Compute the directional derivative of f at the given point in the direction of the indicated vector. $f(x, y)=\cos (2 x-y),(\pi, 0)$, u in the direction from $(\pi, 0)$ to $(2 \pi, \pi)$

In the gas phase, phosphorus pentachloride exists as separate molecules. In the solid phase, however, the compound is composed of alternating PC4+ and PCl6- ions. What change(s) in molecular shape occur(s) as PCI5 solidifies? How does the Cl-P-Cl angle change?

Water is released from a 0.8-m-deep reservoir into a 4-m-wide open channel through a sluice gate with a 0.1-m-high opening at the channel bottom. The flow depth after all turbulence subsides is 0.5 m. The rate of discharge is $(a) 0.92 m^3/s\ (b) 0.79 m^3/s\ (c) 0.66 m^3/s\ (d) 0.47 m^3/s\ (e) 0.34 m^3/s$

A music download website charges its non-members a $2.50 fee to download plus$1.25 for every song. The total download fee (f) for non-members is a function of the number of downloads (n):

$$f = \$ 2.50 + \$ 1.25 n$$

. Create a table of prices for the first 6 downloads.

Some people are guessing the number of jelly beans in a jar. Each person who guesses within 15 of the correct number will win a prize. The correct number of jelly beans is 389. What values of n represent the numbers that will win a prize? F. n = 389 or n = 404, G. n = 389 and n = 404, H. 389 ≤ n ≤ 404, I. 374 ≤ n ≤ 404

The Arctic Sea ice extent, the area of the sea covered by ice, grows seasonally over the winter months each year, typically from November to March, and is modeled by G(t), in millions of square kilometers, t months after November 1, 2014. (a) What is the sign of G'(t) for 0 < t < 4? (b) Suppose G''(t) < 0 for 0 < t < 4. What does this tell us about how the Arctic Sea ice extent grows? (c) Sketch a graph of G(t) for $0 \leq t \leq 4,$ given that G(0) = 10.3, G(4) = 14.4, and G'' is as in part (b). Label your axes, including units.

The vectors $\mathbf { u }$ and $\mathbf { v}$ are given. Calculate the dot product $\mathbf { u } \cdot \mathbf { v }$. $\mathbf { u } = \langle 4,5 , - 6 \rangle$, $\mathbf { v } = \langle 0 , - 2 , - 3 \rangle$

Solve the system of linear equations using the substitution method.

$$\left. \begin{array} { l } { x + y + z = 4 } \\ { 5 x + 5 y + 5 z = 12 } \\ { x - 4 y + z = 9 } \end{array} \right.$$

Find the percent of decrease if the original population was 800 and the new population is 716.

Explain what is wrong with the statement. The function $P(x)=x^{2} e^{x}$ is a cumulative distribution function.

find the indicated term of the sequence. an = 4n / 2n^2 - 3, a11 = ?

Solve each equation. $x-4\dfrac{1}{2}=6\dfrac{3}{4}$

Write the power of 10 in standard form. Then multiply the factors. $2.5 \times 10 ^ { - 3 }$

An object moves so that its position depends on time as $x=+12-4 t+t^{2}$. Which statement below is not true? (a) The object is accelerating. (b) The speed of the object is always decreasing. (c) The object first moves in the negative direction and then in the positive direction. (d) The acceleration of the object is $+2 \mathrm{m} / \mathrm{s}^{2}$ (e) The object stops for an instant at 2.0 s.