A formula for approximating the stopping distance, d, in...

A formula for approximating the stopping distance, $d$, in feet, for a specific car on snow is $d=\frac{1}{6} x^{2}$, where $x$ is the speed of the car, in miles per hour, before the brakes are applied. If the car's stopping distance was 24 feet, what was the car's speed before the brakes were applied?

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Key Concepts

Quadratic Equations

A quadratic equation is an equation that involves the square of the unknown variable and has the general form ax² + bx + c = 0. Solving quadratic equations requires techniques that may include factoring, taking square roots, or applying the quadratic formula, which are fundamental methods in algebra.

Algebraic Manipulation

Algebraic manipulation entails rearranging equations using operations such as multiplication, division, addition, and subtraction to isolate a desired variable. This process is essential in solving equations and understanding the relationships between different variables.

Inverse Operations

Inverse operations are mathematical procedures that reverse the effect of an operation; for instance, taking the square root of a squared number is the inverse of squaring. These operations are crucial in solving equations, especially when undoing effects such as exponentiation to isolate a variable.

Mathematical Modeling

Mathematical modeling involves using mathematical expressions and equations to represent real-world phenomena. By establishing relationships between variables, such models allow us to predict or analyze behaviors in practical contexts, making them an essential component of applied mathematics.

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