How to find one value in terms of other variables?

In summary, the process for finding one value in terms of other variables is called solving an equation, which involves manipulating the equation using mathematical operations to isolate the desired variable and solve for its value. Any equation with at least one unknown variable can be solved to find its value in terms of other known variables, although some may require more advanced problem-solving techniques. Common mathematical operations used to solve equations include addition, subtraction, multiplication, division, and exponentiation. There are specific rules and guidelines, such as the order of operations and balancing method, that are commonly used when solving equations. To check the accuracy of solutions, one can substitute the found value back into the original equation or use estimation and approximation techniques.
  • #1
Eddie10
27
1

Homework Statement



I need to find q in terms of f and p.

Homework Equations


I am dealing with this equation at the moment:
1/p + 1/q = 1/f.

The Attempt at a Solution


I think I should isolate the q, so that I have the variables p and f on one side of the equals sign, and q on the other side of the equals sign.

Am I correct in thinking this?
 
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  • #2
Yes.
 
  • #3
My results:

1/q =(1/f) - (1/p)

1/q= (p-f)/(pf)

q= pf/(p-f)

Are they correct?
 
  • #4
Yes.
 
  • #5


Yes, you are correct. To find q in terms of f and p, you can rearrange the equation 1/p + 1/q = 1/f to isolate q on one side of the equals sign. This can be done by subtracting 1/p from both sides, which gives you 1/q = 1/f - 1/p. Then, you can take the reciprocal of both sides to get q = 1/(1/f - 1/p). This means that q is equal to the reciprocal of the difference between 1/f and 1/p. This is one way to express q in terms of f and p.
 

FAQ: How to find one value in terms of other variables?

What is the process for finding one value in terms of other variables?

The process for finding one value in terms of other variables is known as solving an equation. This involves manipulating the equation using mathematical operations to isolate the desired variable and solve for its value.

Can any equation be solved to find one value in terms of other variables?

Yes, any equation with at least one unknown variable can be solved to find the value of that variable in terms of other known variables. However, some equations may involve complex or advanced mathematical concepts and may require more advanced problem-solving techniques.

What are some common mathematical operations used to solve equations and find one value in terms of other variables?

Some common mathematical operations used to solve equations include addition, subtraction, multiplication, division, and exponentiation. These operations can be applied to both sides of an equation to manipulate and isolate the desired variable.

Are there any specific rules or guidelines for solving equations to find one value in terms of other variables?

Yes, there are several rules and guidelines that are commonly used when solving equations. These include the order of operations, which dictates the sequence in which mathematical operations should be performed, and the balancing method, which involves keeping both sides of an equation equal by performing the same operation on both sides.

What are some strategies for checking the accuracy of solutions when finding one value in terms of other variables?

One strategy for checking the accuracy of solutions is to substitute the found value back into the original equation and see if it satisfies the equation. Another strategy is to use estimation and approximation techniques to make sure the solution falls within a reasonable range of values.

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