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natishtaylor1p8dirz
16.03.2020 •
Mathematics
A 165 inch rod is leaning up against a wall, but is sliding down the wall so that the vertical distance between the top of the rod and the floor is decreasing at a rate of 2 inches per second. How fast the is the horizontal distance between the bottom of the rod and the base of the wall changing when the vertical distance is 153 inches
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Ответ:
the horizontal distance is increasing at a rate of 4.953 in/s
Step-by-step explanation:
since the rod is leaning up against the wall and its length L is constant , then the relationship between y ( vertical distance ) , x (horizontal distance ) and L is
x² + y² = L²
then using derivatives with respect to the time t in both sides of the equation
2*x*dx/dt + 2*y*dy/dt = 0
dx/dt = y/x*dy/dt
since we know that x² + y² = L² → x= √(L² -y²) , then
dx/dt = -y/√(L² -y²)*dy/dt
replacing values
dx/dt = -153 in /√[(165 in)² -(153 in)²]* (-2 in/s) = 4.953 in/s
therefore the horizontal distance is increasing at a rate of 4.953 in/s
Ответ:
ask teacher for help or parent for help.
Step-by-step explanation: