An online direct variation calculator is programmed to determine the consonant of variation, equation of the variation, and relationship among variables involved. Let’s go through the contextual reading of the topic for a proper knowledge about it.
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What Is Variation?
In mathematics:
“Any deviation among two variables x and y is termed the variation”
Equation:
$$ y = kx $$
Where:
Y = Dependent Variable
X = Independent Variable
k = Variation Constant
Types Of Variation:
Generally, there exist two main types of the variation.
Direct Variation:
Direct relationship exists only when deviation in one variable causes the same amount of deviation in the other respective variable. In a direct variation:
- If x increases, y also increases
- If x decreases, y gets decreased as well
Further Cases:
Here we will be discussing further cases that arise in case of direct relationship among quantities.
Y Varies Directly With X:
$$ y = kx $$
Y Varies As The Square Of X:
$$ y = kx^{2} $$
Y Varies Directly As Cube Of X:
$$ y = kx^{3} $$
Y Varies Directly As Square Root Of X:
$$ y = \frac{k}{\sqrt{x}} $$
The free direct variation calculator also solves all these cases and represents the final equation on your screen.
Inverse Variation:
Inverse variation represents the relationship among two variables in which change in one variable causes the change in other variable too, but in the opposite direction.
In inverse relationship:
- If x increases, y gets decreased
- If in case the value of x is decreased, the corresponding value of the y is increased
Further Cases:
Like that of the direct relationship, inverse variation also exhibits the following cases:
Y Varies Inversely As X:
$$ y = k\frac{1}{x} $$
Y Varies Inversely As The Square Of X:
$$ y = k\frac{1}{x^{2}} $$
Y Varies Inversely As The Cube Of X:
$$ y = k \frac{1}{x^{3}} $$
Y Varies Inversely As The Square Root Of x:
y$$ y = \sqrt{kx} $$
In case you find it difficult to resolve these cases, try using the inverse variation calculator for free.
Constant Of Variation:
The subsequent k is known as the proportionality constant for the variation. It shows the ratio of the two variables involved in the examination.
Mathematically:
$$ \text{Constant Of Variation} = \frac{y}{x} $$
$$ k = \frac{y}{x} $$
This constant represents an unchanged relation among quantities and can be easily determined by using a constant of variation calculator.
How To Determine The Variance Equation?
Example # 01:
Y varies directly as the square of x: where:
$$ y = 100 $$
$$ X = 4 $$
Solve for Y when X = 6.
Solution:
Here we will apply the following case:
Y varies as the square of X:
$$ y = kx^{2} $$
Putting the values of x and y in the above equation:
$$ 100 = k4^{2} $$
$$ 100 = k16 $$
$$ k = \frac{100}{16} $$
$$ k = \frac{100}{16} $$
$$ k = \frac{25}{4} $$
So the constant of proportionality becomes:
$$ k = 6.25 $$
Now we have the variation equation as follows:
$$ y = kx^{2} $$
$$ y = 6.25x^{2} $$
$$ y = 6.25 * 6^{2} $$
$$ y = 225 $$
As this is a direct relationship, you can also put the values in a direct variation calculator to find accurate results in seconds.
Example # 02:
Y varies inversely as the square root of x: where:
$$ Y = 24 $$ and
$$ X = 2 $$
Resolve for the value of Y if the value of X gets increased and becomes 8.
Solution:
Here we have:
Y varies inversely as the square root of x:
$$ y = \frac{k}{\sqrt{x}} $$
$$ 24 = \frac{k}{\sqrt{2}} $$
$$ 24 = \frac{k}{1.414} $$
$$ k = 24 * 1.414 $$
$$ k = 33.936 $$
The equation of variance becomes:
$$ y = \frac{33.936}{\sqrt{8}} $$
$$ y = \frac{33.936}{2.828} $$
$$ y = 12 $$
Also, the direct variation equation calculator goes for generating the more precise outcomes in a short span of seconds
Example # 03:
Determine the constant of variation k when;
$$ Y = 6 $$
$$ x = 2 $$
Solution:
$$ k = \frac{y}{x} $$
$$ k = \frac{6}{2} $$
$$ k = 3 $$
Here the constant variation calculator provides you another edge of swift computations in a couple of simple steps that you need to follow.
How Direct And Inverse Variation Calculator Works?
Make a use of this free variation constant calculator to obtain absolute answers in a moment. Let us guide you how to use it.
Input:
- Make a selection of the variation relationship among variables from the drop down list
- After you do that, write down the value of y
- As well, write the value of x
- Tap the calculate button
Output:
The direct variation calculator determines:
- Constant of proportionality
- Equation of variation
- Step by step calculations
FAQ’s:
What do you mean by joint variation?
A particular situation in which a single variable depends upon two or more than two variables is known as the joint variation. In joint variation, any change in each of the independent variables causes a change in the dependent variable.
What is the formula of the combined variation?
The compound variation involves both direct and inverse variations as follows:
$$ \text{ Compound Variation} = Y = \frac{k\left(x\right)}{z} $$
What is partial variation?
In mathematics, if a certain variable is represented as a relation of sum of two variables, then it is known as the partial variation.
$$ X =kY + C $$
Conclusion:
Being a mathematician or engineer, you need to find various relationships among variables to generate answers. This is why this direct variation calculator has been programmed. So make a free use of this inverse variation equation calculator to attain accuracy in your calculations for sure.
References:
From the source of Wikipedia: Proportionality, Direct proportionality, Inverse proportionality
From the source of VarsitTutors: Combined Variation
