Find the distance between the cities. Assume that Earth is a sphere of radius 4000 miles and the cities are on the same longitude (one city is due north of the other).

$$\begin{matrix} \text{City} & \text{Latitude}\\ \text{Dallas, Texas} & \ {32^{\circ} 47^{\prime} 39^{\prime \prime} \mathrm{N}}\\ \text{Omaha, Nebraska} & \ {41^{\circ} 15^{\prime} 50^{\prime \prime} \mathrm{N}}\\ \end{matrix}$$

Simplify the expression. 3(2x - 7) + 8(4 - x)

Trejo says that if you know the x-intercepts, y-intercepts, domain, and range of an equation then you automatically know the x-intercepts, y-intercepts, domain, and range for the inverse. Hilary disagrees. She says you know the intercepts but that is all you know for sure. Who is correct? Justify your answer.

Find a closed-form formula for the nth partial sum of the series

$$\sum _ { n = 2 } ^ { \infty } \ln \left( 1 - \left( 1 / n ^ { 2 } \right) \right)$$

and use it to determine the convergence or divergence of the series.

Solve each compound inequality. 6 < x + 3 < 8

Which equation has x = 8 for a solution? (A) 2x + 3 = 13 (B) 4x + 6 = 38 (C) 3x - 5 = 29 (D) 5x - 8 = 48

Consider an atomic nucleus to be equivalent to a onedimensional infinite potential well with

$$L = 1.4\times10^{-14}m$$

, a typical nuclear diameter. What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)

The maximum horizontal distance a boy can throw a ball is 50 m. Assume he can throw with the same initial speed at all angles. How high does he throw the ball when he throws it straight upward?

Solve the equation. Check your solution. 12 = f/2 - 8

Write an equation for a circle if the endpoints of a diameter are at (8, 31) and (32,49).

An industrial process involves evaporation of a thin water film from a contoured surface by heating it from below and forcing air across it. Laboratory measurements for this surface have provided the following heat surface have provided the following heat transfer correlation: $\overline{N u}_{L}=0.43 R e_{L}^{0.58} P r^{0.4}$. The air flowing over the surface has a temperature of 290 K, a velocity of 10 m/s, and is completely dry $\left(\phi_{\infty}=0\right.)$. The surface has a length of 1 m and a surface area of $1 \mathrm{m}^{2}$. Just enough energy is supplied to maintain its steady-state temperature at 310 K. (a) Determine the heat transfer coefficient and the rate at which the surface loses heat by convection. (b) Determine the mass transfer coefficient and the evaporation rate (kg/h) of the water on the surface. (c) Determine the rate at which heat must be supplied to the surface for these conditions.

Write the expression in simplest form.

$$\sqrt [ 4 ] { 567 }$$

$$\frac { 5760 } { 8 }$$

Find the centroid of the region lying underneath the graph of the function over the given interval.

$$f ( x ) = \left( 1 + x ^ { 2 } \right) ^ { - 1 / 2 },$$

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