Answer:
The volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
Step-by-step explanation:
The volume of a is given by:
Where:
r: is the radius = 55 m
h: is the height = 88 m
We can express the rate of change of the volume of the cylinder as follows:
If dr/dt = 11 m/h and dh/dt = -44m/h, we have:
Therefore, the volume of the cylinder is decreasing at a rate of 83629.2 m³/h.
I hope it helps you!
You have the right idea that things need to get multiplied.
What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.
Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.
The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.
So we multiply the entire complex fraction by (5)(x + 6)(x -3).
Numerator:
= (x+6)(x-3) - (5)(5)(x-3)
= (x+6)(x-3) - 25(x-3)
= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3
= (x -3)(x - 19)
Denominator:
Now we put the pieces together.
Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)