12-7 Combined and joint variation Find an equation of joint variation ...
12-7 Combined and joint variation Find an equation of joint variation ...
12-7 Combined and joint variation Find an equation of joint variation ...
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<strong>12</strong>-7 <strong>Combined</strong> <strong><strong>an</strong>d</strong> <strong>joint</strong> <strong>variation</strong><strong>Find</strong> <strong>an</strong> <strong>equation</strong> <strong>of</strong> <strong>joint</strong> <strong>variation</strong>. Then solve for the missing value.1. R varies directly as S <strong><strong>an</strong>d</strong> T. One set <strong>of</strong> values is R =28, S =7, <strong><strong>an</strong>d</strong> T =8. <strong>Find</strong> R whenS =<strong>12</strong> <strong><strong>an</strong>d</strong> T =9.2. M varies <strong>joint</strong>ly as N <strong><strong>an</strong>d</strong> P. One set <strong>of</strong> value is M =86.4, N =9, P =<strong>12</strong>. <strong>Find</strong> Mwhen N =20 <strong><strong>an</strong>d</strong> P =6.53. Q varies <strong>joint</strong>ly as R <strong><strong>an</strong>d</strong> S. One set <strong>of</strong> values is Q =2.4, R =0.6, <strong><strong>an</strong>d</strong> S =0.8. <strong>Find</strong> Qwhen R =1.6 <strong><strong>an</strong>d</strong> S =0.14. A varies <strong>joint</strong>ly as B <strong><strong>an</strong>d</strong> C. One set <strong>of</strong> values is A =1, B =5, C =0.2. <strong>Find</strong> A whenB =2.4 <strong><strong>an</strong>d</strong> C =0.015. X varies <strong>joint</strong>ly as W, Y, <strong><strong>an</strong>d</strong> Z. One set <strong>of</strong> values is X =18, W= 2, Y =6 <strong><strong>an</strong>d</strong> Z=5.<strong>Find</strong> X when W =5, Y= <strong>12</strong>, <strong><strong>an</strong>d</strong> Z =3<strong>Find</strong> <strong>an</strong> <strong>equation</strong> <strong>of</strong> combined <strong>variation</strong>. Then solve for the missing value.6. A varies directly as B <strong><strong>an</strong>d</strong> inversely as C. One set <strong>of</strong> values is A =14, <strong><strong>an</strong>d</strong> B =7, <strong><strong>an</strong>d</strong> C=3. <strong>Find</strong> A when B =4 <strong><strong>an</strong>d</strong> C =87. M varies directly as N <strong><strong>an</strong>d</strong> inversely as P. One set <strong>of</strong> values is M =5, N = 2, <strong><strong>an</strong>d</strong> P= 4.<strong>Find</strong> M when N= 10 <strong><strong>an</strong>d</strong> P= 508. W varies directly as X <strong><strong>an</strong>d</strong> inversely as Y. One set <strong>of</strong> values is W =3, X =9 <strong><strong>an</strong>d</strong> Y=2.<strong>Find</strong> W when X =15 <strong><strong>an</strong>d</strong> Y = 59. P varies directly as Q <strong><strong>an</strong>d</strong> inversely as R. One set <strong>of</strong> values is P =0.8 <strong><strong>an</strong>d</strong> Q = 8 <strong><strong>an</strong>d</strong> R=7. <strong>Find</strong> P when Q =<strong>12</strong> <strong><strong>an</strong>d</strong> R =310. U varies directly as V <strong><strong>an</strong>d</strong> inversely as W. One set <strong>of</strong> values is U =5.75, V =2.3<strong><strong>an</strong>d</strong> W =0.6. <strong>Find</strong> U when V =0.5 <strong><strong>an</strong>d</strong> W =0.8
1. R varies directly as S <strong><strong>an</strong>d</strong> T. One set <strong>of</strong> values is R =28, S =7, <strong><strong>an</strong>d</strong> T =8. <strong>Find</strong> Rwhen S =<strong>12</strong> <strong><strong>an</strong>d</strong> T =9.28= 7 x 8 x K28=56k28/56=56k/56R=1/2 STR=1/2 x <strong>12</strong> x 9R= ½ x 108R= 542. M varies <strong>joint</strong>ly as N <strong><strong>an</strong>d</strong> P. One set <strong>of</strong> value is M =86.4, N =9, P =<strong>12</strong>. <strong>Find</strong> Mwhen N =20 <strong><strong>an</strong>d</strong> P =6.586.4= 9 x <strong>12</strong> x K86.4= 108k86.4/108= 108k/108M= 3.6/4 NPM=3.6/4 x 20 x 6.5M= 3.6/4 x 130M = 1173. Q varies <strong>joint</strong>ly as R <strong><strong>an</strong>d</strong> S. One set <strong>of</strong> values is Q =2.4, R =0.6, <strong><strong>an</strong>d</strong> S =0.8. <strong>Find</strong>Q when R =1.6 <strong><strong>an</strong>d</strong> S =0.<strong>12</strong>.4=0.6 x 0.8 x K2.4=0.48K2.4/0.48=0.48k/0.48Q=5 RSQ= 5 x 1.6 x 0.1Q=0.84. A varies <strong>joint</strong>ly as B <strong><strong>an</strong>d</strong> C. One set <strong>of</strong> values is A =1, B =5, C =0.2. <strong>Find</strong> A whenB =2.4 <strong><strong>an</strong>d</strong> C =0.011= 5 x 0.2 x K1= 1KA= 1 BCA= 1 x 2.4 x 0.01A= 0.0245. X varies <strong>joint</strong>ly as W, Y, <strong><strong>an</strong>d</strong> Z. One set <strong>of</strong> values is X =18, W= 2, Y =6 <strong><strong>an</strong>d</strong> Z=5.<strong>Find</strong> X when W =5, Y= <strong>12</strong>, <strong><strong>an</strong>d</strong> Z =318=2 x 6 x 5 x K18= 60K18/60= 60K/60X= 3/10X= 3/10 x 5 x <strong>12</strong>x 3X=54
6. A varies directly as B <strong><strong>an</strong>d</strong> inversely as C. One set <strong>of</strong> values is A =14, <strong><strong>an</strong>d</strong> B =7,<strong><strong>an</strong>d</strong> C =3. <strong>Find</strong> A when B =4 <strong><strong>an</strong>d</strong> C =814= K7/314= K x 7/3A= 6 B/CA= 4x6/8A=24/8A=37. M varies directly as N <strong><strong>an</strong>d</strong> inversely as P. One set <strong>of</strong> values is M =5, N = 2, <strong><strong>an</strong>d</strong>P= 4. <strong>Find</strong> M when N= 10 <strong><strong>an</strong>d</strong> P= 505= 2/4 x KM= 10N/PM=10 x 10/50M=100/50M= 28. W varies directly as X <strong><strong>an</strong>d</strong> inversely as Y. One set <strong>of</strong> values is W =3, X =9 <strong><strong>an</strong>d</strong>Y=2. <strong>Find</strong> W when X =15 <strong><strong>an</strong>d</strong> Y = 53=9/2W=2 X/ YW= 2 x 15/ 5W= 30/ 5W= 69. P varies directly as Q <strong><strong>an</strong>d</strong> inversely as R. One set <strong>of</strong> values is P =0.8 <strong><strong>an</strong>d</strong> Q = 8<strong><strong>an</strong>d</strong> R =7. <strong>Find</strong> P when Q =<strong>12</strong> <strong><strong>an</strong>d</strong> R =30.8= 8/7P=0.7 Q/RP=0.7 x <strong>12</strong>/ 3P= 2 <strong>12</strong>/1510. U varies directly as V <strong><strong>an</strong>d</strong> inversely as W. One set <strong>of</strong> values is U =5.75, V =2.3<strong><strong>an</strong>d</strong> W =0.6. <strong>Find</strong> U when V =0.5 <strong><strong>an</strong>d</strong> W =0.85.75= 2.3/0.6
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