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Y varies directly as x and inversely as the square of z. Y=8 when x=25 and z =25 and z =5. Find y when x =3 and z=9

2 Answers

4 votes

Answer:

The answer is
y=(8)/(27).

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:


y=k* (x)/(z^2)


y=(kx)/(z^2)......(1)

Now, to find
k as the direct variation is:


Y=k(x)/(z^2)


Y=k* (x)/(z^2)

(As, the value of Y = 8, x=25 and z=5.)


8=k* (25)/(5^2)


8=k* (25)/(25)


8=k


k=8.

Now, to get the value of y when x=3 and z=9 by putting the value of
k in equation (1):


y=(kx)/(z^2)


y=(8* 3)/(9^2)


y=(24)/(81)


y=(8)/(27)

Therefore, the answer is
y=(8)/(27).

User Ericmp
by
8.7k points
7 votes

Answer:

For x =3 , y =
(24)/(25)

And for z = 9 , y =
(200)/(81)

Explanation:

Given as :

y = 8

x = 25

z = 5

The statements are

(i) y varies directly as x

i.e y ∝ x

Or , y =
k_1 × x

Now, for y = 8 , and x = 25

Or, 8 =
k_1 × 25


k_1 =
(8)/(25)

Again

(ii) y varies inversely as the square of z

i.e y ∝
(1)/(z^(2) )

Or, y =
k_2 ×
(1)/(z^(2) )

Or, y =
(k_2)/(z^(2) )

Now, for y = 8 and z = 5

i.e 8 =
(k_2)/(5^(2) )


k_2 = 8 × 25

Or,
k_2 = 200

Again

For, for x = 3 and z = 9

∵ y =
k_1 × x and
k_1 =
(8)/(25)

So, y =
(8)/(25) × 3

Or, y =
(24)/(25)

Similarly

∵ y =
(k_2)/(z^(2) ) and
k_2 = 200

So, y =
(200)/(9^(2) )

Or, y =
(200)/(81)

Hence, For x =3 , y =
(24)/(25)

And for z = 9 , y =
(200)/(81) Answer

User Petomalina
by
8.8k points

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