Solving for variables

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In summary, solving for variables means finding unknown values in an equation or expression by manipulating it or using mathematical operations. It is important in science as it helps us understand relationships between variables and make accurate calculations. Common techniques include using the order of operations, substitution, and elimination. To solve for variables, a good understanding of algebraic concepts is necessary. This skill is also applicable to other fields such as engineering, economics, and statistics.
  • #1
zekester
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i have an equation ((r^2)*(-i/(w*c)))+(r/(w*c))
divided by (r^2) + (1/(wc)^2)
equals -951 - (i*13026)

where i is the square root of negative one and w is known. How do I get two equations to solve for both c and r.
 
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  • #2
Assuming "r" and "c" to be real numbers, equate the real parts in your equation, and the imaginary parts in your equation:
[tex]\frac{\frac{r}{wc}}{r^{2}+\frac{1}{(wc)^{2}}}=-951[/tex]
And:
[tex]-\frac{\frac{r^{2}}{wc}}{r^{2}+\frac{1}{(wc)^{2}}}=-13026[/tex]
 
  • #3


To solve for both c and r, you can use the following steps:

1. Multiply both sides of the equation by the denominator (r^2 + (1/(wc)^2)) to get rid of the fraction on the left side.

2. Simplify the left side by using the distributive property. This will give you a new equation with only c and r variables.

3. To get two equations, you can substitute different values for r and c in the new equation. For example, you can substitute r=0 and solve for c, then substitute c=0 and solve for r. This will give you two equations with one variable each.

4. Once you have the two equations, you can solve them simultaneously using algebraic methods such as substitution or elimination.

Alternatively, you can also use a system of equations solver or a graphing calculator to solve for both c and r simultaneously.
 

What does it mean to solve for variables?

Solving for variables means finding the unknown values in an equation or expression. This involves manipulating the equation or using mathematical operations to isolate the variable on one side of the equation.

Why is solving for variables important in science?

Solving for variables is important in science because it allows us to understand and predict relationships between different variables. It also helps us to make accurate calculations and draw conclusions from data.

What are some common techniques used to solve for variables?

Some common techniques used to solve for variables include using the order of operations, substitution, and elimination. These techniques involve manipulating equations and using mathematical rules to isolate the variable.

What do we need to know in order to solve for variables?

In order to solve for variables, we need to have a good understanding of algebraic concepts such as equations, expressions, and mathematical operations. It is also important to be able to apply these concepts to real-world problems.

Can solving for variables be applied to other fields besides science?

Yes, solving for variables is a fundamental concept in mathematics and can be applied to various fields such as engineering, economics, and statistics. It is a valuable skill that can be used in problem-solving and decision making in many different areas.

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