VARIATION
DIRECT VARIATION: y/x = k or(y = kx )
Examples;
Express as an equation.
1. s varies directly as t ^^..,.T.TT
2. j is proportional to d
3. r is directly proportional to w2
Read "y varies direcHy as x" or
*y is directly proportional to x" or
"y is proportional to x."
k is colled the constant of variation
and k cannot equal 0,
_
4, Suppose m varies directly as z. If m = 10 when z = 3, find m when z = 5..
5. Suppose q varies directly as y2. If q = 9 when y = 2, find y when q - 15. _
INVERSE VARIATION: ( y - k/x ) or y • X =
fe
Read "y varies inversely as x* or
*y is inversely proportional to x.*
Examples:
Express as an equation.
1. p varies inversely as z
2. n is inversely proportional to c3
3. Suppose b is inversely proportional to d. If b = 12 when d = 5, find b when d = 7..
4. Suppose e varies inversely as uz\ If e = 13 when u = 8, find u when e = 6. ______
JOINT VARIATION: / y = kxzftar k = y/xz
( y = kx/z\or k = yz/x
Examples:
^-~__/
Express as an equation.
1. w varies jointly as c and d.
2. r varies directly as s and inversely as g2 and m
Read "y varies jointly as x and z.*
Read "y varies directly as x and inversely as z."
•3. Suppose-p varies ^irzcKy as the square of z and inversely as r. If p ="3275 when 2 = 4 and r- 10,
find p when z = 2 and r = 16. __„._
VARIATION PROBLEMS
Express each of the following statements as an equation.
1. A varies directly as b
2. M is proportional to n
3. X is inversely proportional to y
4. P varies inversely as y
5. ft varies jointly as s and t
6. R is proportional to m and p
7. W is proportional to x2 and inversely proportional to y
8. C varies directly as d and inversely as fz and g
Solve each of the following problems,
9. If m varies directly as x and y, and m = 10 when x = 4 and y = 7, find m when x = 11 and y = 8.
10. Suppose m varies directly as z and p. If m = 10 when z = 3 and p = 5, find m when 2 = 5 and p = 7.
11. Suppose r varies directly as the souare of m and inversely as s. If r = 12 when m = 6 and s = 4,
find r when m = 4 and s = 10.
12. Let a be proportional to m and nz, and inversely proportional to y3. If a = 9 when m = 4, n = 9, and
y = 3, find a if m = 6, n = 2, and y = 5.
13. If y varies directly as x, and inversely as m2 and r2, and y = 5/3 when x = 1, m = 2, and r = 3, find
yif x = 3, m = 1, andr = 8.