Suppose the football from the example problem (v0 = 20 m/s, 0 = 37.0o) was a punt, and left the punter’s foot at a height of 1.00 m above the ground. How far did the football travel before hitting the ground? Set x0 = 0, y0 = 0. [Hint: yf = -1 m, and so you will have to use the quadratic formula to find the time.]

Asequence of numbers begins with 12 and progresses geometrically. each number is the previous number divided by 2. which value can be used as the common ratio in an explicit formula that represents the sequence? 1/2 2 6 12

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

If you prove that ∆wxz is congruent to ∆yzx, which general statement best describes what you have proved?