ANY help with these Calculus Problems would be greatly appreciated :D?

1.) A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.6 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft from the wall?

2.)Two cars start moving from the same point. One travels south at 56 mi/h and the other travels west at 42 mi/h. At what rate is the distance between the cars increasing two hours later?

3.The top of a ladder slides down a vertical wall at a rate of 0.375 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of .5 m/s how long is the ladder?

4.)Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 400 cm3, the pressure is 120 kPa, and the pressure is increasing at a rate of 30 kPa/min. At what rate is the volume decreasing at this instant?

1 Answer

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  • ted s
    Lv 7
    6 years ago
    Best Answer

    1 . y = wall distance , x = ground distance ; tan Θ = y / x ; x² + y² = 100 ;

    differentiate with respect to t ; evaluate...{ ≈ - 0.13 rads / sec }

    #2. w² = [ (56 t)² + (42 t)² ] ; w = distance between cars...find dw / dt when t = 2

    #3. similar to #1

    #4 .take a time derivative of [ P V = C ] ; C = (120)(400) is given...find dV/dt

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