Let d be the smaller cap cut from a solid ball of radius 2 units by a plane 1 unit from the center of the sphere. express the volume of d as an iterated triple integral in (a) spherical, (b) cylindrical, and (c) rectangular coordinates.
in each case, let the center of the solid ball be the origin and let the plane be z=1. then (d) find the volume by evaluating one of the three triple integrals.

The average number of vehicles waiting in line to enter a parking lot can be modeled by the function f left parenthesis x right x squared over 2 left parenthesis 1 minus x right parenthesis endfraction , where x is a number between 0 and 1 known as the traffic intensity. find the rate of change of the number of vehicles waiting with respect to the traffic intensity for the intensities (a) xequals0.3 and (b) xequals0.6.

Parabolas y=−2x^2 and y=2x^2 +k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.

15 and 14.7 are 1 apart, so 15 – 14.7 must be 1.