If three sides of a triangle are given, the Law of ________ is used to solve the triangle.

The logistic model can be used for situations in which the initial population $P_0$ is above the carrying capacity K. For example, consider a deer population of 1500 on an island where a fire has reduced the carrying capacity to 1000 deer. Assuming a base growth rate of $r_0$ 0.1 and an initial population of P(0) = 1500, write a logistic growth function for the deer population and graph it. Based on the graph, what happens to the deer population in the long run?

Subtract. Use models if needed. (7x + 5) - (3x + 2)

The functions are one-to-one. For each function, find an equation for

$$f ^ { - 1 } ( x ),$$

the inverse function. f(x) = x + 3

Find all real solutions of the equation.

$$(x - 2 ) ^ { 1 / 5 } = 2$$

A segment has endpoints M(8, -7) and N(1, 2). a. Use matrices to represent a translation of

$$\overline { M N } \text { to } \overline { R S }$$

by 6 units left and 3 units down. What are the coordinates of R and S? b. Use matrices to represent a dilation of

$$\overline { M N } \text { to } \overline { D E }$$

by a scale factor of 3, centered at the origin. What are the coordinates of D and E?

Find the point on the surface z = xy + 1 nearest the origin.

Describe and correct the error in finding the sum or difference.

$$\left. \begin{array} { r } { x ^ { 3 } - 4 x ^ { 2 } + 3 } \\ { \frac { + - 3 x ^ { 3 } + 8 x - 2 } { - 2 x ^ { 3 } + 4 x ^ { 2 } + 1 } } \end{array} \right.$$

Give the two critical values t* from Table C that the bracket t. What are the upper tail probabilities p for this two entries?

Andrew and Meghan moved into an apartment in the city and pay $2,700 rent per month. The landlord told them the rent has increased 11.1% per year on average. Express the rent y as an exponential function of x, the number of years they rent the apartment. Show.

Water emerges straight down from a faucet with a 1.80-cm diameter at a speed of 0.500 m/s. (Because of the construction of the faucet, there is no variation in speed across the stream.) (a) What is the flow rate in cm³/s? (b) What is the diameter of the stream 0.200 m below the faucet? Neglect any effects due to surface tension.

An urn contains 5 white marbles, 10 green marbles, 8 yellow marbles, and 7 black marbles. If one marble is selected, determine the probability that it is white.

True or False. To eliminate the xy-term from the equation $x^{2}-2 x y+y^{2}-2 x+3 y+5=0$ rotate the axes through an angle $\theta$ where $\cot \theta=B^{2}-4 A C$

Find a particular solution $y_p$ of the given equation. In all these problems, primes denote derivatives with respect to $x$.

$$4 y ^ { \prime \prime } + 4 y ^ { \prime } + y = 3 x e ^ { x }$$