1) 2) 3) A street light is at the top of a 16 ft tall pole. A woman 6 ft tall wa
ID: 2831844 • Letter: 1
Question
1)
2)
3)
A street light is at the top of a 16 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 7 ft/see along a straight path. How fast is the tip of her shadow moving when she is 40 ft from the base of the pole? Rate = A baseball diamond is a square with sides of length 90 ft. A batter hits the ball and runs toward first base with a speed of 21 ft/s. At what rate is his distance from second base changing when he is halfway to first base? At what rate is his distance from third base changing at the same moment? The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 4 cm2/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 95 cm2 ?Explanation / Answer
1)let x be the distance from the pole and y be the length of the shadow,now consider tan(theta) for both the triangles formed,poleheight/(x+y)=heightofwoman/y,
implies16y=6x+6y,10y=6x,implies derivating on both sides w.r.t 'time'
speed of shadow is:21/5 ft/sec
2)let y be the distance from 2nd base,x be the distance from first base
by pythagorous theorem,y^2=x^2+8100
differentiating w.r.t time we get,y*y'=x*x',impliesy'=21*45/77.94=12.12ft/s
the rate at which the 2nd base is changing is:12.12 ft/s
the rate at which the 3rd base is changing is:12.12 ft/s
3)area=1/2*altitude*base
differentiating on both sides
4=0.5*19+5*(rate of change of base)
rate of change of base is 1.1 cm/min decreasing
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.