{"id":1426,"date":"2023-06-05T14:51:37","date_gmt":"2023-06-05T14:51:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-parametric-equations-graphs\/"},"modified":"2023-06-05T14:51:37","modified_gmt":"2023-06-05T14:51:37","slug":"solutions-for-parametric-equations-graphs","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/tulsacc-math1613\/chapter\/solutions-for-parametric-equations-graphs\/","title":{"raw":"Solutions 63: Parametric Equations: Graphs","rendered":"Solutions 63: Parametric Equations: Graphs"},"content":{"raw":"\n

Solutions to Odd-Numbered Exercises<\/h2>\n1. plotting points with the orientation arrow and a graphing calculator\n\n3. The arrows show the orientation, the direction of motion according to increasing values of [latex]t[\/latex].\n\n5. The parametric equations show the different vertical and horizontal motions over time.\n\n7.\n\"Graph\n\n9.\n\"Graph\n\n11.\n\"Graph\n\n13.\n\"Graph\n\n15.\n\"Graph\n\n17.\n\"Graph\n\n19.\n\"Graph\n\n21.\n\"Graph\n\n23.\n\"Graph\n\n25.\n\"Graph\n\n27.\n\"Graph\n\n29.\n\"Graph\n\n31.\n\"Graph\n\n33.\n\"Graph\n\n35.\n\"Graph\n\n37.\n\"Graph\n\n39. There will be 100 back-and-forth motions.\n\n41. Take the opposite of the [latex]x\\left(t\\right)[\/latex] equation.\n\n43. The parabola opens up.\n\n45. [latex]\\begin{cases}x\\left(t\\right)=5\\cos t\\\\ y\\left(t\\right)=5\\sin t\\end{cases}[\/latex]\n\n47.\n\"Graph\n\n49.\n\"Graph\n\n51.\n\"Graph\n\n53. [latex]a=4,b=3,c=6,d=1[\/latex]\n\n55. [latex]a=4,b=2,c=3,d=3[\/latex]\n\n57.\n\"Graph\n\"Graph\n\"Graph\n\n59.\n\"Graph\n\"Graph\n\"Graph\n\n61. The [latex]y[\/latex] -intercept changes.\n\n63. [latex]y\\left(x\\right)=-16{\\left(\\frac{x}{15}\\right)}^{2}+20\\left(\\frac{x}{15}\\right)[\/latex]\n\n65. [latex]\\begin{cases}x\\left(t\\right)=64t\\cos \\left(52^\\circ \\right)\\\\ y\\left(t\\right)=-16{t}^{2}+64t\\sin \\left(52^\\circ \\right)\\end{cases}[\/latex]\n\n67. approximately 3.2 seconds\n\n69. 1.6 seconds\n\n71.\n\"Graph\n\n73.\n\"Graph\n","rendered":"

Solutions to Odd-Numbered Exercises<\/h2>\n

1. plotting points with the orientation arrow and a graphing calculator<\/p>\n

3. The arrows show the orientation, the direction of motion according to increasing values of [latex]t[\/latex].<\/p>\n

5. The parametric equations show the different vertical and horizontal motions over time.<\/p>\n

7.
\n\"Graph<\/p>\n

9.
\n\"Graph<\/p>\n

11.
\n\"Graph<\/p>\n

13.
\n\"Graph<\/p>\n

15.
\n\"Graph<\/p>\n

17.
\n\"Graph<\/p>\n

19.
\n\"Graph<\/p>\n

21.
\n\"Graph<\/p>\n

23.
\n\"Graph<\/p>\n

25.
\n\"Graph<\/p>\n

27.
\n\"Graph<\/p>\n

29.
\n\"Graph<\/p>\n

31.
\n\"Graph<\/p>\n

33.
\n\"Graph<\/p>\n

35.
\n\"Graph<\/p>\n

37.
\n\"Graph<\/p>\n

39. There will be 100 back-and-forth motions.<\/p>\n

41. Take the opposite of the [latex]x\\left(t\\right)[\/latex] equation.<\/p>\n

43. The parabola opens up.<\/p>\n

45. [latex]\\begin{cases}x\\left(t\\right)=5\\cos t\\\\ y\\left(t\\right)=5\\sin t\\end{cases}[\/latex]<\/p>\n

47.
\n\"Graph<\/p>\n

49.
\n\"Graph<\/p>\n

51.
\n\"Graph<\/p>\n

53. [latex]a=4,b=3,c=6,d=1[\/latex]<\/p>\n

55. [latex]a=4,b=2,c=3,d=3[\/latex]<\/p>\n

57.
\n\"Graph
\n\"Graph
\n\"Graph<\/p>\n

59.
\n\"Graph
\n\"Graph
\n\"Graph<\/p>\n

61. The [latex]y[\/latex] -intercept changes.<\/p>\n

63. [latex]y\\left(x\\right)=-16{\\left(\\frac{x}{15}\\right)}^{2}+20\\left(\\frac{x}{15}\\right)[\/latex]<\/p>\n

65. [latex]\\begin{cases}x\\left(t\\right)=64t\\cos \\left(52^\\circ \\right)\\\\ y\\left(t\\right)=-16{t}^{2}+64t\\sin \\left(52^\\circ \\right)\\end{cases}[\/latex]<\/p>\n

67. approximately 3.2 seconds<\/p>\n

69. 1.6 seconds<\/p>\n

71.
\n\"Graph<\/p>\n

73.
\n\"Graph<\/p>\n\n\t\t\t

\n\t\t\t

Candela Citations<\/h3>\n\t\t\t\t\t
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CC licensed content, Specific attribution<\/div>