Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. s = (1/2)gt^2, for t

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This includes operations such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. Understanding how to manipulate equations is crucial for solving for a variable, as it allows you to express one variable in terms of others.

Quadratic Equations

The equation s = (1/2)gt^2 is a quadratic equation in terms of t, where t is squared. Quadratic equations typically take the form ax^2 + bx + c = 0 and can be solved using various methods, including factoring, completing the square, or using the quadratic formula. Recognizing the structure of quadratic equations is essential for finding solutions.

Isolating Variables

Isolating a variable means rearranging an equation so that the variable of interest is on one side of the equation by itself. In the context of the given equation, this involves manipulating the equation to express t in terms of s and g. This concept is fundamental in algebra as it allows for solving equations and understanding relationships between variables.