maths...20 pts!!! @ gpjqem1的部落格

標題:

maths...20 pts!!!

發問:

At noon, a point is at (30,40), its x-coordinate is increasing at 10 units per hour, and it's distance from the origin is increasing at 5 units per hour.What's happening to it's y-coordinate at noon?

最佳解答:

At noon, a point is at (30,40). Its x-coordinate is increasing at 10 units per hour and its distance from the origin is increasing at 5 units per hour. What's happening to its y-coordinate at noon? Let its distance from the origin be r. r = √ ( x2 + y2 ) dr/dt = 5 dx/dt = 10 dr/dt = ( 1/2 ) [√(x2+y2) ]-1/2 [ 2x ( dx/dt ) + 2y ( dy/dt ) ] 5 = ( 1/2 ) [ 1/√(302+402) ] [ 2 X 30 X 10 + 2 X 40 ( dy/dt ) ] 5 = ( 1/2 ) ( 1/50 ) [ 600 + 80 ( dy/dt ) ] 5 = ( 1/5 ) [ 30 + 4 ( dy/dt ) ] 25 = 30 + 4 ( dy/dt ) 4 ( dy/dt ) = -5 dy/dt = -5/4 = -1.25 Its y-coordinate at noon is decreasing at 1.25 units per hour.

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