Answer to Question #62490 in Mechanics | Relativity for Sedrick

Question

1. At what point of the parabola y= x^2-3x-5 is the tangent line parallel to 3x-y=2? Find the equation of the tangent line.
2. For the curve y=x^2+x at what point does the normal line at (0,0) intersects the tangent line at (1,2)?
3. A water bucket containing 10 gal of water develops a leak at time t=0 and the volume V of water in the bucket t seconds later is given by
V(t)=10(〖1-t/100)〗^2
until the bucket is empty.
a) At what time would the bucket be emptied?
b) At what rate is water leaking from the bucket after exactly 1 minute has passed?
c) When is the instantaneous rate of change of V equal to the average rate of change of V from t=0 to t=100?
4. A car is travelling at 100 fps when the driver suddenly applies the brakes. The position function of the skidding car is
s=100t-〖5t〗^2
how far and for how long does the car skid before it comes to a stop?