Write the following statement as a mathematical expression. State whether the expression is linear or nonlinear. If it is nonlinear, then explain why

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Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?

Time (minutes) amount of water (gallons) practice 1. jin fills up a 510-gallon pool in the backyard for her children. she fills it with the garden hose at a rate of 17 gallons per minute. after it is filled, she lets it sit for 30 minutes in order to let the water temperature rise. the children then get in and have fun for an hour. the pool loses about 5 gallon of water each minute due to their splashing and playing. at the end of the hour, they tear the pool while getting out, which causes a leak the pool then begins to lose water at a rate of 2 gallons per minute. a. complete the table to show the amount of water in the pool after each minute. b. create a graph to model the problem situation. include when the pool will be empty. c. write a piecewise function that models this problem situation. explain your reasoning for each piece of the function. d. identify the x- and y-intercept. explain what they mean in terms of the problem situation, atamantha a cul 80 100 120 150 200 ning, inc