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14 December, 02:36

A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 7 cm per second. Write a formula to expresses the radius of the circle, r (in cm), in terms of the number of seconds, t, since the circle started growing.

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  1. 14 December, 02:57
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    r = 7t

    or not mathematically,

    r (t) = 7t

    r (t) means, r, which is a function of t.

    Step-by-step explanation:

    Initial size of the radius = 0 cm, at t = 0 s

    Rate of increase of the radius of the circle = 7 cm/s

    dr/dt = 7

    dr = 7 dt

    ∫ dr = 7 ∫ dt

    r = 7t + C (C is the constant of integration)

    At t = 0, r = 0,

    0 = 0 + C

    C = 0

    r = 7t.

    r (t) = 7t
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