Cumulative Problems SECTION 3.1 X 5Y 2 34) 4 Z 3 SECTION 3.2 60) Science and medicine. Archimedes estimated the universe to be 2.3 _ 1019 millimeters (mm) in diameter. If this number were written in standard or decimal form, how many 0s would follow SECTION 3.3 28) 9a 2 5a from 11a 2 10a SECTION 3.4 32) s 12s 8 SECTION 3.5 40) 3 x x 2 2 SECTION 3.6 2 x 4 y 4 z 4 3x 3 y 3 z 3 xy 2 z 3 20) xy 2 z 3 SECTION 4.1 18) 18 x 3 y 2 z 3 , 27 x 4 y 2 z 3 , 81x y 2 z SECTION 4.2 32) t 2 4t 60 SECTION 4.3 56) 2 y3 y 2 3y SECTION 4.4 52) x 2 8 x 16 SECTION 4.5 18) 2 p 4 3 p 3 q 2 p 3 q 3 p 2 q 2 SECTION 4.6 38) x 2 11x 24 SECTION 4.7 34) 12x 1 17x 1 6 2 SECTION 4.8 50) Business and finance. The relationship between the number of calculators x that a company can sell per month and the price of each calculator p is given by x _ 1700 _ 100p. Find the price at which a calculator should be sold to produce a monthly revenue of $7000. (Hint: Revenue _ xp.) SECTION 5.1 14 x 2 y 20) 21xy 4 SECTION 5.2 24) 3 x 15 4 x x 2 3x 5 x SECTION 5.3 18) 11 4 x7 x7 SECTION 5.4 52) 7a 4 a a 12 a 4 2 SECTION 5.5 26) x 3 x 1 6 4 4 SECTION 5.6 28) Science and medicine. How many centiliters (cL) of pure acid must be added to 200 cL of a 40% acid solution to produce a 50% solution? SECTION 5.7 a 2 b 16) 2 a 4 b2 SECTION 9.1 256 25 14) SECTION 9.2 7a 2 16) SECTION 9.3 20 2 5 5 34) SECTION 9.4 38) a 4 a 4 SECTION 9.5 18) 2 x 3x 2 8 SECTION 9.6 10) Geometry. Find the length of a rectangle whose diagonal is 9 in. and whose width is 6 in. SECTION 10.1 20) 16 x 2 3 SECTION 10.2 24) x 2 2 x 1 SECTION 10.3 12) x 2 5 x 2 0 SECTION 10.4 32) y x 2 5x 4 SECTION 10.5 16) Geometry. The sum of the lengths of one side of a right triangle and the hypotenuse is 20 cm. The other leg is 5 cm shorter than the hypotenuse. Find the length of each side.