Answer:

Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:

Therefore:

Next, the surface area of a sphere S is given by:

Therefore:

We can divide both sides by 2:

We can substitute this into dV/dt. Rewriting:

So:

Since dV/dt = 0.03 or 3/100:

Therefore:

Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
Answer:
In disguise right arrow In Standard Form a, b and c
x2 = 3x − 1 Move all terms to left hand side x2 − 3x + 1 = 0 a=1, b=−3, c=1
2(w2 − 2w) = 5 Expand (undo the brackets),
and move 5 to left 2w2 − 4w − 5 = 0 a=2, b=−4, c=−5
z(z−1) = 3 Expand, and move 3 to left z2 − z − 3 = 0 a=1, b=−1, c=−3
Step-by-step explanation:
sorry it took so long