calculus

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A car leaves an intersection traveling east. Its position t sec later is given by
x = t2 + t
ft. At the same time, another car leaves the same intersection heading north, traveling
y = t2 + 3t ft
in t sec. Find the rate at which the distance between the two cars will be changing 3 sec later. (Round your answer to one decimal place.)

  • calculus -

    x = t^2 + 1t which is 10 at t=3
    y = t^2 + 3t which is 18 at t=3

    dx/dt = 2 t + 1 which is 7 at t=3
    dy/dt = 2 t + 3 which is 9 at t=3

    r^2 = x^2 + y^2 = 434 at t = 3
    so at t = 3, r = 20.6

    2 r dr/dt = 2 x dx/dt + 2 y dy/dt
    20.6 dr/dt = 10(7) + 18(9)
    dr/dt = 11.3 ft/s

  • calculus -

    apple

  • calculus -

    x would actually be 12 not 10

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