To generate areawide watersheds from a DEM, we must create several intermediate rasters. Draw a flow chart that starts with a DEM, followed by the intermediate rasters, and ends with a watershed raster.

Use the sum and difference identities to verify the following identities. See the earlier example.

$$\tan \left(\alpha-\frac{5 \pi}{4}\right)=\dfrac{\tan \alpha-1}{1+\tan \alpha}$$

The region bounded by the graphs of $y=\sin x, y=0$, $x=0$, and $x=\pi$ is revolved about the line $x=-1$. Find the volume of the solid generated.

State the number of electrons that must be lost by atoms of the Cs to achieve a stable electron configuration.

Cub Company, a calendar-year entity, had 2,100 geothermal heating pumps in its beginning inventory for 20X1. On December 31, 20X0, the heating pumps had been adjusted down to $850 per unit from an actual cost of$920 per unit. It was the lower of cost or market. Cub purchased no additional units during 20X1. The following additional information is provided for 20X1:

$$\begin{array}{clrr} && \textbf{Inventory} & \textbf{Unit Market}\\ \textbf{Quarter} & \textbf{Date} & \textbf{(units)} & \textbf{Value}\\ \\ 1 & \text{March 31, 20X1} & 1,700 & \$845\\ 2 & \text{June 30, 20X1} & 1,400 & 860\\ 3 & \text{September 30, 20X1} & 1,300 & 830\\ 4 & \text{December 31, 20X1} & 900 & 840\\ \end{array}$$

Required

Case 1: The company does not have sufficient experience with the seasonal market for geothermal pumps and assumes that any reductions in market value during the year will be permanent.

$\quad$ (1) Determine the cost of goods sold for each quarter.

$\quad$ (2) Verify the total cost of goods sold by computing annual cost of goods sold on a lower-of-cost-or-market basis.

Carry out the indicated operations in the agreed-upon order.\

$$12+3 \times 2$$

From Hughes's essay (Langston Hughes, “Negro Artist and the Racial Mountain,), what conclusions can you make regarding his perspective of race relations in the early twentieth century? How have those social relations impacted relationships within the black community?

Explain the reason, according to Bohr’s atomic model, why atomic emission spectra contain only certain frequencies of light.

Use the Chain Rule to find δz/δs and δz/δt.

$$z = arcsin(x - y), x = s^2 + t^2 y = 1 - 2st$$

Use Version 2 of the Chain Rule to calculate the derivatives of the following functions.

$$y = \left( 3 x ^ { 2 } + 7 x \right) ^ { 10 }$$

Find the area of the region bounded by the curve $y=-x^{2}-x+2$ and the x-axis.

For a chi-squared distribution, find $\chi^2_{\alpha}$ such that

$$\text{(a) } P(X^2 > \chi^2_{\alpha} ) = 0.01 \text{ when } v = 21;$$

$$\text{(b) } P(X^2 < \chi^2_{\alpha} ) = 0.95 \text{ when } v = 6;$$

$$\text{(c) } P( \chi^2_{\alpha} < X^2 < 23.209 ) = 0.015 \text{ when } v = 10;$$

For a chi-squared distribution, find $\chi^2_{\alpha}$ such that

$$\text{(a) } P(X^2 > \chi^2_{\alpha} ) = 0.99 \text{ when } v = 4;$$

$$\text{(b) } P(X^2 > \chi^2_{\alpha} ) = 0.025 \text{ when } v = 19;$$

$$\text{(c) } P( 37.652 < X^2 < \chi^2_{\alpha} ) = 0.045 \text{ when } v = 25;$$

write the coefficient matrix and the augmented matrix of the given system of linear equation

$$x_1+4 x_2=15$$

$$6 x_1=18$$