pre calc

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I am sooo confused on my homework.

#1 Two cars lave an intersection at the same time. One is headed south at a constant speed of 30mph. the other is heading west at a constant speed of 40mph. Build a model that expresses the distance (d) between thec ars as a funtion of time (t)?

#2 Inscribe a right cylinder of height (h) and radius (r) in a a sphere of fixed radius (R) expressed the volume (V) of the cylinder as a function of (h)

  • pre calc -

    d^2 = (30t)^2 + (40t)^2 = 2500t^2
    d = 50 t

    (did you notice that the triangle is the 3:4:5 right-angled triangle? )

    #2
    volume(cylinder) = πr^2 h

    make a sketch, let the radius of the cylinder be r
    the radius of the sphere R, and the height of the cylinder as h
    let 2H = h , that is let the distance from the centre of the sphere to the centre of the cylinder base be h.
    then r^2 + H^2 = R^2, where R is a constant

    r^2 = R^2 - H^2
    Volume = πr^2 H = π(R^2 - H^2)h
    = π(R^2H - H^3)

    but H = h/2

    Vol = π(R^2 h/2 - h^3/8)
    or
    (1/8)π(4R^2 h - h^3)

    check my arithmetic, I should have written it out on paper first.

  • pre calc -

    thanks so much! where di the 3/8 come from??

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