Need Help Solving This Homework

FOR THE SOCIAL AND MANAGEMENT SCIENCES
Math 1051-11 Fall 2015 CRN: 60251

HOMEWORK I — DUE Wednesday, September 16, at the beginning of the lecture

1. Determine (the x and y coordinates of) the point(s) where the graph of x2y+xy2−3×2+2y2 = 8 cuts (a) the x-axis, (b) the y-axis, (c) the vertical line that goes through the point (−2, 3), and (d) the horizontal line that goes through the point (−2, 3).
2. Find equations for the following straight-line graphs:
   (a) The straight line that goes through the points (−3, 1) and (2, −3).
   (b) The straight line with x-intercept at x = −3 and y-intercept at y = 5.
   (c) The straight line that goes through (−3, 1) and is parallel to the line 2x + 3y = −6.
3. In your solutions to the following, clearly tell me what each of your variables denotes.
   1. (a)  A coffee shop has fixed costs (space rental, salaries, etc.) of $215 per day and unit costs of $0.65 per cup of coffee, and sells its coffee at $1.75 per cup. Express the daily profit as a linear function of the number of cups sold each day.
   2. (b)  Jane began a part-time job in the New Year and, on the first Saturday in January 2014 she deposited $8.50 into her savings account (which already had some money in it). She deposits the same amount into her account every Saturday from then on. After making her deposit last Saturday, 35 weeks into the year, with no money taken out from her account and no money added other than her weekly $8.50 deposits, Jane had exactly $500 in her savings account. Express the amount of money in Jane’s savings account as a linear function of the number of weeks passed in 2014.
   3. (c)  A daytime telephone call from Washington to Melbourne, Australia costs 5 cents for the first minute and 6.5 cents for each additional minute. At night the rate is a flat 6 cents per minute. Express the amount of money (in cents) that I would save by calling at night as a linear function of the length of the call (in minutes).
4. Determine, just by looking, how many points of intersection each of the following systems of equations has (zero, one, or infinitely many), and briefly describe the geometry of each system.

(a) 2x −4y =6 (b) 2x −4y

=6 (c) 2x −4y =6 (d) 2x −4y =0 =6 3x −6y =6 3x −6y =0

3x −2y =6
2x −4y +6z =2

(e) 3x −6y +9z =3 4x −8y +12z =4

3x
2x

(f) 4x 3x

−4y +6z =3 −8y +12z =6 −6y +9z =9

2x −4y +6z =3 (g) 4x −8y +12z =6 9x +9y +9z =9

5. Use Gauss-Jordan to find the points of intersection of the following two 3-D systems of linear equations (a single point of intersection in each case):

x +2y +3z =1 (a) 2x +5y +7z =2 3x+5y+7z=3

x −2y −3z =1 (b) y +4z =2 −x +y+z=3

You must use the Gauss-Jordan algorithm described in class … and clearly depict your ele- mentary operations.

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