Answer :
Answer:
The answer is [tex]y=\frac{8}{27}[/tex].
Step-by-step explanation:
Given:
Y varies directly as x and inversely as the square of z.
Y=8 when x=25 and z =5.
Now. to find y when x=3 and z=9.
As given, Y varies directly as x and inversely as the square of z:
Y ∝ x/z².
Now, we multiply by k the constant of variation to convert to an equation:
[tex]y=k\times \frac{x}{z^2}[/tex]
[tex]y=\frac{kx}{z^2}[/tex]......(1)
Now, to find [tex]k[/tex] as the direct variation is:
[tex]Y=k\frac{x}{z^2}[/tex]
[tex]Y=k\times \frac{x}{z^2}[/tex]
(As, the value of Y = 8, x=25 and z=5.)
[tex]8=k\times \frac{25}{5^2}[/tex]
[tex]8=k\times \frac{25}{25}[/tex]
[tex]8=k[/tex]
[tex]k=8.[/tex]
Now, to get the value of y when x=3 and z=9 by putting the value of [tex]k[/tex] in equation (1):
[tex]y=\frac{kx}{z^2}[/tex]
[tex]y=\frac{8\times 3}{9^2}[/tex]
[tex]y=\frac{24}{81}[/tex]
[tex]y=\frac{8}{27}[/tex]
Therefore, the answer is [tex]y=\frac{8}{27}[/tex].
Answer:
For x =3 , y = [tex]\dfrac{24}{25}[/tex]
And for z = 9 , y = [tex]\dfrac{200}{81}[/tex]
Step-by-step explanation:
Given as :
y = 8
x = 25
z = 5
The statements are
(i) y varies directly as x
i.e y ∝ x
Or , y = [tex]k_1[/tex] × x
Now, for y = 8 , and x = 25
Or, 8 = [tex]k_1[/tex] × 25
∴ [tex]k_1[/tex] = [tex]\dfrac{8}{25}[/tex]
Again
(ii) y varies inversely as the square of z
i.e y ∝ [tex]\dfrac{1}{z^{2} }[/tex]
Or, y = [tex]k_2[/tex] × [tex]\dfrac{1}{z^{2} }[/tex]
Or, y = [tex]\dfrac{k_2}{z^{2} }[/tex]
Now, for y = 8 and z = 5
i.e 8 = [tex]\dfrac{k_2}{5^{2} }[/tex]
∴ [tex]k_2[/tex] = 8 × 25
Or, [tex]k_2[/tex] = 200
Again
For, for x = 3 and z = 9
∵ y = [tex]k_1[/tex] × x and [tex]k_1[/tex] = [tex]\dfrac{8}{25}[/tex]
So, y = [tex]\dfrac{8}{25}[/tex] × 3
Or, y = [tex]\dfrac{24}{25}[/tex]
Similarly
∵ y = [tex]\dfrac{k_2}{z^{2} }[/tex] and [tex]k_2[/tex] = 200
So, y = [tex]\dfrac{200}{9^{2} }[/tex]
Or, y = [tex]\dfrac{200}{81}[/tex]
Hence, For x =3 , y = [tex]\dfrac{24}{25}[/tex]
And for z = 9 , y = [tex]\dfrac{200}{81}[/tex] Answer