Question

True or false? (Picture provided)

Answer 1

False

Explanation:

We have given:

Y= kxz/w²

Where k is constant of proportionality.

To find the value of k we have:

y = 3, x=3 , z=10 , w = 2

Putting in the equation we get,

3 = 30k/4

30k = 12

k = 12/30

k = 2/5

k = 0.4

Putting the value of k in given equation we get,

where x = 4, z=20 , w =4 , y = 4

4 = (0.4)(4)(20)/(4)²

4 = (2/5)80/16

4=160/80

4≠2

So, it is false.

Answer 2

False

Explanation:

If we say that y varies in conjunction with x and z then and inversely with
`w^2`, this means that:

`y = k(xz)/(w^2)`

Where k is the proportionality constant of the equation.

To find k we need to know the values of the variables in the equation.

We know that when
`y = 3` then:

`x = 3\\z = 10\\w = 2`

With these values we can find k.

`3 = k((3)(10))/(2^2)\\\\k = 3((4)/(30))\\\\k = (2)/(5)\\\\k=0.4`

Now we need to prove that when
`y = 4` then:

`x = 4\\z =20\\w = 4`

Then we see if equality is satisfied for these values

`4 = (2)/(5)((4)(20))/(4^2)\\\\4 = 2`

Equality is not satisfied. Then the statement is false