Respuesta :

InesWalston

Answer-

The value of y is [tex]\dfrac{56}{3}[/tex] when x=7 and z=4.

Solution-

As given in the question, y is directly proportional to x, so

[tex]y\propto x[/tex]   -----------------1

And also y is directly proportional to z, so

[tex]y\propto z[/tex]   -----------------2

Combining equation 1 and 2,

[tex]\Rightarrow y\propto x.z[/tex]

[tex]\Rightarrow y=k.x.z[/tex]

Where,

k = proportionality constant

When x=6 and z=1, y=4. Putting theses values,

[tex]\Rightarrow 4=k\times 6\times 1[/tex]

[tex]\Rightarrow 4=6k[/tex]

[tex]\Rightarrow k=\dfrac{4}{6}[/tex]

[tex]\Rightarrow k=\dfrac{2}{3}[/tex]

Now, we have to find the value of y, when x=7 and z=4

[tex]\Rightarrow y=\dfrac{2}{3}\times 7\times 4[/tex]

[tex]\Rightarrow y=\dfrac{56}{3}[/tex]

Therefore, the value of y is [tex]\dfrac{56}{3}[/tex] when x=7 and z=4.

Answer:

[tex]y=\frac{56}{3}[/tex]

Step-by-step explanation:

We have been given that y varies directly as x and z.

We know that equation of two directly proportional quantities is in form [tex]y=kx[/tex], where, k is constant of proportionality.

Since y varies directly as x and z, so our equation would be [tex]y=k\cdot x\cdot z[/tex]

We are also told that [tex]y=4[/tex], [tex]x=6[/tex] and [tex]z=1[/tex]. Let us find constant of proportionality as:

[tex]4=k\cdot 6\cdot 1[/tex]

[tex]4=k\cdot 6[/tex]

[tex]\frac{4}{6}=\frac{k\cdot 6}{6}[/tex]

[tex]\frac{2}{3}=k[/tex]

[tex]y=\frac{2}{3}\cdot x\cdot z[/tex]

Now, we will solve for y by substituting [tex]k=\frac{2}{3}[/tex], [tex]x=7[/tex] and [tex]z=4[/tex]

[tex]y=\frac{2}{3}\cdot 7\cdot 4[/tex]

[tex]y=\frac{56}{3}[/tex]

Therefore, [tex]y=\frac{56}{3}[/tex].