Suppose that a particle following the given path c(t)=(t2,t3−3t,0)c(t)=(t2,t3−3t,0) flies off on a tangent at t0=2t0=2. compute the position of the particle at the given time t1=3t1=3. (use symbolic notation and fractions where needed. )

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes. t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

This is the substance(s) formed in a chemical reaction.

The graph represents the distance a car travels over time while on the highway. which statement about the car's trip is accurate? a) the car does not move over time. b) the car travels at a constant velocity. c) the car's velocity increases constantly over time. d) the car's velocity decreases constantly over time.