What type of function is the gradient function $f^{\prime}(x)$?

For the examples below, explain whether a physical or a chemical change has occurred. Justify your answer. a. When you mix baking soda and vinegar, carbon dioxide is released. b. You build a tall sand castle at the beach. After a wave washes over it, the sand castle turns into a big pile of sand. c. Boiling water turns a raw egg into a hardboiled egg. d. Max divided cookie dough into small piles on a cookie sheet. e. A loaf of freshly-baked bread tastes better and looks much different than a lump of bread dough. f. A glass of water is left in the sun. In time, the water evaporates leaving the glass empty.

What is the heat capacity $(C_v)$ of the calorimeter?
(a) 5.15 kJ/°C (b) 5.08 kJ/°C (c) 5.12 kJ/°C (d) 4.97 kJ/°C

Determine the coefficient and the degree of each term in each polynomial:

$$2a^5 + a^2 + 8a + 10$$

Give an example of a molecule or ion having a formula of each of the following types and structures. (a) AB3 (planar), (b) AB3 (pyramidal), (c) AB^-2 (bent), (d) AB^2- 3 (planar)

Use a word from the list to complete each analogy, creating a second word pair that matches the relationship between the first two given words. fester, barren, paradoxical, abash. empty : full :: _____ : fruitful

Use computer to find the eigenvalues and determinant of each of the following matrices:

$$A=\left( \begin{array}{ll}{6} & {-8} \\ {4} & {-6}\end{array}\right)$$

,

$$B=\left( \begin{array}{rr}{-11} & {-16} \\ {8} & {13}\end{array}\right)$$

and

$$C=\left( \begin{array}{rrr}{7} & {-21} & {-11} \\ {5} & {-13} & {-5} \\ {-5} & {9} & {1}\end{array}\right)$$

.

You are standing on a straight stretch of road and watching the motion of a bicycle; you choose your position as the origin. At one instant, the position of the bicycle is negative and its velocity is positive. Is the bicycle getting closer to you or farther away? Explain.

Write a square root function for which the domain is

$$\{ x | x \geq 8 \}$$

and the range is

$$\{ y | y \leq 14 \}$$

Compare the amount of movement possible in synarthrotic, amphiarthrotic, and diarthrotic joints. Relate these terms to the structural classification of joints; that is, to fibrous, cartilaginous, and synovial joints.

Solve the inequality. Graph the solution.

$$z - ( - 7 ) < 5$$

write the quotient in standard form. 8+16i / 2i

Find the Taylor polynomial of degree n for x near the given point a. cos x, $a=\pi / 2,$ n = 4

The cost per day of running a hospital is 200,000 + .002x2 dollars, where x = patients served per day. What size hospital minimizes the per-patient cost of running the hospital?