Let

$$\sin t = a , \cos t = b , \text { and } \tan t = c.$$

Write each expression in terms of a, b, and c.

$$4 \cos ( - t ) - \cos t$$

How does sky propagation differ from line-of-sight propagation?

Simplify the expression. Write your answer using only positive exponents.

$$\left( \frac { 3 m ^ { - 5 } n ^ { 2 } } { 4 m ^ { - 2 } n ^ { 0 } } \right) ^ { 2 } \cdot \left( \frac { m n ^ { - 1 } } { 9 n } \right) ^ { 2 }$$

Differentiate the function.

$$W(t)=\sqrt{t}-2 e^{t}$$

Pertain to the following input-output model: Assume that an economy is based on three industrial sectors: agriculture $(A)$, building $(B)$, and energy $(E)$. The technology matrix $M$ and final demand matrices (in billions of dollars) are

$$D_1=\left[\begin{array}{r} 5 \\ 10 \\ 15 \end{array}\right] \quad D_2=\left[\begin{array}{l} 20 \\ 15 \\ 10 \end{array}\right]$$

Use $(I-M)^{-1}$ in the previous problem to find the output for each sector that is needed to satisfy the final demand $D_2$.

Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there?

$y=-3 x^2+6 x-\frac{1}{2}, y=\sqrt{7-\frac{7}{12} x^2} ; \quad[-4,4]$ by $[-1,3]$

The system of government set up by the Articles of Confederation included

A a congress to make the laws.

B an agency to collect a national income tax.

C national judges to apply the laws.

D an executive to carry out the laws.

Find the slope of the tangent line to the given polar curve at the point specified by the value of $\theta$.

$$r=\cos 2 \theta, \quad \theta=\pi / 4$$

A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is proportional to her velocity, and the constant of proportionality is 0.2. It can be shown that the downward velocity of the sky diver at time t is given by $v(t)=180\left(1-e^{-0.2 t}\right)$ where t is measured in seconds (s) and v(t) is measured in feet per second (ft/s). Find the initial velocity of the sky diver.

Use the substitutions $x=\sinh \theta, \cosh \theta, \text { or } \tanh \theta .$ Express the final answers in terms of the variable x. $\int \frac{d x}{\sqrt{x^{2}-1}}$

How are sedimentary rocks formed through chemical processes?

Use a benchmark to find an equivalent percent for the fraction.

$$\frac{9}{10}$$

B vitamins often act as
a. antioxidants
b. blood clotting factors
c. coenzymes
d. none of the above

Materials used by the Instrument Division of XPort Industries are currently purchased from outside suppliers at a cost of $210 per unit. However, the same materials are available from the Components Division. The Components Division has unused capacity and can produce the materials needed by the Instrument Division at a variable cost of$160 per unit.

Assume that a transfer price of $190 has been established and that 60,000 units of materials are transferred, with no reduction in the Components Division’s current sales.

D. If the negotiated price approach is used, what would be the range of acceptable transfer prices and why?