A person 6 feet tall is walking away from a lamppost that is 15 ft …
2018年1月29日 · The tip of the shadow is moving at the rate of =4(ft)/sec Let the distance of the person from the bottom of the light post be =x ft And the length of his shadow is =y ft Form the similar triangles (x+y)/(15)=y/6 6(x+y)=15y 6x+6y=15y 9y=6x y=2/3x Differentiating wrt t dy/dt=2/3dx/dt We know that dx/dt=6(ft)/sec Therefore, dy/dt=2/3*6=12/3=4(ft ...
A 7 ft tall person is walking away from a 20 ft tall ... - Socratic
2018年1月19日 · The length of the shadow is changing at =2.69(ft)/sec Let the distance of the person from the bottom of the light post be =x ft And the length of his shadow is =y ft Form the similar triangles (x+y)/(20)=y/7 7(x+y)=20y 7x+7y=20y 13y=7x y=7/13x Differentiating wrt t dy/dt=7/13dx/dt We know that dx/dt=5(ft)/sec Therefore, dy/dt=7/13*5=35/13=2.69 ...
A person 1.8m tall is walking away from a lamppost 6m high
= 13/7 m/s approx 1.86 m/s the point of what follows and the choice of variables in the drawing is this. we know that dot x = 1.3. we have been asked to find the rate at which the end of the shadow is moving away from the lamppost - that's dot y ! so similar triangles tells us that 6/y = 1.8/(y - x) y = (6x)/4.2 = 10/7 x and now for the little bit of calculus, taking the deriv of each side ...
Andy is 6 feet tall and is walking away from a street light ... - Socratic
2016年11月2日 · 2.5 feet/sec Let the man be x feet away from the street light, and his shadow length be y, Let the tip of the shadow be l feet away from the light such that l=x+y and we are given that dx/dt=2 By similar triangles: y/6=(x+y)/30 :. 30y=6(x+y) :. 30y=6x+6y :. 30y-6y=6x :. 24y=6x :. y=1/4x Now, l=x+y => l=x+1/4x :. l=5/4x Differentiating wrt x gives; (dl)/dx=5/4 And …
A six foot tall person is walking away from a 14 foot tall ... - Socratic
2018年1月17日 · A six foot tall person is walking away from a 14 foot tall lamp post at 3 feet per second. When the person is 10 feet from the lamp post, how fast is the tip of the shadow moving away from the lamp post?
A street light is mounted at the top of a 15-ft-tall pole. A ... - Socratic
2017年12月22日 · 20/3 (ft)/s in this diagram, x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar. by similarity, (y-x)/y=6/15 15(y-x)=6y 15y-15x=6y 9y=15x y=5/3x differentiate both sides with respect to t or time. dy/dt=5/3dx/dt you …
Related rates-Weight on rope word problem? - Socratic
2017年7月29日 · A person walks away from a pulley pulling a rope slung over it. The rope is being held at a height 10 ft below the pulley. Suppose that the weight at the opposite end of the rope is rising at 4 ft/sec. At what rate is the person walking when she/he is …
As a man walks away from a 12-foot lamppost, the tip of his
2017年11月28日 · 6 feet Please excuse the slightly crude diagram... If this represents an instant of time, where the man has proceeded some distance d from the base of the lamp, then the base of the large triangle is 2d, i.e. twice the base of the upper small triangle. Since the triangles are similar, the height of the large triangle is also twice the height of the smaller triangle.
A street light is mounted at the top of a 15ft tall pole. A ... - Socratic
2018年1月17日 · 8.33(ft.)/(sec.) The street light is mounted at the top of a 15ft tall pole. Let us consider the man 6ft tall xft away from the pole. His shadow forms two ends - one end is at his feet and the shadow extends away from the pole till the tip of the shadow. Let this be depicted by the figure shown below. Here the distance of the man from lamp post be xft. and let his …
A 6ft tall person is standing 24ft away from a street light ... - Socratic
2018年4月25日 · A 6ft tall person is standing 24ft away from a street light that is 15ft tall. How long is her shadow?