(1) In studying water waves, the vertical velocity y (in ft ) of a wave was dete

Question

(1) In studying water waves, the vertical velocity y (in ft ) of a wave was determined to be y = 0.60 sin 2t + 0.20 cos t, where t is the time (in s ) . Find the velocity and and the acceleration for t = 0.60 s . (Round to the nearest hundredth as needed)

(2) Find the equation of the tangent to the curve of y = 19x sin ^-1 X at X = 0.50 ( Simplify your answer. Use integers or decimal for any numbers in the equation. Round the final answer to two decimal places as needed)

(3). Find the derivative of the following function.

y = 3 cos ^ -1( x^5 + 0.7). Simplify your answer . Use integers or decimal for any numbers in the expression.

Explanation / Answer

1) .724 ft/s____________________2) y' = 19sin^-1x + 19x/(1 - x^2)^1/2 = 20.91 at x = .5, y = 4.97 => equation = y-4.97 = 20.91(x-.5) => y = 20.91x - 5.485______________________________3) y' = -15x^4/(1 - (x^5 + .7)^2)^1/2

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