A stream becomes a river as it moves down gradient. Give the sequence in the evolution of a stream: (a) meandering pattern, (b) rapids, (c) delta.

What does the associated graph indicate about a stream?

A. Silt and clay are carried in suspension under most stream velocities.

B. Sand and gravel are deposited at low velocities but transported at higher velocities.

C. Sand is carried in suspension only at high velocities.

D. As fast-moving water slows down, fine sand can switch from transport by suspension to the bed load.

E. All of these.

Water slows down when it reaches (permeable/impermeable) material.

Identify a wave that speeds up when it passes from air to water as well as one that slows down.

As a stream slows down, which sediments are deposited first—large ones or small ones?

A steady stream of water falls straight down from a pipe. As- sume the flow is incompressible; the flow is similar to earlier Fig. How does the pressure in the water vary with height in the falling stream? $\quad(A)$ The pressure in the water is higher at lower points in the stream. $\quad(B)$ The pressure in the water is lower at lower points in the stream. $\quad(C)$ The pressure in the water is the same at all points in the stream.

Water flows in a horizontal pipe that is narrow but then widens and the speed of the water becomes less. The pressure in the water moving in the pipe is (a) greater in the wide part. (b) greater in the narrow part. (c) the same in both parts. (d) greater where the speed is higher. (e) greater where the speed is lower.

A sheet of water passing over a waterfall is thicker near the top than near the bottom. Similarly, a stream of water emerging from a water faucet becomes narrower as it falls. Explain.

What materials make up an aquifer layer?

An important idea in calculus involves the ratio $\frac{\sin x}{x^{2}}$ for values of x close to 0. Make a table with columns headed x and $\frac{\sin x}{x^{2}}$. a. Using radian mode, complete one table for x = 1, 0.5, 0.25, 0.1, 0.01, 0.001, and 0.0001. What appears to be happening to $\frac{\sin x}{x^{2}}$ as x approaches 0 in radian mode? b. Using degree mode, complete a second table with the same headings and same values of x. What appears to be happening to $\frac{\sin x}{x^{2}}$ as x approaches 0 in degree mode? c. Compare your results in Parts a and b to the difference in scale of degrees and radians. Do you see any connection?

Under the transformation

$$u=\frac{1}{5}(2 x+y) \quad v=\frac{1}{5}(x-2 y)$$

the square D in the xy-plane with vertices (0,0), (1,-2), (3,-1),(2,1) is mapped onto a square in the uv-plane. Use this information to find the integral.

$$\iint_{D}(2 x+y)(x-2 y)^{2} d y \ d x$$

The probability that a man will be alive in 25 years is $\frac{3}{5}$, and the probability that his wife will be alive is $\frac{2}{3}$. Determine the probability that in 25 years: only the wife will be alive.

The amount of money spent at West Outlet Mall continues to increase. The total T(x) in millions of dollars can be estimated by the function

$$T(x) = 12(1.12)^x$$

, where x is the number of years after it opened in 2005. Find the amount of sales in 2015, 2016, and 2017.

In Exercise : (a) Make the indicated u-substitution, and then use the Endpaper Integral Table to evaluate the integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a).

$$\int \frac { 1 } { \sqrt { 9 x ^ { 2 } - 4 } } d x , u = 3 x$$