How can you use ratios and rates to solve problems?

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?

Astudent was asked to find the square of 7x+3. the student quickly wrote (7x+3)^3= 49x^2+9. identify the student's error and provide the correct answer.

Larger pets need to be transported in larger portable kennels. using a graphing calculator and the relationship between the width, length, and height, find the dimensions of a portable kennel whose volume is 7.4 ft3. the dimensions of a portable kennel can be expressed as width x, length x + 0.4, and height x − 0.2? what are the dimensions of a portable kennel with a volume of 7.4 ft3? use a graphing calculator to solve. round the dimensions to the nearest tenth.