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Related Rates Setup and Solution
Grade Level
Calculus I
CAL1.87 Related Rates Setup and Solution
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A rectangular prism has side lengths x = 2, y = 3, and h = 6, so its space diagonal z satisfies z
2
= x
2
+ y
2
+ h
2
. The rates are dx/dt = 1, dy/dt = 2, and dh/dt = -1. Which option gives the correctly differentiated equation and dz/dt?
A
Differentiated equation: 2z(dz/dt)=2x(dx/dt)+2y(dy/dt)-2h(dh/dt); dz/dt = 14/7 units/s
B
Differentiated equation: 2z(dz/dt)=2x(dx/dt)+2y(dy/dt)+2h(dh/dt); dz/dt = 2/7 units/s
C
Differentiated equation: dz/dt = dx/dt+dy/dt+dh/dt; dz/dt = 2 units/s
D
Differentiated equation: z(dz/dt)=2x(dx/dt)+2y(dy/dt)+2h(dh/dt); dz/dt = 4/7 units/s
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