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1. e varies jointly as f and g and e = 24 when f = 3 and g = 2
2. w is inversely proportional to the cube of x and w is 54 when x = 3
3. h is directly proportional to j and h = 12 when j = 8
4. a is jointly proportional with the square of x and the square root of y and a = 25 when x = 5 and y = 9
5. m is inversely proportional to n and m = 1.8 when n = 2.1
Answers
Given : 1. e varies jointly as f and g and e = 24 when f = 3 and g = 2
2. w is inversely proportional to the cube of x and w is 54 when x = 3
3. h is directly proportional to j and h = 12 when j = 8
4. a is jointly proportional with the square of x and the square root of y and a = 25 when x = 5 and y = 9
5. m is inversely proportional to n and m = 1.8 when n = 2.1
To Find : Equations
Solution
Direct variation if a variable increases then other variable also increases with a constant factor y = kx
inverse variation if a variable increases then other variable decreases with a constant factor xy = k
Joint variation is a relationship between atleast three variables, where one variable varies directly with all other variables.
y = kxz
Combined Variation is a relationship between three or more variables where it is in direct variation with few variable and in inverse variation with other variable y = kx/z
1. e varies jointly as f and g and e = 24 when f = 3 and g = 2
=> e ∝ fg
=> e = kfg
24 = k (3)(2)
=> k = 4
=> e = 4fg
2. w is inversely proportional to the cube of x and w is 54 when x = 3
=> w ∝ 1/x³
=> w = k/x³
=> 54 = k/3³
=> k = 1458
=> w = 1458/x³
or wx³ = 1458
h is directly proportional to j and h = 12 when j = 8
=> h = 3j/2
a is jointly proportional with the square of x and the square root of y and
=> a = kx²√y
=> a = x²√y/3
. m is inversely proportional to n and m = 1.8 when n = 2.1
=> mn = k
=> mn = 3.78
or m = 3.78/n
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