Work in a group of at most 4. Explain to those who do not understand. Ask questions if you do not understand.
- (25 points)
- Write the equation of the line with slope 2 that passes through the point \((1,-7)\).
- Solve the equation \(|2x+1|=3\).
- Solve the inequality \(|x^2-9| \ge 6\).
- (15 points)
Given \(p(x) = x^3 +6x^2-9x-14\),
- Completely factor \(p(x)\), using the fact that \(p(2)=0\) to help you.
- Sketch a graph of \(p(x)\) and label the points where
the graph intersects the \(x\)-axis and the \(y\)-axis.
- (10 points)
Simplify \[\frac{5(x+h)+(x+h)^2-(5x+x^2)}{h} \,.\]
- (20 points)
- Solve the inequality \( e^{7x-8} \ge 2\) and express your answer in interval notation.
- Solve the equation \(\log_6(x+4)+\log_6(3-x)=1\) and express your answer in set notation.
- (15 points) Given that \(\csc(\theta) = 11\)
with \(\theta\) in the second quadrant, find the exact values
of all six trigonometric functions evaluated at \(\theta\):
- \(\sin(\theta)=\)
- \(\cos(\theta)=\)
- \(\sec(\theta)=\)
- \(\csc(\theta)=11\)
- \(\tan(\theta)=\)
- \(\cot(\theta)=\)
- (15 points) A superhero, standing on the
ground, launches 50 feet of wire from a grappling gun, held at
an angle of elevation of \(\pi/3\) radians. The grapple hits
and catches the top edge of the building.
- How tall is the building?
- How far from the base of the building is the superhero standing?
Last modified: Sun Jan 2 18:32:48 UTC 2022