What was the Tariff of 1816? Why did Congress pass the tariff?

Solve the given problems and explain your answers.

If the consumption of natural gas is $5.00+0.01t$ billion ft$^3$/year, find the volume $V$ that will be consumed in the next $t$ years. (In $2010$, the United States had reserves of natural gas of about $275$ trillion ft$^3$.)

Predict the outcome of using an illegal drug to escape from personal problems.

The $R$ factor for housing insulation gives the thermal resistance in units of $\mathrm{ft}^2{ }^{\circ} \mathrm{F}$ h/BTU. A good wall for harsh climates, corresponding to about $10.0$ in of fiberglass, has $R=40.0 \mathrm{ft}^2{ }^{\circ} \mathrm{F}$ h/BTU. a) Determine the thermal resistance in SI units.

Solve the given problems.
If $f(x)=x^{-2}+3 x^{-1}$, find $f(4+j)$.

Solve the given problems by integration.

A marathon runner's speed (in $\mathrm{km} / \mathrm{h}$ ) is $v=\frac{48}{0.25 t^2+4}$. This runner is in the same race as the runners in the previous exercise. (a) Who is ahead after $3.00 \mathrm{~h}$ ? (b) Who is first, second and third after $4.00 \mathrm{~h}$ ?

(a) What are the ratios of the resistances of (a) silver and (b) aluminum wire to the resistance of copper wire $\left( R _ { \mathrm { Ag } } / R _ { \mathrm { Cu } }\right.$ and $R _ { \mathrm { A } } / R _ { \mathrm { Cu } } )$ for wires of the same length and the same diameter? (c) Which material is the best conductor, for wires of equal length and diameter?

Describe what happens to an ecosystem when a keystone species is removed.

Angle

$$\theta$$

lies in quadrant 2. Without using a calculator, which ratios must be false? Justify your reasoning. a)

$$\cos \theta = 2.3151$$

b)

$$\tan \theta = 2.3151$$

c)

$$\sec \theta = 2.3151$$

d)

$$\csc \theta = 2.3151$$

e)

$$\cot \theta = 2.3151$$

f)

$$\sin \theta = 2.3151$$

Cramer's Rule breaks down when detA = 0. Example (a) has no solution, whereas (b) has infinitely many. What are the ratios xⱼ = detBⱼ/detA? (a) 2x₁ + 3x₂ = 1; 4x₁ + 6x₂ = 1. (parallel lines), (b) 2x₁ + 3x₂ = 1; 4x₁ + 6x₂ = 2. (same line)

A triangle undergoes a rigid motion on a coordinate plane. Tell whether the given characteristic is preserved. Write Yes or No. The classification of the triangles by sides (scalene, etc.)

From 1960 to 2003, the per capita consumption C of cigarettes by Americans (age 18 and older) can be modeled by

$$C=4299-1.8 t-1.36 t^2, \quad 0 \leq t \leq 43$$

where $t$ is the year, with $t=0$ corresponding to 1960 . Use a graphing utility to graph the model.

Obtain the following derivatives from first principles: (a) the first derivative of $3 x+4$; (b) the first, second and third derivatives of $x^2+x$; (c) the first derivative of $\sin x$.

An equation of motion is $s=2 t^3-9 t^2$$, where s is in meters and t in seconds. Find the times at which the acceleration is 0.