Question

Please help
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​

Answer 1

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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