Need help with calculus AB?

so I'm in calc AB, and for awhile I was doing well, but I'm slowly getting further behind every week...

Could anyone PLEASE explain at least one of these problems to me step by step?

1) a point P moves from left to right along the curve y=x^2, at a constant horizontal speed of 3m/sec. How fast does the y coordinate of P increase at the moment when P passes through (1,1)? when P pas senses (2,4)?

2) a 6meter ladder is against a wall. If its bottom is pulled at a constant 1/2 m/sec, how fast is the ladder top sliding when it reaches 5m up the wall?

3) a man 6ft tall walks away from a lamp post 15ft tall at 5ft/sec. how fast is his shadow lengthening? how fast is the tip of his shadow moving?

4) Boyle's law states that if the temperature of a gas remains constant, then PV=c where c is a constant. If the volume is decreasing at the rate of 10 in^3 per sec, how fast is the pressure increasing when P is 100lbs/in^2 and V is 20 in^3

1 Answer

  • ted s
    Lv 7
    6 years ago
    Best Answer

    [ dy / dt ] = 2 x [ dx /dt] and you are given dx/dt = 3

    so x² + y² = 36 ---> x [dx/dt] + y [ dy/dt] = 0

    here 15 / 6 = [ x + s ] / s...find ds/dt...DRAW the diagram

    same concept for the last

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