Answer:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Step-by-step explanation:
The area of a sphere is given by the following formula:
In which A is the area, measured in cm², and r is the radius, measured in cm.
Assume that the radius r of a sphere is expanding at a rate of 40 cm/min.
This means that
Determine the rate of change in surface area when r = 20 cm.
This is when . So
Applying implicit differentiation.
We have two variables, A and r, so:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Answer:
Check explanation
Step-by-step explanation:
Here, we want to make a prove;
Mathematically , since D is the midpoint of CE
Then;
CE = CD + DE
Also, since D splits the line segment into two equal parts as the midpoint, then CD must be equal to DE
I.e CD = DE
Hence, we can express CE as follows;
CE = DE + DE
CE = 2 DE
Divide both sides by 2
CE/2 = DE
Hence; DE = 1/2 CE
Picture? I cant answer when there us no picture?
Answer:
169.1 unit^2 to the nearest tenth.
Step-by-step explanation:
Area of the parallelogram = base * height
= 24 * 6 unit^2.
Area of the semicircle = 1/2 pi r^2.
Here r = 1/2 * 8 = 4.
So the area is 1/2 * pi * 4^2
= 8pi unit^2.
The area of the whole figure = 24*6 + 8pi
= 169.13 unit^2.