Question

How do you solve for h in \[P = mgh\]?

Answer 1

Hint: : The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. The given equation is a linear equation we are asked to solve for h in \[P = mgh\] and to solve this equation, combine all the terms and then simplify the terms to get the value for h.

Complete step by step solution:
The given equation is
\[P = mgh\]
To solve for h, divide both sides by mg giving:
\[\dfrac{P}{{mg}} = \dfrac{{mgh}}{{mg}}\]
Let us simplify the terms,
\[\dfrac{P}{{mg}} = \dfrac{m}{m} \times \dfrac{g}{g} \times h\]
Here, \[\dfrac{m}{m}\] and \[\dfrac{g}{g}\] implies one.
Hence, we get
\[\dfrac{P}{{mg}} = 1 \times 1 \times h\]
\[ \Rightarrow \]\[\dfrac{P}{{mg}} = h\]
\[ \Rightarrow \]\[h = \dfrac{P}{{mg}}\]

Additional information: Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time.

Solving simultaneous equations by Substitution: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved.

Note: The key point to solve this type of equation is to combine all the like terms and evaluate for the variable asked and combine all the like terms i.e., finding out the common term and evaluate for the variable asked. Equations that have more than one unknown can have an infinite number of solutions, finding the values of letters within two or more equations are called simultaneous equations because the equations are solved at the same time.