If a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation. s(t)=4 t+5 t^2 (a) Find the velocity after 2 seconds. 28 Incorrect: Your answer is incorrect. m/s (b) How long does it take for the velocity to reach 45 m/s?

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.

Waves are used in many practical applications to support work, entertainment, and health. one example is the use of ultrasound imaging to safely track the development of a growing fetus. what is a specific example of a practical application of waves in medicine, entertainment, safety, or other fields? provide a brief explanation of how the properties of waves are useful to that application.

Which best describes how fluids change as they travel through different portions of the convection currents? they change to solids at the outer portion of the convection currents. they change to solids at the inner portion of the convection currents. they become more dense at the outer portion of the convection currents. they become more dense at the inner portion of the convection currents