Precalculus by Richard Wright

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Better a little with righteousness than much gain with injustice. Proverbs‬ ‭16‬:‭8‬ ‭NIV‬‬‬

7-Review

Take this test as you would take a test in class. When you are finished, check your work against the answers. On this assignment round your answers to three decimal places unless otherwise directed.

  1. Find the inclination of \(2x + y - 3 = 0\) in degrees.
  2. Find the angle between the lines \(2x + y - 3 = 0\) and \(x - 2y + 1 = 0\).
  3. Find the distance between (2, 4) and \(2x + y - 3 = 0\).
  4. Classify the conic \(4x^2 + 9y^2 - 8x + 36y + 4 = 0\).
  5. Find the foci of \(4x^2 + 9y^2 - 8x + 36y + 4 = 0\).
  6. Graph \(4x^2 + 9y^2 - 8x + 36y + 4 = 0\).
  7. Find the standard form of the equation of the parabola with focus (3, 0) and directrix \(x = -1\).
  8. Find the standard form of the hyperbola with vertices (2, 5) and (−4, 5) and b = 5.
  9. Classify the conic \(x^2 - 2xy + 2y^2 + 3x - 5y + 12 = 0\).
  10. What degree is \(x^2 - 2xy + 2y^2 + 3x - 5y + 12 = 0\) rotated?
  11. Graph the parametric equations \(x = \sqrt{t}\) and \(y = 2t^2\).
  12. Eliminate the parameter from \(x = \sqrt{t}\) and \(y = 2t^2\).
  13. Convert \(\left(4, \frac{π}{3}\right)\) to rectangular coordinates.
  14. Find another polar coordinate that represents \(\left(4, \frac{π}{3}\right)\).
  15. Convert \(r = 4 \sec θ\) to rectangular form.
  16. Graph the polar coordinate \(\left(2, \frac{7π}{6}\right)\).
  17. Classify the graph of \(r = \frac{6}{1 - 3 \cos θ}\).
  18. Find one focus of \(r = \frac{6}{1 - 3 \cos θ}\).
  19. Classify the graph of \(r = \frac{3}{1 + \sin θ}\).
  20. Find the polar equation for an ellipse with directrix x = −6 and \(e = \frac{1}{3}\).
  21. Find the polar equation for a hyperbola with the vertices \(\left(2, \frac{π}{2}\right)\) and \(\left(-6, \frac{3π}{2}\right)\).

Answers

  1. 116.6°
  2. 90°
  3. \(\sqrt{5}\)
  4. Ellipse
  5. \(\left(1 ± \sqrt{5}, -2\right)\)
  6. ans
  7. \(y^2 = 8\left(x - 1\right)\)
  8. \(\frac{\left(x + 1\right)^2}{9} - \frac{\left(y - 5\right)^2}{25} = 1\)
  9. Ellipse
  10. 31.7°
  11. ans
  12. \(y = 2x^4\)
  13. \(\left(2, 2\sqrt{3}\right)\)
  14. \(\left(4, \frac{7π}{3}\right)\) or \(\left(-4, \frac{4π}{3}\right)\)
  15. \(x = 4\)
  16. ans
  17. Hyperbola with vertical directrix to the left of the pole
  18. (0, 0)
  19. Parabola with horizontal directrix above the pole
  20. \(r = \frac{6}{3 - \cos θ}\)
  21. \(r = \frac{6}{1 + 2 \sin θ}\)