Answer:
[tex]a. \: k = \frac{4}{9} [/tex]
[tex]b. \: r = \frac{4}{3} [/tex]
[tex]c. \: s = 36[/tex]
[tex]d. \: u = 4[/tex]
Step-by-step explanation:
[tex]r = k \frac{s}{ {u}^{2} } [/tex]
a. Substitute the given value of r, s, u and solve for k.
[tex]2 = k \times \frac{18}{ {2}^{2} } \\ 2 = k \times \frac{18}{4} [/tex]
multiply both sides by 4/18
[tex] \frac{4}{18} \times 2 = k \\ \frac{8}{18} = k \\ \frac{4}{9} = k \\ k = \frac{4}{9} [/tex]
b. the formula became
[tex]r = \frac{4}{9} \times \frac{s}{ {u}^{2} } [/tex]
substitute the given value of s=27 and u=3 then solve for r.
[tex]r = \frac{4}{9} \times \frac{27}{ {3}^{2} } = \frac{4}{9} \times \frac{27}{9} = \frac{4}{3}[/tex]
c. Use the formula and substitute the given value of r=4 and u=2 then solve for s.
[tex]4 = \frac{4}{9} \times \frac{s}{ {2}^{2} } \\ 4 = \frac{4}{9} \times \frac{s}{ {4}} \\ 4 = \frac{s}{9} \\ 36 = s \\ s = 36[/tex]
d. Use the formula and substitute the given value of r=1 and s=36 then solve for u.
[tex]1 = \frac{4}{9} \times \frac{36}{ {u}^{2} } \\ 1 = \frac{16}{ {u}^{2} } \\ {u}^{2} = 16 \\ u = 4[/tex]
