Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25 and z = 5. How do you write the equation that models the relationship?
Solution:
Two quantities as said to follow a direct variation if both increase or decrease by the same factor.
If y varies jointly with x and inversely with z
y ∝ x
y ∝ 1/z
So the equation is
y = k x/z where k is the constant of variation
According to the statement
If y varies jointly with x and w and inversely with z
y = k wx/z …. (1)
It is given that
y = 400 when w = 10, x = 25 and z = 5
400 = k (10) (25)/5
400 = 250k/5
400 = 50k
Dividing both sides by 50
8 = k
So we get
y = 8 wx/z
Therefore, y = 8 wx/z is the equation that models the relationship.
Suppose that y varies jointly with w and x and inversely with z and y = 400 when w = 10, x = 25 and z = 5. How do you write the equation that models the relationship?
Summary:
Suppose that y varies jointly with w and x and inversely with z and y=400 when w=10, x=25 and z=5. y = 8 wx/z is the equation that models the relationship.
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