👤
Answered

if z is jointly proportional to x and y and z=8,when x=5 and y=6,find z when x=9 and y=6

Sagot :

KAntoineDoixgo

✒️VARIATIONS

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \:\: \rm z = \frac{72}5 \\ [/tex]

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

Formulate the equation of the variation where k is the constant of the variation.

  • [tex] z = kxy [/tex]

Find the value constant when z is 8, x is 5, and y is 6.

  • [tex] 8 = k(5)(6) [/tex]

  • [tex] 8 = k(30) [/tex]

  • [tex] \frac8{30} = \frac{k(30)}{30} \\ [/tex]

  • [tex] \frac4{15} = k \\ [/tex]

Thus, the constant is 4/15 Find z when x is 9 and y is 6.

  • [tex] z = \frac4{15}xy \\ [/tex]

  • [tex] z = \frac4{15}(9)(6) \\ [/tex]

  • [tex] z = \frac4{15}(54) \\ [/tex]

  • [tex] z = \frac{216}{15} \\ [/tex]

  • [tex] z = \frac{72}{5} \\ [/tex]

Therefore, the value of z is 72/5

[tex]••••••••••••••••••••••••••••••••••••••••••••••••••[/tex]

(ノ^_^)ノ

Go Training: Other Questions