MATH 0310
NAME (Print)__________________________
Worksheet 10.7, 11.1
DATE___________________
(Section 10.7) Set up each variation:
1. p varies directly as the square of q
2. y varies inversely as the cube root of q
3. b varies jointly as c cubed and d
4. y varies directly as x; if y = 2 when x = 6, find k and the direct variation equation.
k=_____;
5. y varies directly as x 4 and inversely as the square root of z
6. At sea, the distance to the horizon is directly proportional to the square root of the elevation of the
observer. If a person who is 36 feet above the water can see 7.4 miles, find how far a person 64 feet
above the water can see. Round your answer to the nearest tenth of a mile.
7. Because it is more efficient to produce large quantities of items, the cost of producing a certain
computer DVD is inversely proportional to the number produced. If 4000 can be produced at a cost of
$1.20 each, find the cost per DVD when 6000 are produced.
8. The number of cars manufactured on an assembly line at a Toyota plant varies jointly as the number of
workers and the time they work. If 200 workers can produce 60 cars in 2 hours, find how many cars 240
workers should be able to make in 3 hours.
(Section 11.1) Simplify each radical. Assume all variables represent positive real numbers.
1.
4.
7.
81
 4 16 p16
3
64x15
2.
3
5.
3
15 3
a b
3.
27
6.
100a 2
49
144
Approximate using a calculator. Round answer to one decimal place.
8.
27 = _______________
Choose the correct letter(s). A problem may have more than one correct answer.
_______9.
Which radical(s) is not a real number?
a.
c.
2
3
 12
b.  13
d.
 12
_______10.
a.
c.
Which radical(s) simplify to 2?
4
3
8
b.   4
d.
Matching. From the above examples, the following general conclusions can be reached.
11.
even
negative number  ___________
a. a positive real number
b. a negative real number
12.
odd
negative number  ___________
c. not a real number
3
8