Suppose that 6 j of work is needed to stretch a spring from its natural length of 32 cm to a length of 47 cm. (a) how much work is needed to stretch the spring from 34 cm to 39 cm? (round your answer to two decimal places.) incorrect: your answer is incorrect. j (b) how far beyond its natural length will a force of 45 n keep the spring stretched? (round your answer one decimal place.) incorrect: your answer is incorrect. cm

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.

A1000-kg weather rocket is launched straight up. the rocket motor provides a constant acceleration for 16-s, then the motor stops. the rocket altitude 20-s after launch is 510-m. you can ignore any effects of air resistance. a. what was the rocket’s acceleration during the first 16-s? b. what is the rocket’s speed as it passes through a cloud 5100-m above the ground?

At very high pressures, gases become and will eventually a) more dense; become hotter b) more dense; change to a liquid or solid c) less dense; combust d) less dense; turn into a liquid