{"id":1598,"date":"2021-12-02T19:38:42","date_gmt":"2021-12-03T00:38:42","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-7\/"},"modified":"2023-09-01T12:16:43","modified_gmt":"2023-09-01T16:16:43","slug":"answer-key-2-7","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-2-7\/","title":{"raw":"Answer Key 2.7","rendered":"Answer Key 2.7"},"content":{"raw":"
    \r\n \t
  1. [latex]x=ky[\/latex]<\/li>\r\n \t
  2. [latex]x=kyz[\/latex]<\/li>\r\n \t
  3. [latex]x=\\dfrac{k}{y}[\/latex]<\/li>\r\n \t
  4. [latex]x=ky^2[\/latex]<\/li>\r\n \t
  5. [latex]x=kzy[\/latex]<\/li>\r\n \t
  6. [latex]x=\\dfrac{k}{y^3}[\/latex]<\/li>\r\n \t
  7. [latex]x=ky^2\\sqrt{z}[\/latex]<\/li>\r\n \t
  8. [latex]x=\\dfrac{k}{y^6}[\/latex]<\/li>\r\n \t
  9. [latex]x=\\dfrac{ky^3}{\\sqrt{z}}[\/latex]<\/li>\r\n \t
  10. [latex]x=\\dfrac{k}{y^2\\sqrt{z}}[\/latex]<\/li>\r\n \t
  11. [latex]x=\\dfrac{kzy}{p^3}[\/latex]<\/li>\r\n \t
  12. [latex]x=\\dfrac{k}{y^3z^2}[\/latex]<\/li>\r\n \t
  13. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nA&=&kB \\\\ \\\\\r\n(15)&=&k(5) \\\\ \\\\\r\n\\dfrac{15}{5}&=&\\dfrac{k(5)}{5} \\\\ \\\\\r\nk&=&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  14. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nP&=&kQR \\\\ \\\\\r\n(12)&=&k(8)(3) \\\\ \\\\\r\n\\dfrac{12}{24}&=&\\dfrac{k(8)(3)}{24} \\\\ \\\\\r\nk&=&\\dfrac{1}{2}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nA&=&\\dfrac{k}{B} \\\\ \\\\\r\n(7)&=&\\dfrac{k}{(4)} \\\\ \\\\\r\n(4)7&=&\\dfrac{k}{\\cancel{4}}\\cancel{(4)} \\\\ \\\\\r\nk&=&28\r\n\\end{array}[\/latex]<\/li>\r\n \t
  16. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nA&=&kB^2 \\\\ \\\\\r\n(6)&=&k(3)^2 \\\\ \\\\\r\n\\dfrac{6}{9}&=&\\dfrac{k(3)^2}{9} \\\\ \\\\\r\nk&=&\\dfrac{6}{9}\\text{ or }\\dfrac{2}{3}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  17. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nC&=&kAB \\\\ \\\\\r\n(24)&=&k(3)(2) \\\\ \\\\\r\n\\dfrac{24}{6}&=&\\dfrac{k(3)(2)}{6} \\\\ \\\\\r\nk&=&4\r\n\\end{array}[\/latex]<\/li>\r\n \t
  18. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\ny&=&\\dfrac{k}{x^3} \\\\ \\\\\r\n(54)&=&\\dfrac{k}{(3)^3} \\\\ \\\\\r\n54&=&\\dfrac{k}{27} \\\\ \\\\\r\n27\\cdot 54&=&\\dfrac{k}{\\cancel{27}}\\cdot \\cancel{27} \\\\ \\\\\r\nk&=&1458\r\n\\end{array}[\/latex]<\/li>\r\n \t
  19. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nx&=&kY \\\\ \\\\\r\n(12)&=&k(8) \\\\ \\\\\r\n\\dfrac{12}{8}&=&\\dfrac{k(8)}{8} \\\\ \\\\\r\nk&=&\\dfrac{12}{8}\\text{ or }\\dfrac{3}{2}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  20. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nA&=&kB^2\\sqrt{C} \\\\ \\\\\r\n(25)&=&k(5)^2\\sqrt{(9)} \\\\ \\\\\r\n25&=&k(75) \\\\ \\\\\r\nk&=&\\dfrac{25}{75} \\\\ \\\\\r\nk&=&\\dfrac{1}{3}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  21. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\ny&=&\\dfrac{kmn^2}{d} \\\\ \\\\\r\n(10)&=&\\dfrac{k(4)(5)^2}{(6)} \\\\ \\\\\r\nk&=&\\dfrac{\\cancel{10}\\cancel{5}\\cdot \\cancel{6}3}{\\cancel{(4)}(5)^{\\cancel{2}}} \\\\ \\\\\r\nk&=&\\dfrac{3}{5}\r\n\\end{array}[\/latex]<\/li>\r\n \t
  22. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrl}\r\nP&=&\\dfrac{kT}{V} \\\\ \\\\\r\n(10)&=&\\dfrac{k(250)}{(400)} \\\\ \\\\\r\nk&=&\\dfrac{10(400)}{250} \\\\ \\\\\r\nk&=&16\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n
      \r\n \t
    1. [latex]I=kV[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nI&=&5 \\text{ A} \\\\\r\nV&=&15\\text{ V} \\\\\r\nk&=&\\text{find} \\\\ \\\\\r\nI&=&kV \\\\\r\n5\\text{ A}&=&k(\\text{15 V}) \\\\ \\\\\r\nk&=&\\dfrac{\\text{5 A}}{\\text{15 V}} \\\\ \\\\\r\nk&=&\\dfrac{1}{3}\\text{ A\/V}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nI&=&\\text{find} \\\\\r\nk&=&\\dfrac{1}{3} \\\\ \\\\\r\nV&=&\\text{25 V} \\\\ \\\\\r\nI&=&kV \\\\\r\nI&=&\\left(\\dfrac{1}{3}\\right)(25) \\\\ \\\\\r\nI&=&8\\dfrac{1}{3}\\text{ A}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    2. [latex]I=\\dfrac{k}{R} [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nI&=&\\text{12 A} \\\\\r\nk&=&\\text{find} \\\\\r\nR&=&240\\Omega \\\\ \\\\\r\nI&=&\\dfrac{k}{R} \\\\ \\\\\r\n\\text{12 A}&=&\\dfrac{k}{240\\Omega} \\\\ \\\\\r\nk&=&(\\text{12 A})(240\\Omega) \\\\\r\nk&=&2880\\text{ A}\\Omega\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nI&=&\\text{find} \\\\\r\nk&=&2880 \\\\\r\nR&=&540\\Omega \\\\ \\\\\r\nI&=&\\dfrac{k}{R} \\\\ \\\\\r\nI&=&\\dfrac{2880\\text{ A}\\Omega}{540\\Omega} \\\\ \\\\\r\nI&=&5.\\bar{3}\\text{ A or }5\\dfrac{1}{3}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    3. [latex]d_{\\text{s}}=km [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nd_{\\text{s}}&=&18\\text{ cm} \\\\\r\nk&=&\\text{find} \\\\\r\nm&=&3\\text{ kg} \\\\ \\\\\r\n18\\text{ cm}&=&k(3\\text{ kg}) \\\\ \\\\\r\nk&=&\\dfrac{\\text{18 cm}}{\\text{3 kg}} \\\\ \\\\\r\nk&=&\\text{6 cm\/kg}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nd_{\\text{s}}&=&\\text{find} \\\\\r\nk&=&\\text{6 cm\/kg} \\\\\r\nm&=&\\text{5 kg} \\\\ \\\\\r\nd_{\\text{s}}&=&(\\text{6 cm\/kg})(\\text{5 kg}) \\\\\r\nd_{\\text{s}}&=&\\text{30 cm}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    4. [latex]V=\\dfrac{k}{P} [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nP&=&32\\text{ kg\/cm}^2 \\\\\r\nV&=&200\\text{ cm}^3 \\\\\r\nk&=&\\text{find} \\\\ \\\\\r\n200\\text{ cm}^3&=&\\dfrac{k}{32\\text{ kg\/cm}^2} \\\\ \\\\\r\nk&=&(200\\text{ cm}^3)(32\\text{ kg\/cm}^2) \\\\\r\nk&=&6400\\text{ kg cm}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nP&=&40 \\\\\r\nV&=&\\text{find} \\\\\r\nk&=&6400 \\\\ \\\\\r\nV&=&\\dfrac{6400}{40} \\\\ \\\\\r\nV&=&160\\text{ cm}^3\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    5. [latex]c=kP [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nc&=&60,000 \\\\\r\nk&=&\\text{find} \\\\\r\nP&=&250 \\\\ \\\\\r\n60,000&=&k(250) \\\\ \\\\\r\nk&=&\\dfrac{60,000}{250} \\\\ \\\\\r\nk&=&240\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&& \\textbf{2nd Data} \\\\\r\nc&=&\\text{find} \\\\\r\nk&=&240 \\\\\r\nP&=&1,000,000 \\\\ \\\\\r\nc&=&(240)(1,000,000) \\\\\r\nc&=&240,000,000\\text{ or 240 million}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    6. [latex]t=\\dfrac{k}{b}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nt&=&5\\text{ h} \\\\\r\nk&=&\\text{find} \\\\\r\nb&=&7 \\\\ \\\\\r\n5\\text{ h}&=&\\dfrac{k}{7} \\\\ \\\\\r\nk&=&\\text{(5 h)}(7) \\\\\r\nk&=&35\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nt&=&\\text{find} \\\\\r\nk&=&35 \\\\\r\nb&=&10 \\\\ \\\\\r\nt&=&\\dfrac{35}{10} \\\\ \\\\\r\nt&=&3.5\\text{ h}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    7. [latex]\\lambda=\\dfrac{k}{f} [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\n\\lambda&=&250\\text{ m} \\\\\r\nk&=&\\text{find} \\\\\r\nf&=&1200\\text{ kHz} \\\\ \\\\\r\n250&=&\\dfrac{k}{1200} \\\\ \\\\\r\nk&=&(250)(1200) \\\\\r\nk&=&300,000\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\n\\lambda&=&\\text{find} \\\\\r\nk&=&300,000 \\\\\r\nf&=&60\\text{ kHz} \\\\ \\\\\r\n\\lambda&=&\\dfrac{300,000}{60} \\\\ \\\\\r\n\\lambda&=&5000\\text{ m}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    8. [latex]w=km [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&& \\textbf{1st Data} \\\\\r\nw&=&64\\text{ kg} \\\\\r\nk&=&\\text{find} \\\\\r\nm&=&96\\text{ kg} \\\\ \\\\\r\n64&=&k(96) \\\\ \\\\\r\nk&=&\\dfrac{64}{96} \\\\ \\\\\r\nk&=&\\dfrac{2}{3}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nw&=&\\text{find} \\\\\r\nk&=&\\dfrac{2}{3} \\\\\r\nm&=&60\\text{ kg} \\\\ \\\\\r\nw&=&\\left(\\dfrac{2}{3}\\right)(60\\text{ kg}) \\\\ \\\\\r\nw&=&40\\text{ kg}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    9. [latex]t=\\dfrac{d}{v}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nt&=&\\text{5 h} \\\\\r\nd&=&\\text{find} \\\\\r\nv&=&\\text{80 km\/h} \\\\ \\\\\r\n\\text{5 h}&=&\\dfrac{d}{\\text{80 km\/h}} \\\\ \\\\\r\nd&=&5(80) \\\\\r\nd&=&\\text{400 km}\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nt&=&\\text{4.2 h} \\\\\r\nd&=&\\text{400 km} \\\\\r\nv&=&\\text{find} \\\\ \\\\\r\n4.2&=&\\dfrac{400}{v} \\\\ \\\\\r\nv&=&\\dfrac{400}{4.2} \\\\ \\\\\r\nv&=&95.24\\text{ km\/h}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    10. [latex]V=khr^2 [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nV&=&33.5\\text{ cm}^3 \\\\\r\nk&=&\\text{find} \\\\\r\nh&=&\\text{8 cm} \\\\\r\nr&=&\\text{2 cm} \\\\ \\\\\r\n33.5&=&k(8)(2)^2 \\\\ \\\\\r\nk&=&\\dfrac{33.5}{(8)(2)^2} \\\\ \\\\\r\nk&=&1.046875\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nV&=&\\text{find} \\\\\r\nk&=&1.046875 \\\\\r\nh&=&\\text{6 cm} \\\\\r\nr&=&\\text{4 cm} \\\\ \\\\\r\nV&=&khr^2 \\\\\r\nV&=&(1.046875)(6)(4)^2 \\\\\r\nV&=&100.5\\text{ cm}^3\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    11. [latex]F_{\\text{e}}=\\dfrac{kv^2}{r} [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nF_{\\text{e}}&=&100\\text{ N} \\\\\r\nk&=&\\text{find} \\\\\r\nv&=&10\\text{ m\/s} \\\\\r\nr&=&\\text{0.5 m} \\\\ \\\\\r\n100\\text{ N}&=&\\dfrac{k(10 \\text{ m\/s})^2}{\\text{0.5 m}} \\\\ \\\\\r\nk&=&\\dfrac{(0.5)(100)}{(10)^2} \\\\ \\\\\r\nk&=&0.5\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nF_{\\text{e}}&=&\\text{find} \\\\\r\nk&=&0.5 \\\\\r\nv&=&25\\text{ m\/s} \\\\\r\nr&=&1.0\\text{ m} \\\\ \\\\\r\nF_{\\text{e}}&=&\\dfrac{0.5(25)^2}{1.0} \\\\ \\\\\r\nF_{\\text{e}}&=&312.5\\text{ N}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    12. [latex]L_{\\text{max}}=\\dfrac{kd^4}{h^2} [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nL_{\\text{max}}&=&64\\text{ tonnes} \\\\\r\nk&=&\\text{find} \\\\\r\nd&=&2.0\\text{ m} \\\\\r\nh&=&8.0\\text{ m} \\\\ \\\\\r\n64&=&\\dfrac{k(2)^4}{(8)^2} \\\\ \\\\\r\nk&=&\\dfrac{64(8)^2}{(2)^4} \\\\ \\\\\r\nk&=&256\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nL_{\\text{max}}&=&\\text{find} \\\\\r\nk&=&256 \\\\\r\nd&=&3.0\\text{ m} \\\\\r\nh&=&12.0\\text{ m} \\\\ \\\\\r\nL_{\\text{max}}&=&\\dfrac{(256)(3.0)^4}{(12.0)^2} \\\\ \\\\\r\nL_{\\text{max}}&=&144\\text{ tonnes}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    13. [latex]V=\\dfrac{kT}{P}[\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nV&=&225\\text{ cc} \\\\\r\nk&=&\\text{find} \\\\\r\nT&=&300\\text{ K} \\\\\r\nP&=&100\\text{ N\/cm}^2 \\\\ \\\\\r\nV&=&\\dfrac{kT}{P} \\\\ \\\\\r\n225&=&\\dfrac{k(300)}{100} \\\\ \\\\\r\nk&=&\\dfrac{225(100)}{300} \\\\ \\\\\r\nk&=&75\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nV&=&\\text{find} \\\\\r\nk&=&75 \\\\\r\nT&=&270 \\\\\r\nP&=&150 \\\\ \\\\\r\nV&=&\\dfrac{75(270)}{150} \\\\ \\\\\r\nV&=&135\\text{ cc}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    14. [latex]R=\\dfrac{kl}{d^2} [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nR&=&20\\Omega \\\\\r\nk&=&\\text{find} \\\\\r\nl&=&5.0\\text{ m} \\\\\r\nd&=&0.25\\text{ cm} \\\\ \\\\\r\nR&=&\\dfrac{kl}{d^2} \\\\ \\\\\r\n20\\Omega&=&\\dfrac{k(5.0\\text{ m})}{\\text{(0.25 cm)}^2} \\\\ \\\\\r\nk&=&\\dfrac{(20 \\Omega)\\text{(0.25 cm)}^2}{\\text{5.0 m}} \\\\ \\\\\r\nk&=&0.25\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nR&=&\\text{find} \\\\\r\nk&=&0.25 \\\\\r\nl&=&10.0\\text{ m} \\\\\r\nd&=&0.50\\text{ cm} \\\\ \\\\\r\nR&=&\\dfrac{(0.25)\\text{(10.0 m)}}{\\text{(0.50 cm)}^2} \\\\ \\\\\r\nR&=&10\\Omega\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n \t
    15. [latex]V=khd^2 [\/latex]\r\n[latex]\\begin{array}[t]{ll}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{1st Data} \\\\\r\nV&=&377\\text{ m}^3 \\\\\r\nk&=&\\text{find} \\\\\r\nh&=&30\\text{ m} \\\\\r\nd&=&2.0\\text{ m} \\\\ \\\\\r\n377\\text{ m}^3&=&k(30)(2.0)^2 \\\\ \\\\\r\nk&=&\\dfrac{377}{(30)(2.0)^2} \\\\ \\\\\r\nk&=&3.1416\r\n\\end{array}\r\n& \\hspace{0.5in}\r\n\\begin{array}[t]{rrl}\r\n&&\\textbf{2nd Data} \\\\\r\nV&=&225\\text{ m}^3 \\\\\r\nk&=&3.1416 \\\\\r\nh&=&\\text{find} \\\\\r\nd&=&1.75\\text{ m} \\\\ \\\\\r\n225&=&\\pi h(1.75)^2 \\\\ \\\\\r\nh&=&\\dfrac{225}{\\pi (1.75)^2} \\\\ \\\\\r\nh&=&23.4\\text{ m}\r\n\\end{array}\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
        \n
      1. [latex]x=ky[\/latex]<\/li>\n
      2. [latex]x=kyz[\/latex]<\/li>\n
      3. [latex]x=\\dfrac{k}{y}[\/latex]<\/li>\n
      4. [latex]x=ky^2[\/latex]<\/li>\n
      5. [latex]x=kzy[\/latex]<\/li>\n
      6. [latex]x=\\dfrac{k}{y^3}[\/latex]<\/li>\n
      7. [latex]x=ky^2\\sqrt{z}[\/latex]<\/li>\n
      8. [latex]x=\\dfrac{k}{y^6}[\/latex]<\/li>\n
      9. [latex]x=\\dfrac{ky^3}{\\sqrt{z}}[\/latex]<\/li>\n
      10. [latex]x=\\dfrac{k}{y^2\\sqrt{z}}[\/latex]<\/li>\n
      11. [latex]x=\\dfrac{kzy}{p^3}[\/latex]<\/li>\n
      12. [latex]x=\\dfrac{k}{y^3z^2}[\/latex]<\/li>\n
      13. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} A&=&kB \\\\ \\\\ (15)&=&k(5) \\\\ \\\\ \\dfrac{15}{5}&=&\\dfrac{k(5)}{5} \\\\ \\\\ k&=&3 \\end{array}[\/latex]<\/li>\n
      14. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} P&=&kQR \\\\ \\\\ (12)&=&k(8)(3) \\\\ \\\\ \\dfrac{12}{24}&=&\\dfrac{k(8)(3)}{24} \\\\ \\\\ k&=&\\dfrac{1}{2} \\end{array}[\/latex]<\/li>\n
      15. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} A&=&\\dfrac{k}{B} \\\\ \\\\ (7)&=&\\dfrac{k}{(4)} \\\\ \\\\ (4)7&=&\\dfrac{k}{\\cancel{4}}\\cancel{(4)} \\\\ \\\\ k&=&28 \\end{array}[\/latex]<\/li>\n
      16. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} A&=&kB^2 \\\\ \\\\ (6)&=&k(3)^2 \\\\ \\\\ \\dfrac{6}{9}&=&\\dfrac{k(3)^2}{9} \\\\ \\\\ k&=&\\dfrac{6}{9}\\text{ or }\\dfrac{2}{3} \\end{array}[\/latex]<\/li>\n
      17. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} C&=&kAB \\\\ \\\\ (24)&=&k(3)(2) \\\\ \\\\ \\dfrac{24}{6}&=&\\dfrac{k(3)(2)}{6} \\\\ \\\\ k&=&4 \\end{array}[\/latex]<\/li>\n
      18. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} y&=&\\dfrac{k}{x^3} \\\\ \\\\ (54)&=&\\dfrac{k}{(3)^3} \\\\ \\\\ 54&=&\\dfrac{k}{27} \\\\ \\\\ 27\\cdot 54&=&\\dfrac{k}{\\cancel{27}}\\cdot \\cancel{27} \\\\ \\\\ k&=&1458 \\end{array}[\/latex]<\/li>\n
      19. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} x&=&kY \\\\ \\\\ (12)&=&k(8) \\\\ \\\\ \\dfrac{12}{8}&=&\\dfrac{k(8)}{8} \\\\ \\\\ k&=&\\dfrac{12}{8}\\text{ or }\\dfrac{3}{2} \\end{array}[\/latex]<\/li>\n
      20. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} A&=&kB^2\\sqrt{C} \\\\ \\\\ (25)&=&k(5)^2\\sqrt{(9)} \\\\ \\\\ 25&=&k(75) \\\\ \\\\ k&=&\\dfrac{25}{75} \\\\ \\\\ k&=&\\dfrac{1}{3} \\end{array}[\/latex]<\/li>\n
      21. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} y&=&\\dfrac{kmn^2}{d} \\\\ \\\\ (10)&=&\\dfrac{k(4)(5)^2}{(6)} \\\\ \\\\ k&=&\\dfrac{\\cancel{10}\\cancel{5}\\cdot \\cancel{6}3}{\\cancel{(4)}(5)^{\\cancel{2}}} \\\\ \\\\ k&=&\\dfrac{3}{5} \\end{array}[\/latex]<\/li>\n
      22. [latex]\\phantom{a}[\/latex]
        \n[latex]\\begin{array}[t]{rrl} P&=&\\dfrac{kT}{V} \\\\ \\\\ (10)&=&\\dfrac{k(250)}{(400)} \\\\ \\\\ k&=&\\dfrac{10(400)}{250} \\\\ \\\\ k&=&16 \\end{array}[\/latex]<\/li>\n<\/ol>\n
          \n
        1. [latex]I=kV[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ I&=&5 \\text{ A} \\\\ V&=&15\\text{ V} \\\\ k&=&\\text{find} \\\\ \\\\ I&=&kV \\\\ 5\\text{ A}&=&k(\\text{15 V}) \\\\ \\\\ k&=&\\dfrac{\\text{5 A}}{\\text{15 V}} \\\\ \\\\ k&=&\\dfrac{1}{3}\\text{ A\/V} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ I&=&\\text{find} \\\\ k&=&\\dfrac{1}{3} \\\\ \\\\ V&=&\\text{25 V} \\\\ \\\\ I&=&kV \\\\ I&=&\\left(\\dfrac{1}{3}\\right)(25) \\\\ \\\\ I&=&8\\dfrac{1}{3}\\text{ A} \\end{array} \\end{array}[\/latex]<\/li>\n
        2. [latex]I=\\dfrac{k}{R}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ I&=&\\text{12 A} \\\\ k&=&\\text{find} \\\\ R&=&240\\Omega \\\\ \\\\ I&=&\\dfrac{k}{R} \\\\ \\\\ \\text{12 A}&=&\\dfrac{k}{240\\Omega} \\\\ \\\\ k&=&(\\text{12 A})(240\\Omega) \\\\ k&=&2880\\text{ A}\\Omega \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ I&=&\\text{find} \\\\ k&=&2880 \\\\ R&=&540\\Omega \\\\ \\\\ I&=&\\dfrac{k}{R} \\\\ \\\\ I&=&\\dfrac{2880\\text{ A}\\Omega}{540\\Omega} \\\\ \\\\ I&=&5.\\bar{3}\\text{ A or }5\\dfrac{1}{3} \\end{array} \\end{array}[\/latex]<\/li>\n
        3. [latex]d_{\\text{s}}=km[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ d_{\\text{s}}&=&18\\text{ cm} \\\\ k&=&\\text{find} \\\\ m&=&3\\text{ kg} \\\\ \\\\ 18\\text{ cm}&=&k(3\\text{ kg}) \\\\ \\\\ k&=&\\dfrac{\\text{18 cm}}{\\text{3 kg}} \\\\ \\\\ k&=&\\text{6 cm\/kg} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ d_{\\text{s}}&=&\\text{find} \\\\ k&=&\\text{6 cm\/kg} \\\\ m&=&\\text{5 kg} \\\\ \\\\ d_{\\text{s}}&=&(\\text{6 cm\/kg})(\\text{5 kg}) \\\\ d_{\\text{s}}&=&\\text{30 cm} \\end{array} \\end{array}[\/latex]<\/li>\n
        4. [latex]V=\\dfrac{k}{P}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ P&=&32\\text{ kg\/cm}^2 \\\\ V&=&200\\text{ cm}^3 \\\\ k&=&\\text{find} \\\\ \\\\ 200\\text{ cm}^3&=&\\dfrac{k}{32\\text{ kg\/cm}^2} \\\\ \\\\ k&=&(200\\text{ cm}^3)(32\\text{ kg\/cm}^2) \\\\ k&=&6400\\text{ kg cm} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ P&=&40 \\\\ V&=&\\text{find} \\\\ k&=&6400 \\\\ \\\\ V&=&\\dfrac{6400}{40} \\\\ \\\\ V&=&160\\text{ cm}^3 \\end{array} \\end{array}[\/latex]<\/li>\n
        5. [latex]c=kP[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ c&=&60,000 \\\\ k&=&\\text{find} \\\\ P&=&250 \\\\ \\\\ 60,000&=&k(250) \\\\ \\\\ k&=&\\dfrac{60,000}{250} \\\\ \\\\ k&=&240 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} && \\textbf{2nd Data} \\\\ c&=&\\text{find} \\\\ k&=&240 \\\\ P&=&1,000,000 \\\\ \\\\ c&=&(240)(1,000,000) \\\\ c&=&240,000,000\\text{ or 240 million} \\end{array} \\end{array}[\/latex]<\/li>\n
        6. [latex]t=\\dfrac{k}{b}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ t&=&5\\text{ h} \\\\ k&=&\\text{find} \\\\ b&=&7 \\\\ \\\\ 5\\text{ h}&=&\\dfrac{k}{7} \\\\ \\\\ k&=&\\text{(5 h)}(7) \\\\ k&=&35 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ t&=&\\text{find} \\\\ k&=&35 \\\\ b&=&10 \\\\ \\\\ t&=&\\dfrac{35}{10} \\\\ \\\\ t&=&3.5\\text{ h} \\end{array} \\end{array}[\/latex]<\/li>\n
        7. [latex]\\lambda=\\dfrac{k}{f}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ \\lambda&=&250\\text{ m} \\\\ k&=&\\text{find} \\\\ f&=&1200\\text{ kHz} \\\\ \\\\ 250&=&\\dfrac{k}{1200} \\\\ \\\\ k&=&(250)(1200) \\\\ k&=&300,000 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ \\lambda&=&\\text{find} \\\\ k&=&300,000 \\\\ f&=&60\\text{ kHz} \\\\ \\\\ \\lambda&=&\\dfrac{300,000}{60} \\\\ \\\\ \\lambda&=&5000\\text{ m} \\end{array} \\end{array}[\/latex]<\/li>\n
        8. [latex]w=km[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} && \\textbf{1st Data} \\\\ w&=&64\\text{ kg} \\\\ k&=&\\text{find} \\\\ m&=&96\\text{ kg} \\\\ \\\\ 64&=&k(96) \\\\ \\\\ k&=&\\dfrac{64}{96} \\\\ \\\\ k&=&\\dfrac{2}{3} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ w&=&\\text{find} \\\\ k&=&\\dfrac{2}{3} \\\\ m&=&60\\text{ kg} \\\\ \\\\ w&=&\\left(\\dfrac{2}{3}\\right)(60\\text{ kg}) \\\\ \\\\ w&=&40\\text{ kg} \\end{array} \\end{array}[\/latex]<\/li>\n
        9. [latex]t=\\dfrac{d}{v}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ t&=&\\text{5 h} \\\\ d&=&\\text{find} \\\\ v&=&\\text{80 km\/h} \\\\ \\\\ \\text{5 h}&=&\\dfrac{d}{\\text{80 km\/h}} \\\\ \\\\ d&=&5(80) \\\\ d&=&\\text{400 km} \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ t&=&\\text{4.2 h} \\\\ d&=&\\text{400 km} \\\\ v&=&\\text{find} \\\\ \\\\ 4.2&=&\\dfrac{400}{v} \\\\ \\\\ v&=&\\dfrac{400}{4.2} \\\\ \\\\ v&=&95.24\\text{ km\/h} \\end{array} \\end{array}[\/latex]<\/li>\n
        10. [latex]V=khr^2[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ V&=&33.5\\text{ cm}^3 \\\\ k&=&\\text{find} \\\\ h&=&\\text{8 cm} \\\\ r&=&\\text{2 cm} \\\\ \\\\ 33.5&=&k(8)(2)^2 \\\\ \\\\ k&=&\\dfrac{33.5}{(8)(2)^2} \\\\ \\\\ k&=&1.046875 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ V&=&\\text{find} \\\\ k&=&1.046875 \\\\ h&=&\\text{6 cm} \\\\ r&=&\\text{4 cm} \\\\ \\\\ V&=&khr^2 \\\\ V&=&(1.046875)(6)(4)^2 \\\\ V&=&100.5\\text{ cm}^3 \\end{array} \\end{array}[\/latex]<\/li>\n
        11. [latex]F_{\\text{e}}=\\dfrac{kv^2}{r}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ F_{\\text{e}}&=&100\\text{ N} \\\\ k&=&\\text{find} \\\\ v&=&10\\text{ m\/s} \\\\ r&=&\\text{0.5 m} \\\\ \\\\ 100\\text{ N}&=&\\dfrac{k(10 \\text{ m\/s})^2}{\\text{0.5 m}} \\\\ \\\\ k&=&\\dfrac{(0.5)(100)}{(10)^2} \\\\ \\\\ k&=&0.5 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ F_{\\text{e}}&=&\\text{find} \\\\ k&=&0.5 \\\\ v&=&25\\text{ m\/s} \\\\ r&=&1.0\\text{ m} \\\\ \\\\ F_{\\text{e}}&=&\\dfrac{0.5(25)^2}{1.0} \\\\ \\\\ F_{\\text{e}}&=&312.5\\text{ N} \\end{array} \\end{array}[\/latex]<\/li>\n
        12. [latex]L_{\\text{max}}=\\dfrac{kd^4}{h^2}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ L_{\\text{max}}&=&64\\text{ tonnes} \\\\ k&=&\\text{find} \\\\ d&=&2.0\\text{ m} \\\\ h&=&8.0\\text{ m} \\\\ \\\\ 64&=&\\dfrac{k(2)^4}{(8)^2} \\\\ \\\\ k&=&\\dfrac{64(8)^2}{(2)^4} \\\\ \\\\ k&=&256 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ L_{\\text{max}}&=&\\text{find} \\\\ k&=&256 \\\\ d&=&3.0\\text{ m} \\\\ h&=&12.0\\text{ m} \\\\ \\\\ L_{\\text{max}}&=&\\dfrac{(256)(3.0)^4}{(12.0)^2} \\\\ \\\\ L_{\\text{max}}&=&144\\text{ tonnes} \\end{array} \\end{array}[\/latex]<\/li>\n
        13. [latex]V=\\dfrac{kT}{P}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ V&=&225\\text{ cc} \\\\ k&=&\\text{find} \\\\ T&=&300\\text{ K} \\\\ P&=&100\\text{ N\/cm}^2 \\\\ \\\\ V&=&\\dfrac{kT}{P} \\\\ \\\\ 225&=&\\dfrac{k(300)}{100} \\\\ \\\\ k&=&\\dfrac{225(100)}{300} \\\\ \\\\ k&=&75 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ V&=&\\text{find} \\\\ k&=&75 \\\\ T&=&270 \\\\ P&=&150 \\\\ \\\\ V&=&\\dfrac{75(270)}{150} \\\\ \\\\ V&=&135\\text{ cc} \\end{array} \\end{array}[\/latex]<\/li>\n
        14. [latex]R=\\dfrac{kl}{d^2}[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ R&=&20\\Omega \\\\ k&=&\\text{find} \\\\ l&=&5.0\\text{ m} \\\\ d&=&0.25\\text{ cm} \\\\ \\\\ R&=&\\dfrac{kl}{d^2} \\\\ \\\\ 20\\Omega&=&\\dfrac{k(5.0\\text{ m})}{\\text{(0.25 cm)}^2} \\\\ \\\\ k&=&\\dfrac{(20 \\Omega)\\text{(0.25 cm)}^2}{\\text{5.0 m}} \\\\ \\\\ k&=&0.25 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ R&=&\\text{find} \\\\ k&=&0.25 \\\\ l&=&10.0\\text{ m} \\\\ d&=&0.50\\text{ cm} \\\\ \\\\ R&=&\\dfrac{(0.25)\\text{(10.0 m)}}{\\text{(0.50 cm)}^2} \\\\ \\\\ R&=&10\\Omega \\end{array} \\end{array}[\/latex]<\/li>\n
        15. [latex]V=khd^2[\/latex]
          \n[latex]\\begin{array}[t]{ll} \\begin{array}[t]{rrl} &&\\textbf{1st Data} \\\\ V&=&377\\text{ m}^3 \\\\ k&=&\\text{find} \\\\ h&=&30\\text{ m} \\\\ d&=&2.0\\text{ m} \\\\ \\\\ 377\\text{ m}^3&=&k(30)(2.0)^2 \\\\ \\\\ k&=&\\dfrac{377}{(30)(2.0)^2} \\\\ \\\\ k&=&3.1416 \\end{array} & \\hspace{0.5in} \\begin{array}[t]{rrl} &&\\textbf{2nd Data} \\\\ V&=&225\\text{ m}^3 \\\\ k&=&3.1416 \\\\ h&=&\\text{find} \\\\ d&=&1.75\\text{ m} \\\\ \\\\ 225&=&\\pi h(1.75)^2 \\\\ \\\\ h&=&\\dfrac{225}{\\pi (1.75)^2} \\\\ \\\\ h&=&23.4\\text{ m} \\end{array} \\end{array}[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":21,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1598","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1598","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":5,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1598\/revisions"}],"predecessor-version":[{"id":2201,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1598\/revisions\/2201"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1598\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1598"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1598"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1598"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}