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solve for the value of the consant of variation k, and then find the missing value.
1.)z varies jointly as the square root of the product of x and y, if z=3 when x=3 and y=12, find x when z=6 and y=64
2.)d varies jointly as h and g. if d=15 when h=14 and g=5, find g when h=21 and h=8.
3) q varies jointly as r and s. if q=2.4, when r=0.6 and s=0.8, find q when r=1.6 and s=.01

Sagot :

1)  [tex]z = k \sqrt{(x)(y)} [/tex]
      [tex] 3 = k \sqrt{(3)(12)} [/tex]
       [tex]3 = k \sqrt{36} [/tex]
       [tex] \frac{3}{6} = k \frac{6}{6} [/tex]
       [tex]k = \frac{1}{2} [/tex]
   
      [tex]6 = \frac{1}{2} \sqrt{(x)(64)} [/tex]
      [tex]6 = \frac{1}{2} (8) \sqrt{x} [/tex]
     [tex] \frac{6}{4} = \frac{6}{4} \sqrt{x} [/tex]
     [tex] ( \frac{3}{2}) ^{2} = ( \sqrt{x} )^{2} [/tex]
     [tex]x = \frac{9}{4} [/tex]

2.  d = k (h)(g)
     15 = k (14)(5)
     15 = k (70)
      [tex] \frac{15}{70} = k \frac{70}{70} [/tex]
      [tex] k = \frac{3}{14} [/tex]
   
     use the equation : 
     
     d = 3/14 (h)(g)   for the next set.  check that your values has no d, but 2 h's

3)  q = krs
      2.4 = k (0.6) (0.8)
      2.4 = k (0.48)
     0.48       0.48
         k = 5
     
      q = krs
      q = 5 (1.6) (0.01)
     q = 0.08