Find the slope of the curve at the indicated point.
-The velocity of water $\mathrm { ft } / \mathrm { s }$ at the point of discharge is given by $\mathrm { v } = 14.33 \sqrt { \mathrm { P } }$, where $\mathrm { P }$ is the pressure lb/in 2 of the water at the point of discharge. Find the rate of change of the velocity with respect to pressure if the pressure is $30.00 \mathrm { lb } / \mathrm { in } ^ { 2 }$.
A) $0.2388 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
B) $2.62 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
C) $1.3081 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
D) $39.24 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$

Question

Find the slope of the curve at the indicated point.
-The velocity of water $\mathrm { ft } / \mathrm { s }$ at the point of discharge is given by $\mathrm { v } = 14.33 \sqrt { \mathrm { P } }$, where $\mathrm { P }$ is the pressure lb/in 2 of the water at the point of discharge. Find the rate of change of the velocity with respect to pressure if the pressure is $30.00 \mathrm { lb } / \mathrm { in } ^ { 2 }$.
A) $0.2388 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
B)  $2.62 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
C) $1.3081 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
D)  $39.24 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$

Quizplus · Accepted Answer

The derivative of $ v = 14.33 \sqrt{P} $ with respect to $ P $ is $ \frac{dv}{dP} = \frac{14.33}{2\sqrt{P}} $. Substituting $ P = 30 $, the rate of change is $ \frac{14.33}{2\sqrt{30}} \approx 1.3081 \mathrm{ ft/s} $ per $ \mathrm{ lb/in^2} $.

Find the Slope of the Curve at the Indicated Point ft/s\mathrm { ft } / \mathrm { s }ft/s

Find the Slope of the Curve at the Indicated Point $\mathrm { ft } / \mathrm { s }$