Precalculus Review

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Exercise \(\PageIndex{1}\)

Write down an equation of a line passing through the points \((1,2)\) and \((3,5)\).

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Exercise \(\PageIndex{2}\)

For what value(s) of \(m\) is \(x^{3}+6x^{2}-m\) divisible by \((x+4)\).

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Exercise \(\PageIndex{3}\)

The expression \(\displaystyle\frac{\left(1/x+1/y\right) } {x+y}\) is equal to

\(1\)
\(1/(xy)\)
\(xy/(x+y)^{2}\)
\(x+y\)
\(1/(x+y)^{2}\)

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Exercise \(\PageIndex{4}\)

Solve the following quadratic equation for \(m\), where \[m^2-5m=-6\]

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Exercise \(\PageIndex{5}\)

Simplify \(\displaystyle {\left( {xy \over y^{-3}z^{-1}} \right)^{-1}}\).

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Exercise \(\PageIndex{6}\)

If \(\displaystyle{f(x)={1-x \over 1+x}}\), find \(\displaystyle{f \left( {-1 \over x} \right)}\)

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Exercise \(\PageIndex{7}\)

A hollow cylinder has height \(10{\rm cm}\) and radius \(5{\rm cm}\).
Another cylinder has height \(10{\rm cm}\) and radius \(4{\rm cm}\). The
smaller cylinder is inserted into the larger one. How much space is left
inside the larger cylinder but outside the smaller one (in \({\rm cm}^{3}\))

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Exercise \(\PageIndex{8}\)

An equation for a line parallel to the line \(5x-y=2\) is

\(5y-x=1\),
\(5x+y=0\),
\(x+5y=3\)
\(y-5x=2\)

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Exercise \(\PageIndex{9}\)

Find \(x\) if \(\displaystyle{ -4 = {2x+3 \over 1-x}}\).

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Exercise \(\PageIndex{10}\)

Write down an equation of a line passing through the point \((1,3)\) and with the slope \(m=-1/2\)'

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Exercise \(\PageIndex{11}\)

Express the function in piecewise form without using absolute values \(F(x)=3|x+2|-2|x-1|\).

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Exercise \(\PageIndex{12}\)

In a general triangle \(ABC\), the angle at \(A\) is \(30^{\circ}\),
the length of \(AB\) is \(6\), and the length of \(AC\) is \(4\). Find the length
of \(CE\). (\(E\) is the point on \(AB\) closest to \(C\).)

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Exercise \(\PageIndex{13}\)

Suppose \(\log(a)=2\), \(\log(b)=3\) and \(\log(c)=5\). Find \(\displaystyle{ \log \left( {c \over ab} \right)}\).

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Exercise \(\PageIndex{14}\)

A rectangular field is bounded by a fence \(500{\rm m}\) long. The field is \(150{\rm m}\) longer than it is wide. Find the area of the field (in \({\rm m}^{2}\))

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