A Second Book in Algebra

A Second Book in Algebra

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1920 edition. Excerpt: ...of Curves. What is a symmetrical plane figure as defined in geometry? How many axes of symmetry has a square? An equilateral triangle? A circle? Note that in Ex. 2 on page 169 the ellipse is symmetrical to both the axis of x and the axis of y. The same is true of the hyperbola in Ex. 3 above. How may labor be saved in constructing a graph that is symmetrical to one axis only? To both axes? How can you tell from its equation whether a graph will be symmetrical to the axis of yl To the axis of x? Sug. In Ex. 24 show that whatever the value of y, x always equals 1 or 2. Hence the required graph is two straight lines parallel to the y-axis. 25. y--18 x2. Sug. Let each space on the 2/-axis = 20. 26. 2/2 = 60 x. 28. x2-xy+3y2-4 = 0. 27. y = 100x-16x2. 29. = 2x-l. x 30. Point out two of the above graphs which are symmetrical to the axis of x (but not to the axis of y). 31. Also three which are symmetrical to the axis of y (but not to the x-axis). 32. Also three which are symmetrical to both axes. 33. On one diagram, graph the results obtained by letting a = l, 2, 4, 9 in succession, in x2+y2=a. 34. Treat in like manner xy = a. 106. Graphic Solution of Simultaneous Quadratic Equations. f x2+y2 = 25. y+2x-5 = 0. Ex. Solve graphically Constructing the graph of x1+y1=25, we obtain the circle ABC in the diagram below. Constructing the graph of y+2 x-5=0, we obtain the straight line FH. Measuring the coordinates of the points of intersection of the two graphs, we find the points to be (4, --3) and (0, 5). These results may be verified by solving the two given simultaneous equations algebraically. 107. Special Cases: Imaginary Roots. Construct the graphs of x2+y2=4 and x+y = 5. You will find that these two graphs do not intersect. Then solve the given...show more

Product details

  • Paperback | 50 pages
  • 189 x 246 x 3mm | 109g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236577558
  • 9781236577559