Answer:
Step-by-step explanation:
From table 1,
f(x) = bˣ
For x = -1,
f(-1) = 0.5
0.5 = (b)⁻¹
b =
b = 2
For x = 1.585,
f(1.585) = 3
3 =
3 =
For x = 2.585,
f(2.585) =
=
= 4 × 1.5 [Since, ]
= 6
From table 2,
g(x) =
For x = 0.5,
g(0.5) = -1
-1 =
b⁻¹ = 0.5
b = 2
For x = 2,
g(2) = 1
1 =
For x = 6,
g(6) = 2.585
2.585 =
2.585 =
2.585 =
2.858 - 1 =
For x = 3,
g(3) =
g(3) = 1.585
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.