help with a rate of change qn 10 pts?

The perimeter of a circular sector is 30cm.

(I) Write down an equation relating the radius and angle of the sector.

(II) The radius increases at a rate of 5cm/s^-1. Find the rate at which the angle of the sector is changing when the radius is 10cm.

Do explain it step by step because it is a new topic to me.

Update:

Thank you but I need help with part ii as well :/

1 Answer

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  • iceman
    Lv 7
    8 years ago
    Favorite Answer

    The perimeter of a sector is the sum of the arc length i.e: s and two radii, so:

    P = s + 2 r , but:

    s = r θ , so:

    P = r(θ + 2)

    in this case:

    r(θ + 2) = 30 cm

    so:

    r = 30/(θ + 2)

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