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Advanced Algebra
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Brinkman
TAl DIRTY -TAIRTY ON DIRI(T AND INYIR!I YARIATION
In 1 - 4, write an expression for the variation problem.
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1. Y varies directly as the cube of x. ~ ~
ll- '{..3
2. Y varies inversely as the square of x. ~::;
0.. 3.
Y varies directly as the fourth power of)(.
4. Y varies inversely as the fifth power of X.
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In 5 - 8, use 1 - 4 to answer.
3 5.
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6. In 2, if Y = 20 and x = 1.4, what is the constant of variation?
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3 \.1-'5 ~ \& (1.5)3
In 1, if x = 2.5 and y = 31.25, what is the constant of variation?
7. In3,if)t=1.1
VJ
andy=146.41,whatistheconstantofvariation?
8. In 4, if X = 0.9 and y = 16.9351, what is the constant of variation?
=
db
r 11.ln
3x2, find the rate of change between x
(-2 \2-- )L- \
=
-2 and x
16,
=
(2)~ ) ( tfJ Lf)
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2X2
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m
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12.ln y = - ~~,
find the rate of change between x = 1 and x = 4'_\15"
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yY) ~
=
t¥~t6Dl
find the rate of change between x = 2 and x = 4.
x
~ 13.ln y
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y =
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m:; 3.. @
~ 9. In y = 3x2, find the rate of change between x = 1 and x = 2.
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10.ln y
1-
-e- ~
X
rrl
-=3 ~kJ
when x is tripled, how does the value of y change?
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14. M varies directly as the fourth power of q. How does m change if q is quadrupled?
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\115. p varies
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IS,
A
inversely as the fift power
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n. How does p change if n is multiplied by ~ ?
16. s varies directly as the cube of t. How does s change if t is multiplied by 7?
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YY1V{ l-hplrcd 0.j 34-3
17. Y varies inversely as the fourth power of w. How does y change if w is multiplied by ~?
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dJ'yfulul lo~
if
3
18. a varies in~rSelY as the square of b. How does a change if b is multiplied by (-4)?
ct~~
div1d1cl ~
10
~19. m varies directly as the seventh power of n. How does m change if n is multiplied by ~ ?
m\1l·hplJcui ioy ~
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2
20. Y varies inversely as the cube of x. If Y = 5 when x = 2~
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when x = 6.
~ 21. Y varies inversely as the fourth power of x. If Y = 5 when x =~, fi~d
hen x = ~.
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22. Y varies directly as x. If y = 8 when x = -3, find y w en x = 16.
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~ 23. c is directly proportional to ti", If c = -13,824 when d = 12, find c when d = ~~
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In 24 - 30, use the following
if ¥24.
Which graplt)have
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~25. ~ k
y = kx
eqUations:.
asymptotes?
y
ill
I
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lj-;: ~!)(~
-
,
'$¥ 26. Whi~h gr~plt)a1e
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I
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,,-
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w28. Nfle'A k I
-V 29. Which
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L ~~j~p
L0h£;n ~
qA' JmJ..
4
0, whicl'l ~raf'3lls are contaiAeEHA the ~
tI:tim ~uadran{? ~i
&U) 0'l~/y,
~30. Which grapt($)contain the origin?
j ~~ ~'ly~V
= x and y =
-x?
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0
~
ch ,~~. ~~) ~vt7
C\ VV\~ __()t
graptt)have symmetry to the lines y
~~~
~
<
. . .
(s)
0+ ~:/-O.
~
.fb
y= ~
t1)l4tr~
v1~
symmetric to the y-axis?
~~\C)(2'W2h\Nhca k >==6, wi lich Qraptt;are in th@first iiRd S€'..GioM Cl~a€lrelRt?
~
+y= ;
< Q \/tfflich grapl\S)have some poillts ill the third qUBdrBflt? wYvruh
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iff
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