4x= y
y = 10x
a varies directly as b and a = 12 when b = 4. What is the constant of variation?
y = 3x y = 3*19 = 57
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If P varies directly with the square of Q then the equation would be in the form of P = kQ2, where k is the constant of variation so the new equation would be: P = 6Q2, so when Q = 12 we have P=6*122, or P = 864
Find an equation of variation where y varies directly as x. One pair of values is y = 80 when x = 40
y = 10x
a varies directly as b and a = 12 when b = 4. What is the constant of variation?
57
40
y = -5
y = 8
Since ( y ) varies directly as ( x ), we can express this relationship as ( y = kx ), where ( k ) is the constant of variation. Given the values ( y = 80 ) when ( x = 40 ), we can find ( k ) by substituting these values into the equation: ( 80 = k(40) ). Solving for ( k ) gives ( k = 2 ). Therefore, the equation of variation is ( y = 2x ).
direct variation: y = kx y = kx k = y/x = 0.8/0.4 = 2
y = 3x y = 3*19 = 57
y = kx: 10 = 37k so k = 10/37 and y = 10x/37
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