Show that the general solution of

$$x y ^ { \prime \prime } + 2 y ^ { \prime } + x y = 0$$

is $y ( x ) = x ^ { - 1 } ( A \cos x + B \sin x )$.

Evaluate the expression. 15x when x = 4

What was mercantilism, and what was its relationship to colonial empires?

Compare the following using < or >. The outside temperature in summer is __ the outside temperature in winter

Chaz bought a two-year-old car. He paid D dollars. This make and model depreciates at a rate of E percent per year. Write an expression for the original selling price of the car when it was new.

Management proposed the following regression model to predict sales at a fast-food outlet.

$$y = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 3 } + \epsilon$$

where

$$\begin{array} { l } { x _ { 1 } = \text { number of competitors within one mile } } \\ { x _ { 2 } = \text { population within one mile } ( 1000 \mathrm { s } ) } \end{array}$$

$$x _ { 3 } = \left\{ \begin{array} { l } { 1 \text { if drive-up window present } } \\ { 0 \text { otherwise } } \end{array} \right.$$

$$y = \operatorname { sales } ( \$ 1000 \mathrm { s } )$$

The following estimated regression equation was developed after 20 outlets were surveyed.

$$\hat { y } = 10.1 - 4.2 x _ { 1 } + 6.8 x _ { 2 } + 15.3 x _ { 3 }$$

What is the expected amount of sales attributable to the drive-up window?

Explain the importance of each term, person, or place: apartheid; African National Congress (ANC); Sharpeville; Nelson Mandela; Desmond Tutu; F>W> de Klerk; Hutus; Tutsis; Darfur.

The Cartesian coordinates of a point are given. (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ <2π. (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ <2π. (2, -2)

Fill in the blank with an appropriate word, phrase, or symbol(s). (a) The value of r, the linear correlation coefficient, that represents the strongest positive correlation between two variables is _. (b) The value of r, the Linear correlation coefficient, that represents the strongest negative correlation between two variables is _. (c) The value of r, the linear correlation coefficient, that represents no correlation between two variables is _.

(a) What is a vector in space? How do we represent a vector in a three-dimensional coordinate system? (b) Find the vector with initial point (2, 3, -1) and terminal point (4, 10, 5). (c) How is the magnitude of

$$\mathbf { v } = \left\langle a _ { 1 } , a _ { 2 } , a _ { 3 } \right\rangle$$

defined? Find the magnitude of

$$\mathbf { w } = \langle 3,4,1 \rangle$$

. (d) What are the vectors i, j, and k? Express the vector

$$\mathbf{v} = \langle 5,9 , - 1 \rangle$$

in terms of i, j, and k.

Would a change in the earth's mass affect the performance of the loop-the-loop motorcycle stunt? Give your reasoning.

Find a linear equation whose graph is the straight line with the given properties. Through (1/3, 0) and parallel to the line 6x−2y=11

Find a unit vector in the direction of the given vector.

$$v=⟨1,-1⟩$$

Solve the equation.

$$5 x + 3 = 10 x - 17$$