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

Write the product as a trinomial. (x + 2)(x + 3) x2 + 5x + 6 x2 + 6x + 6 x2 + 6x + 5 x2 + 5

Which mathematical statements are true? 1) if 3 is an odd number, then 3 times 3 is an even number. 2) if 6 is less than 7, then 4 is greater than 7. 3) six is divisible by 3, and 10 is a multiple of 2. 4) the average of the data is greater than the largest value in the data, or it’s less than the largest value in the data. 5) the slope of a linear graph is its rate of change, and the graph’s y-intercept is the initial value. 6) if an equilateral triangle has equal angles, then all its angles will measure 45°.

Which of these tables represents a non-linear function?