Determine the value of $b$ so that the volume of the ellipsoid

$$x^2+\dfrac{y^2}{b^2}+\dfrac{z^2}{9}=1$$

is $16 \pi$.

Construct a food web based on the images in the Picture Bank below. (Hint: Zebras and giraffes eat grass or leaves. Lions eat zebras and giraffes. Vultures eat lions, zebras, and giraffes.)

Analyze the details that you included in the word web. Does the author provide any foreshadowing, or clues early in the story, about MissStrangeworth's real personality? Give examples to support your answer.

In each part, use the Chapter 15 eManipulative activity Coordinate Geoboard on our Web site to determine which, if any, of the triangles with the given vertices is a right triangle.

b. $(4,-4),(0,2)$, and $(-3,0)$

Choose the word from the word web that best completes each sentence. Use context clues to help you or consult a dictionary.

One_____ in the pipe was blocked, causing water to back up into it.

Find the area of the region under the graph of $y=x^2 \ln x$ on the interval $[1, e]$.

During the night, water vapor in the air condensed on this spider web. As water vapor condenses, its molecules (gain/lose) thermal energy. How does the motion of the molecules change during condensation?

Use double integrals to find the total area of the region bounded by $y = x^3$ and $x = y^5.$

Use the proper word to complete each of the following blanks: The flexibility influence coefficient $a_{i j}$ denotes the deflection at point _____ due to a unit load at point ______.

For this scenario, decide if the outcome is random. Names are selected out of a hat to decide roommates in a dormitory. Is your roommate for the year random?

Luke is designing a web page. At the top is a banner ad that is $3 x ^ { 2 } + 6 x + 4$ inches high. The length is $x + 5$ inches. What is the area of the banner ad on Luke's web page?

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients. x^6 / x^2-4

The average number of hits h per day that your website received during the period January 2001 to February 2004 can be modeled by the equation h = -16| m - 30 | + 500 where m is the number of months since January 2001. a. In what month and year did your website receive an average of 100 hits per day? If the model holds for months after February 2004, predict the month and year in which your website will again receive an average of 100 hits per day. b. According to the model, did your website receive an average of 600 hits per day at any time during the period January 2001 to February 2004? Explain your answer. c. Can you use the model to find the month and year in which the average number of hits per day was the greatest? Justify your answer.

True or False. If a function f is continuous on a closed interval [a, b] and $f(a) \neq f(b)$, but both f(a)>0 and f(b)>0, then according to the Intermediate Value Theorem, f does not have a zero on the open interval (a, b).