calculus

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c)The price (in dollars) p and the quantity demanded q are related by the equation: p2+2q2=1100.
If R is revenue, dR/dt can be expressed by the following equation: dR/dt=A(dp/dt),
where A is a function of just q.
i)Find A.
ii)Find dR/dt when q=20 and dp/dt=4.

  • calculus -

    p^2 + 2 q^2 = 1100
    2 p dp/dt + 4 q dq/dt = 0
    dp/dt = -(q/p) dq/dt

    R = p q price times quantity
    dR/dt = p dq/dt + q dp/dt = A dp/dt


    so A is just q

    when q = 20
    p^2 + 2(400) = 1100
    p^2 = 300
    p = 10 sqrt 3

    dR/dt = q dp/dt = 20*4 = 80

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