Solve the following initial value problem: cos(ð¡)2ðyðð¡=1 with y(12)=tan(12). (find y as a function of ð¡.) y= . b. on what interval is the solution valid? (your answer should involve pi.) it is valid for < ð¡< . c. find the limit of the solution as ð¡ approaches the left end of the interval. (your answer should be a number or "pinf" or "minf". "pinf" stands for plus infinity and "minf" stands for minus infinity.)

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?