286 in³/min.
I hope it helps you!