Question

True or false? (Picture provided)

Answer 1

Answer:

False

Step-by-step explanation:

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

$y = k\frac{xz}{w^2}$

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.

$3 = k\frac{(3)(10)}{2^2}\\\\k = 3(\frac{4}{30})\\\\k = \frac{2}{5}\\\\k=0.4$

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

$4 = \frac{2}{5}\frac{(4)(20)}{4^2}\\\\4 = 2$

Equality is not satisfied. Then the statement is false

Answer 2

Answer:

False

Step-by-step 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.