Answer:
a = 32
Step-by-step explanation:
This is a right triangle and the square value of hypotenuse is equal to sum of square value of other two side lengths
68^2 = 60^2 + a^2
4624 = 3600 + a^2
4624 - 3600 = a^2
1024 = a^2 find the root for both sides
32 = a
Hi there, AirConditioning,
The equation we will be using is linear, and takes the form y = slope*x+b, where slope is equivalent to the fireflies caught each minute.
y=total fireflies caught
You : y = 3m+13
Your Friend: ym+6
Fireflies caught each minute
You: 3
Your Friend: 4
3+4=7
A total of 7 fireflies each minute combined.
The answer is - 1.5. subtract -2.5 by -1.5
Answer:
9/16 10/16 11/16 12/16 13/16
Step-by-step explanation:
Answer:
The rate of change of the volume
when the height is 9 centimeters and the radius is 6 centimeters is 
Step-by-step explanation:
This is a related rate problem because you know a rate and want to find another rate that is related to it. If 2 variables both vary with respect to time and have a relation between them, we can express the rate of change of one in terms of the other.
From the information given we know:


- The volume of a cone of radius r and height h is given by

We want to find the rate of change of the volume
when the height is 9 centimeters and the radius is 6 centimeters.
Applying implicit differentiation to the formula of the volume of a cone we get
![\frac{dV}{dt}=\frac{1}{3}\pi [r^2\frac{dh}{dt}+2rh\frac{dr}{dt} ]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5Br%5E2%5Cfrac%7Bdh%7D%7Bdt%7D%2B2rh%5Cfrac%7Bdr%7D%7Bdt%7D%20%5D)
Substituting the values we know into the above formula:
![\frac{dV}{dt}=\frac{1}{3}\pi [(6)^2\frac{1}{2}+2(6)(9)\frac{1}{2} ]\\\\\frac{dV}{dt}=\frac{1}{3}\pi[18+54]\\\\\frac{dV}{dt}=\frac{72\pi}{3}=24\pi \:\frac{cm^3}{s}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%5B%286%29%5E2%5Cfrac%7B1%7D%7B2%7D%2B2%286%29%289%29%5Cfrac%7B1%7D%7B2%7D%20%5D%5C%5C%5C%5C%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5B18%2B54%5D%5C%5C%5C%5C%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B72%5Cpi%7D%7B3%7D%3D24%5Cpi%20%5C%3A%5Cfrac%7Bcm%5E3%7D%7Bs%7D)