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Unformatted text preview: JORDAN KOVALSKY Math - 112 Spring 2010 WeBWorK Assignment Lesson 11 - Lines and Linear Equations Due Date: 10/01/2010 at 11:59pm CDT. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. You can use the Feedback button on each problem page to send e-mail to the course instructors. 1. (1 pt) Compute the slope of the line passing through the given points. The points (4, 4) and (-4, -4). Slope = The points (0, 5) and (-4, 5). Slope = 2. (1 pt) Here is a graph of a line: (Click on the image to enlarge it.) 3. (1 pt) Find an equation for the line having the slope and passing through the given point. Write your answer in the form y = mx + b. With m = 5; through (-4, 3): y= x+ 4 -4 With m = ; through -5, : 5 5 y= x+ 4. (1 pt) Find the equation of a vertical line passing through the point (9, 4). Write your answer in the form Ax + By +C = 0. Line is : =0 Find the equation of a horizontal line passing through the point (9, 4). Write your answer in the form Ax + By +C = 0. Line is : =0 5. (1 pt) Find the equation of the line with slope 0 and intercept 11 and write it in slope-intercept form. y= Compute the slope of the using each pair of points indicated. The points are A(3, -2), B(2, 0), and C(-1, 6). Using A and B: Slope = Using B and C: Slope = Using A and C: Slope = The principle involved here is that no matter which pair of points you choose, the slope is the same.
1 Find the equation of the line with slope 11 and intercept 0 and write it in slope intercept form. y= 6. (1 pt) 9. (1 pt) Find the slope of the line connecting the points (3, 9) and (3 + h, (3 + h)2 ). Simplify your answer. Slope = Are the lines y = x + 6 and y = 3 - 2x parallel, perpendicular, or neither? ? 10. (1 pt) 7. (1 pt) Find an equation for the line that is perpendicular to x-y+6 = 0 and passes through the point (6, 3). Write it in two different forms: y = mx + b and Ax + By +C = 0. In the first form, y= In the second form, the equation is =0 8. (1 pt) After analyzing sales figures for a particular model of CD player, the accountant for College Sound Company has produced the following graph relating the selling price P (in dollars) and the number y of units that can be sold each month at that price. For instance, as the graph shows, setting the selling price at $ 225 yields sales of 260 units per month. Find the equation of the tangent line. Hint: Make use of the theorem from elementary geometry stating that the tangent line is perpendicular to the radius drawn to the point of contact. Write your answer in the form y = mx + b. y= Find the x-intercept of the tangent line. x= Find the y-intercept of the tangent line. y= What is the length of the portion of the tangent line that lies in quadrant IV? Length = Find the equation of the line. Remember to use the letter P (capital P not lower case p) instead of the usual x. y= Use the equation that you found in the previous part to determine how many units can be sold in a month when the price is $ 303 per unit. Units = What should the price be to sell 288 units per month? $
2 Look at the figure below (Click to enlarge). It shows a circle centered at the origin and a line that is tangent to the circle at the point (3, -4). 11. (1 pt) Consider the line y = mx + b. What conditions would you have to impose on m and/or b to guarantee that the line: a) does NOT pass through the first quadrant? b) does NOT pass through the third quadrant? This problem needs to be handed in on paper to your instructor. Download the .pdf file associated to this assignment (in Moodle), print it out, and submit your answer on it. Note: The score for this problem will be adjusted later; you do not need to submit an answer on this problem. 12. (1 pt) Find the linear function satisfying the conditions f (3) = 3 and f (-2) = 8. f (x) = Use your previous answers to find the cost of producing 501 motorcycles. Cost = 13. (1 pt) A manufacturer buys a new machine costing $120000. It is estimated that the machine has a useful lifetime of ten years and a salvage value of $5000 at that time. Find a formula for the value of the machine after t years, where 0 t 10. (Assume that the value is a linear function of t for 0 t 10. Don't use commas in numbers: that will confuse WeBWorK.) Value after t years = Find the value of the machine after 8 years. Value after 8 years = 16. (1 pt) The graphs below relate distance and time for a moving object. Determine the velocity in each case. 14. (1 pt) Let x denote the temperature on the Celsius scale, and let y denote the corresponding temperature on the Farhenheit scale. Find a linear function relating x and y; use the facts that 32 F corresponds to 0C and 212 F corresponds to 100C. Write the function in the form y = Ax + B. y= x+ What Celsius temperature corresponds to 98.6 F? C 98.6 F = Find a number z for which z F = zC. z= 15. (1 pt) Suppose that the cost to a manufacturer of producing x units of a certain motorcycle is given by C(x) = 220x + 2000, where C(x) is in dollars. Find the marginal cost. Marginal Cost = Find the cost of producing 500 motorcycles. Cost =
3 at the same time, running in the same direction, how long will it take Emily to lap Ernie? Time = minutes. 18. (1 pt) Jim and Juan are going to drive their motorcycles from San Francisco to Los Angeles. Jim leaves at 8:00 AM but Juan can't leave until 8:30 AM. If Jim drives at 50 mph and Juan at 55 mph, how long must Juan drive before he catches up with Jim? Time = hours. 19. (1 pt) Annie drives from town A to town B in 3 hours (at a fixed speed). The traffic is heavier on the return trip, so Annie's speed is 14 mph less and the return trip takes 4 hours. What were her speeds on both parts of the trip? Speed A to B = mph Speed B to A = mph (a) (b) (c) Velocity = Velocity = Velocity = ft/sec cm/sec miles/hour 17. (1 pt) Emily and Ernie are going to job on a quarter-mile track. Emily can jog at a pace of 9 min/mile ( = 1/9 mile/min) while Ernie can jog at a pace of 11 min/mile ( = 1/11 mile/min). If they start
c Generated by the WeBWorK system WeBWorK Team, Department of Mathematics, University of Rochester 20. (1 pt) Simplify the expression Simplified = 3 (y + 1)9 . y2 - 1 4 ...
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