(Calculus) The tangent vector to (x(t), y(t)) is (x'(t), y'(t)). The tangent vector's length ||(x', y')|| = √(x'(t))² + (y'(t))² is the speed of the point along the curve at time t. Suppose that a projectile takes the path x(t) = 12t meters/sec, y(t) = -4.9t² + 14.7t meters/sec. (a) Determine the initial velocity of the projectile (at t = 0). (b) The projectile stops when its height y(t) is again 0. Find the value of t when it stops, its velocity at that time, and determine how far it travelled horizontally. (c) The projectile reaches its highest point when y'(t) = 0. Find the value of t at its highest point as well as its velocity and height at that time.

Q: f(3) = -9 and f'(3) = 7 . Then the equation of the tangent line to the graph of y = f(x) at x = 3 is

A: Given Data: The value of function at x=3 is: f(3)=-9 The value of the derivative of the function at…

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Q: (a) y = 3x-1 (b) x² + y² = 1 (c) y = sin(x)

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Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

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Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 9 and f'(2) = 3. |3D

A: GIVEN FOR A FUNCTION f(x) ,f(2) = 9            &  f'(2)=3

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A: According to our guide line we do only the first part of multiple questions. Please re post the…

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

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