Math Help-Grade 10- Equation of a Circle Question!?

A raindrop falls into a puddle, creating a circular ripple. The radius of the ripple grows at a steady rate of 5cm/s. If the origin is used as the location where the raindrop hits the puddle, determine an equation that models the ripple exactly 6 s after the raindrop hits the puddle.

The answer is x2 + y2 = 900.

How do you do this question? In steps?

6 Answers

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  • DWRead
    Lv 7
    9 years ago
    Favorite Answer

    Equation for a circle:

         (x−h)² + (y−k)² = r²

    where

         center is (h, k)

         r is the radius

    radius r = 6 seconds × (5 cm/second) = 30 cm

    center (h, k) = (0, 0)

    (x−0)² + (y−0)² = 30²

    x² + y² = 900

  • Anonymous
    9 years ago

    At t=0 Circle is x^2 + y^2 =0 r=0

    At t=1 Circle is x^2 + y^2 =25 r=5

    At t=2 Circle is x^2 + y^2 =100 r=10

    At t=3 Circle is x^2 + y^2 =225 r=15

    At t=4 Circle is x^2 + y^2 =400 r=20

    At t=5 Circle is x^2 + y^2 =625 r=25

    At t=6 Circle is x^2 + y^2 =900 r=30

    So formula is x^2+y^2= 25 (t)^2

  • Anonymous
    9 years ago

    x^2 + y^2 = C^2 is the equation for a circle with radius C with the origin as the center

    Now after 6 seconds the radius = 6 * 5 = 30

    so x^2 + y^2 = (30)^2

    You can also add that for any time the equation is x^2 + y^2 = (5 * t)^2

  • 9 years ago

    it grows at the rate of 5cm/s

    therefore after 6 seconds, radius = 5x6 = 30

    since the center is the origin

    euation

    x^2 + y^2 = 30^2

    = x^2 + y^2 = 900

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  • ?
    Lv 6
    9 years ago

    If r = 5, you know that x^2 + y^2 = 5^2 because of the Pythagorean theorem.

    (You can make a right triangle for all points that do not intercept the x or y axes.)

    6s x 5cm/s = 30 cm

    x^2 + y^2 = 30^2cm^2 or

    x^2 + y^2 = 900cm^2

  • 4 years ago

    This is a great question, and one that confused me for a very long time.

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