Question A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.) rad/s wall 10 y ground
8A1AWQ The Asker · Calculus
Transcribed Image Text: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.) rad/s wall 10 y ground
More Transcribed Image Text: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 6 ft from the wall.) rad/s wall 10 y ground
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JSKWSD
Step 1Solution:- ste P-y{:[y=thetaquadsec^(2)theta(d theta)/(dt)=(6((dy)/(dt))-8((dx)/(dt)))/(6^(2))],[Cos theta=(x)/( 10)],[cos theta=(6)/(10)],[csc theta=(3)/(5)],[sec theta=(5)/(3)],[((5)/(3))^(2)(d theta)/(dt)=6((dy)/(dt))-0xx0.8],[6^(2)]:}Step 2step-2{:[x^(2)+y^(2)=h^(2)],[2x(dx)/(dt)+2y(dy)/(dt)=2n((dy)/(dt))0^(@)],[2n(dx)/(dt)+2y(dy) ... See the full answer