49 = -7 (t + 1)
49 = -7t + 7
-7 -7
42 = -7t
÷ -7 ÷ -7
-6 = t
t = -7
The y-intercept is 2. The y-intercept occurs when x is 0. In the graph, y is 2 when x is 0.
Answer: dr/dt = 9/(24pi) cm per minute
9/(24pi) is approximately equal to 0.119366
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Work Shown:
Given info
dS/dt = 18 cm^2/min is the rate of change of the surface area
r = 6 cm is the radius, from the fact that the diameter is 12 cm
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Use the surface area equation given, apply the derivative, plug in the given values and then isolate dr/dt which represents the rate of change for the radius
S = 4*pi*r^2
dS/dt = 2*4*pi*r*dr/dt
dS/dt = 8*pi*r*dr/dt
18 = 8*pi*6*dr/dt
18 = 48*pi*dr/dt
48pi*dr/dt = 18
dr/dt = 18/(48pi)
dr/dt = (9*2)/(24*2pi)
dr/dt = 9/(24pi)
The units are cm per minute, which can be written as cm/min.
So to figure out 10% of this would be to remove the 0. that would be six. since 30÷10 is 3, we have to do 6×3. that would be 18, so 30% of 60 is 18
