Video Example EXAMPLE 2 Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 1 - x2 - y2. SOLUTION If we put z = 0 in the equation of the paraboloid, we get x2 + y2 = 1, so the solid lies under the paraboloid and above the circular disk D given by x2 + y2 ≤ 1. In polar coordinates D is given by 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π. Since 1 - x2 - y2 = 1 - r2, the volume is V = int int (1 - x2 - y2)dA = int_0^(2pi) int_0^1 (1 - r2)r dr dθ = int_0^(2pi) dθ int_0^1 (1r - r3)dr = 2π [ [_0^1 =

James wants to promote his band on the internet. site a offers website hosting for $4.95 per month with a $49.95 startup fee. site b offers website hosting for $9.95 per month with no startup fee. for how many months would james need to keep the website for site a to be a better choice than site b? 1. define a variable for the situation. 2. write an inequality that represents the situation. 3.solve the inequality to find out how many months he needs to keep the website for site a to be less expensive than site b. 4. using words, describe how many months he needs to keep the website for site a to be less expensive than site b.

1. are the triangles similar and if so why? what is the value of x? show your work.

Diane owes $387 to her brother. if she debits her bank account $161.25 a month to pay him back, how many months will it take her to pay off the debt?