Exam 12: Mathematical Problem Set

What is the smallest interval for $\theta(0 \leq \theta \leq k)$ that gives a complete graph of the polar equation $r=5 \sin 4 \theta ?$ Sketch the graph to show which petals are generated by positive values of r and which by negative values of r .

$\text { The graph of the polar equation }$ $r=\frac{3}{4-3 \cos \theta}$

For the next eight years, a small company's business volume can be modeled by the function $f(x)=108(1.02)^{x}+2 \sin \frac{\pi x}{3}$ where x is the number of years after 2006 and f is the sales in millions of dollars. (a) What are the company's sales in 2006 ? (b) What does the model project for sales in 2011? (c) How many years are in each economic cycle for this company?

By augmented matrix, solve the following system: x-y-z=3 3 x+4 y+5 z=1 y+2 z=-2

Eliminate the parameter and identify the graph of the parametric curve given by $x=\frac{3}{2 t+3}, y=2 t+2$

Use the discriminant to identify the graph of $2 x^{2}-4 x y+2 y^{2}+3 x-y=5$

By augmented matrix, solve the following system: x +y + z=1 -2 x + y + z=-2 x-2 y + z=-2

What are the three roots of $27\left(\cos \frac{9 \pi}{5}+i \sin \frac{9 \pi}{5}\right) ?$ Express the answers in trigonometric form.

What is the equation, in slope-intercept form, of the line that passes through the points (-3,4) and (5,7)?

Let $f(x)=x^{2}-1$ and $g(x)=\sqrt{x+5}$ Compute $f \circ g$ and state its domain in interval notation.

A computer randomly generates a password that is 6 entries long. The password is 3 letters followed by 3 numbers with repetitions of numbers and/or letters permitted. What is the probability that the computer will generate a password for Kara that has the same three letters followed by the same three numbers, such as GGG444?

The graph of $y=2-a^{x+3} \text { for } a>1$ is best represented by which graph?

What is the focus of the graph of $y^{2}=16 x ?$

For the function f(x) graphed below, which of the following is the $\lim _{x \rightarrow 3} f(x) ?$

Use the binomial theorem to expand $\left(3 x-2 y^{2}\right)^{4}$

Write the parametric form of the equation of the line through the points (-1,2,5) and (3,-1,0) .

Use the binomial theorem to expand $\left(x^{2}-3 y\right)^{5}$

What is a blinded experiment?

Write the equation of the ellipse graphed below.

What is a control group?