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Z varies inversely with x and directly with y. When x=6 and y=2 z=5 what is the value of a when x=4 and y=9

User Bammab
by
7.6k points

2 Answers

6 votes

Answer:

15·9

z = --------- = 135/4

4

Explanation:

The general formula here is as follows:

ky

z = ---------

x

We must find the value of the constant of proportionality. To do this, subst. 6 for x, 2 for y and 5 for z and compute k:

k·2

5 = ---------

6

Multiplying both sides by 6 results in 30 = 2k.

Thus, k = 30/2, or k = 15.

Our formula becomes:

15y

z = ---------

x

if x = 4 and y = 9, we get:

15·9

z = --------- = 135/4

4

User Adolfojp
by
8.6k points
5 votes

Answer:


z=33.75

Explanation:

We are given that z varies inversely with x and directly with y when x=6 and y=2 then z=5

We have to find the value of z when x=4 and y=9

According to question


z\propto(1)/(x)

and
z\proptoy

Therefore, we have
z\propto(y)/(x)


z=k(y)/(x)

k=proportionality constant

Substitute x=6 , y=2 and z=5 then we get


5=k* (2)/(6)


5=(k)/(3)


k=5*3

By division poperty of equality

k=15

Now, substitute the value x=4,y=9 and k=15 then the value of z


z=15* (9)/(4)


z=(135)/(4)


z==33.75

User Bhavesh Vadalia
by
8.3k points

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