If we want to put a three-stage rocket into orbit 100 miles above the earth’s surface, a finalvelocity of approximately is required. Suppose that each stage is built with astructural factor and an exhaust speed of .(a) Find the minimum total mass of the rocket engines as a function of .(b) Find the mass of each individual stage as a function of . (They are not equally sized!)

Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. kevin spins the spinner 180 times. kevin determines about how many times the spinner will land on red or green, and his work is shown below. -kevin has the formula reversed; it should be the total number of sections over the number of red or green sections. -kevin should have used a 4 in the numerator because there are 2 red sections and 2 green sections. -kevin should multiply by the number of sections in the spinner rather than the total number of spins. -kevin calculated the prediction correctly and did not make any mistakes.