# Connected Rates of Changes?

A point is moving along the curve. At the point P the y-coordinate is increasing at half the rate

at which the x-coordinate is increasing. Find the x-coordinate of P.

Eqn of curve is : y = (3x + 4)^1/2

### 2 Answers

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- stanschimLv 74 weeks agoFavorite Answer
dy/dt = (3/2)(dx/dt)(3x + 4)^(-1/2), by the use of the power and chain rules.

(dy/dt) / (dx/dt) = (3/2)(3x + 4)^(-1/2)

1/2 = (3/2)(3x + 4)^(-1/2)

1 = (3)(3x + 4)^(-1/2)

1/3 = (3x + 4)^(-1/2)

1/3 = 1 / (3x + 4)^(1/2)

(3x + 4)^(1/2) = 3

(3x + 4) = 9

3x = 5

x = 5/3

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- Ian HLv 74 weeks ago
dy/dx = (1/2)*3/√(3x + 4) = 1/2

9 = 3x + 4, so, x = 5/3

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