Question

Find f(t) for the function F(s)= 25s²+395s+1494/s²+15s+54

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Express your answer in terms of u(t),δ(t), and t. Express the coefficients using three significant figures.
F(t)=_______________

Answer 1

To find the function F(t) for the given F(s), first find the tangent line to the curve at t = 25 s. Determine the endpoints of the tangent and plug them into the equation to solve for the slope. Then, use the slope and one of the endpoint values to find the equation of the tangent line.

Step-by-step explanation:

1. Find the tangent line to the curve at t = 25 s.
2. Determine the endpoints of the tangent. These correspond to a position of 1300 m at time 19 s and a position of 3120 m at time 32 s.
3. Plug these endpoints into the equation to solve for the slope, v.
4. Use the slope and one of the endpoint values to find the equation of the tangent line.
5. Use the quadratic formula to find the values of t that satisfy the equation.

Therefore, the function F(t) for the given function F(s) is the equation of the tangent line at t = 25 s.