Many situations are more complicated than a basic direct variation or inverse variation model. One variable often depends on multiple other variables. When a variable is dependent on the product or quotient of two or more variables, this is called
joint variation . For example, the cost of busing students for each school trip varies with the number of students attending and the distance from the school. The variable
cost, varies jointly with the number of students,
and the distance,
Joint variation
Joint variation occurs when a variable varies directly or inversely with multiple variables.
For instance, if
varies directly with both
and
we have
If
varies directly with
and inversely with
we have
Notice that we only use one constant in a joint variation equation.
Solving problems involving joint variation
A quantity
varies directly with the square of
and inversely with the cube root of
If
when
and
find
when
and
Begin by writing an equation to show the relationship between the variables.
Substitute
and
to find the value of the constant
Now we can substitute the value of the constant into the equation for the relationship.
To find
when
and
we will substitute values for
and
into our equation.
For the following exercises, write an equation describing the relationship of the given variables.
Questions & Answers
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?