The width is 60!!! Because it says the length is twice as long as the width which would mean the width is half of the length and half of 120 is 60!!! ;)
Yes because simplified 9/15 equals 3/5 and 6/10 also equals 3/5
The answer is C.(<span>Nigeria would become more economically unstable.)
</span>
Answer:
x=0 y=0
Step-by-step explanation:
3x + y = -7y = x
cancel out all y's
3x+ y(0) = -7(0) = x
3x =x
-x -x
2x = 0
divide both sides by 2
x=0
3x + y = -7y =x
cancel out all x's
3(0) +y = -7y = x(0)
y=-7y
-y -y
0 = -7y
divide both sides by -7
y=0
hope this helps!
Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:
![V = \frac{1}{3} \pi r^2h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2h)
Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So
![\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cleft%282rh%5Cfrac%7Bdr%7D%7Bdt%7D%20%2B%20r%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%5Cright%29)
Radius is 107 in. and the height is 151 in.
This means that ![r = 107, h = 151](https://tex.z-dn.net/?f=r%20%3D%20107%2C%20h%20%3D%20151)
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that ![\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D%201.1%2C%20%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%20-2.6)
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is
. So
![\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cleft%282rh%5Cfrac%7Bdr%7D%7Bdt%7D%20%2B%20r%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%5Cright%29)
![\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D%282%28107%29%28151%29%281.1%29%20%2B%20%28107%29%5E2%28-2.6%29%29)
![\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B2%28107%29%28151%29%281.1%29%20-%20%28107%29%5E2%282.6%29%7D%7B3%7D)
![\frac{dV}{dt} = 1926](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%201926)
Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.