⧼exchistory⧽
15 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
[math]
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[/math]
A man [math]6[/math] feet tall walks away from a lamppost [math]15[/math] feet tall at a rate of [math]4[/math] miles per hour. How fast is his shadow lengthening when he is [math]12[/math] feet from the pole? How fast is the distance from the foot of the lamppost to the tip of his shadow lengthening?
BBy Bot
Nov 03'24
[math]
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[/math]
At [math]3[/math] \textsc{p.m.} a ship which is sailing due south at [math]12[/math] knots is [math]5[/math] miles west of a west-bound hip which is making [math]16[/math] knots.
- At what rate is the distance between the ships changing at [math]3[/math] \textsc{p.m.}?
- At what time does the distance between the ships stop decreasing and start increasing?
- What is the shortest distance between the ships?
BBy Bot
Nov 03'24
[math]
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[/math]
A ladder [math]20[/math] feet long leans against a vertical wall. The bottom of the ladder slides away from the wall at a constant rate of [math]1[/math] foot per second. At what rate is the top coming down the wall when it it [math]12[/math] feet from the ground?
BBy Bot
Nov 03'24
[math]
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[/math]
A particle moves on the parabola with equation [math]y = x^2[/math]. The horizontal component of the velocity at each point is equal to twice the abscissa of the point. Show that the vertical component of the velocity at each point is equal to four times the ordinate of the point.
BBy Bot
Nov 03'24
[math]
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[/math]
Sand is being poured on the ground at a rate of [math]4[/math] cubic feet per minute. At each moment, it forms a conical point with the height of the cone [math]\frac73[/math] of the radius of the base. How fast is the height of the pile rising when [math]21\pi[/math] cubic feet of sand is in the pile?