15+25= 40
Mr. Giarmo arrived at work at 7:40 a.m.
How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
To solve the question, we need to know the volume of a sphere
<h3>
Volume of a sphere</h3>
The volume of a sphere V = 4πr³/3 where r = radius of sphere.
<h3>How fast the volume of the sphere is changing</h3>
To find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.
So, dV/dt = d(4πr³/3)/dt
= d(4πr³/3)/dr × dr/dt
= 4πr²dr/dt where
- dr/dt = rate of change of radius of sphere and
- 4πr² = surface area of sphere
Given that
- dr/dt = + 3 cm/s (positive since it is increasing) and
- 4πr² = surface area of sphere = 10 cm²,
Substituting the values of the variables into the equation, we have
dV/dt = 4πr²dr/dt
dV/dt = 10 cm² × 3 cm/s
dV/dt = 30 cm³/s
So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
Learn more about how fast volume of sphere is changing here:
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Midpoint is : (x1 + x2) / 2 , (y1 + y2) / 2
(-1,3)....x1 = -1 and y1 = 3
(7,-1)...x2 = 7 and y2 = -1
now we sub and solve
m = (-1 + 7)/2 , (3 - 1) / 2
m = (6/2, 2/2)
m = (3,1) <===
Repeated multiplication
Power
If multiplying something with like bases, add the exponents together.
Okay, for variable B you have the data points:
1, 2, 3, 5, 6, 6, 7, 7, 10, and 10.
What you need to do to find the mean (or average) is add all the data up and divide by how many pieces of data you had. So, the sum of all the points is 57. There are 10 points overall.
57/10 is 5.7
Your average for variable B is 5.7
