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Math Topics

Intermediate Algebra

Rational Expressions, Equations, and Functions

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1
Basic Properties and Reducing to Lowest Terms

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2
Multiplication and Division of Rational Expressions

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3
Addition and Subtraction of Rational Expressions

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4
Complex Rational Expressions

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5
Rational Equations

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6
Applications

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7
Division of Polynomials

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8
Variation

The distance a skydiver falls is directly proportional to the square of the time he has been falling. If the skydiver falls \(64\) feet in the first \(2\) seconds.

How far will he have fallen after \(3.5\) seconds?

Graph the relationship between distance and time.

How long will it take him to fall \(256\) feet?

In electricity, the resistance of a cable is directly proportional to its length and inversely proportional to the square of the diameter. If a \(100\) foot cable \(0.5\) inch in diameter has a resistance of \(0.2\) ohm, what will the resistance of a cable made from the same material if it is \(200\) feet long with a diameter of \(0.25\) inch?

**Mini Lecture**

\(y\) varies directly as \(x\). If \(y=39\) when \(x=3\), find \(y\) when \(x\) is \(10\).

\(y\) varies inversely as the square of \(x\). If \(y=4\) when \(x=3\), find \(y\) when \(x\) is \(2\).

The power \(P\) is an electric circuit varies directly with the square of the current \(I\). If \(P=30\) when \(I=2\), find \(P\) when \(I=7\).