The Fitzgeralds are installing inground pool in their back yard. They can either install the base model offered by the pool company or add any of the following options: automatic pool cleaner, solar cover, waterfall, hot tub, fountain, slide, diving board. How many different variations of the pool are possible?

A helicopter is flying horizontally at 8.0 m/s and an altitude of 18 m when a package of emergency medical supplies is ejected horizontally backward with a speed of 12 m/s relative to the helicopter. Ignoring air resistance, what is the horizontal distance between the package and the helicopter when the package hits the ground?

Estimate the difference in the value of 50 U.S. dollar s and 100 Mexican pesos. Assume that one Mexican peso is about 0.068 U.S. dollar.

Let u, v, and w be pairwise orthogonal vectors. (a) Show that

$$\| \mathbf { u } + \mathbf { v } + \mathbf { w } \| ^ { 2 } = \| \mathbf { u } \| ^ { 2 } + \| \mathbf { v } \| ^ { 2 } + \| \mathbf { w } \| ^ { 2 }$$

. (b) If u, v, and w are all the same length, show that they all make the same angle with u+v+w.

Graph the function. Compare the graph to the graph of

$$f ( x ) = x ^ { 2 }$$

.

$$k ( x ) = - 0.2 x ^ { 2 }$$

A circular wire loop of radius 15.0 cm carries a current of 3.20 A. It is placed so that the normal to its plane makes an angle of

$$41.0 ^ { \circ }$$

with a uniform magnetic field of magnitude 12.0 T. (a) Calculate the magnitude of the magnetic dipole moment of the loop. (b) What is the magnitude of the torque acting on the loop?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Even if I'm not sure how mathemat icians define irrational and complex numbers, telling me how these sets are related, I can construct a Venn diagram illustrating their relationship.

A set contains nine elements. (a) How many subsets does it have? (b) How many proper subsets does it have?

Explain how to use intercepts to graph the general form of a line's equation.

List all the subsets of the given set. {0}

Solve and check.

$$2 ^ { x } = 4 ^ { x + 1 }$$

Organize the divisions of the geologic time scale in order from longest length of time to shortest length of time.

(This logic problem dates back to the eighth century.) A farmer needs to take his goat , wolf, and cabbage across a stream. His boat can hold him and one other passenger (the goat , wolf, or cabbage). If he takes the wolf with him , the goat will eat the cabbage. If he takes the cabbage, the wolf will eat the goat. Only when the farmer is present are the cabbage and goat safe from their respective predators. How does the farmer get everything across the stream?

For a polygon to be convex means that all of its interior angles are less than 180 degrees. Use mathematical induction to prove that for all integers

$$n \geq 3$$

, the angles of any n-sided convex polygon add up to 180(n-2) degrees.