Algebra 1 : How to find direct variation
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Example Questions
Example Question #5 :其他的数学关系
If an object is hung on a spring, the elongation of the spring varies directly as the mass of the object. A 20 kg object increases the length of a spring by exactly 7.2 cm. To the nearest tenth of a centimeter, by how much does a 32 kg object increase the length of the same spring?
Let
We can find
so
In the second situation, we set
which rounds to 11.5 centimeters.
Example Question #1 :Variable Relationships
None of these answers are correct.
If
If
or
Divide by 5 to get
If
Example Question #1 :How To Find Direct Variation
If an object is hung on a spring, the elongation of the spring varies directly with the mass of the object. A 33 kilogram object increases the length of a spring by exactly 6.6 centimeters. To the nearest tenth of a kilogram, how much mass must an object posess to increase the length of that same spring by exactly 10 centimeters?
Let
We can find
Therefore
Set
Example Question #2 :How To Find Direct Variation
If
The general formula for direct proportionality is
where
Solve for
So
Example Question #1 :How To Find Direct Variation
The amount of money you earn is directly proportional to the nunber of hours you worked. On the first day, you earned $32 by working 4 hours. On the second day, how many hours do you need to work to earn $48.
The general formula for direct proportionality is
where
Before we can figure out how many hours you need to work to earn $48, we need to find the value of
Solve for
So
Plug in $48.
Divide both sides by 8
So you will need to work 6 hours to earn $48.
Example Question #4 :How To Find Direct Variation
The volume of a fixed mass of gas varies inversely as the atmospheric pressure, as measured in millibars, acting on it, and directly as the temperature, as measured in kelvins, acting on it.
A balloon is filled to a capacity of exactly 100 cubic meters at a time at which the temperature is 310 kelvins and the atmospheric pressure is 1,020 millibars. The balloon is released, and an hour later, the balloon is subject to a pressure of 900 millibars and a temperature of 290 kelvins. To the nearest cubic meter, what is the new volume of the balloon?
If
To calculate
The variation equation is
so substitute
Example Question #8 :Equations
The monthly cost to insure your cars varies directly with the number of cars you own. Right now, you are paying $420 per month to insure 3 cars, but you plan to get 2 more cars, so that you will own 5 cars. How much does it cost to insure 5 cars monthly?
The statement, 'The monthly costly to insure your cars varies directly with the number of cars you own' can be mathematically expressed as
Given that it costs $420 a month to insure 3 cars, we can find the k-value.
Divide both sides by 3.
Now, we have the mathematical relationship.
Finding how much it costs to insure 5 cars can be found by substituting 5 for C and solving for M.
Example Question #5 :How To Find Direct Variation
Does the equation below represent a direct variation? If it does, find the constant of variation.
Yes,
Yes,
No,
Yes,
No,
Yes,
Direct Variation is a relationship that can be represented by a function in the form
The equation is in the form
The constant of variation or
Therefore, the answer is,
Yes it is a direct variation,
Example Question #6 :How To Find Direct Variation
Suppose
The general formula for direct proportionality is
where
Solving for
Example Question #7 :How To Find Direct Variation
餐饮公司的成本变化直接智慧h the number of people attending. If the cost is $100 when 20 people attend the party, find the constant of variation.
Because the cost varies directly with the number of people attending, we have the equation
Where
We solve for
And by dividing by 20 on both sides
Yields
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