Respuesta :
The variable z is directly proportional to x, and inversely proportional to y.
[tex] z\alpha x [/tex]
and
[tex] z\alpha \frac{1}{y} [/tex]
So, [tex] z\alpha \frac{x}{y} [/tex]
[tex] z=k\frac{x}{y} [/tex]
where, k is the constant of proportionality.
When, x=8 and y=18, z is 1.33.
So, plugging x,y and z in z=k\frac{x}{y} to get the value of k we get,
[tex] 1.33=k\frac{8}{18} [/tex]
To isolate, k let us multiply by 18 on both sides
1.33*18=k[tex] \frac{8*18}{18} [/tex]
23.99=k[tex] \frac{8*1}{1} [/tex]
So, 23.99=8k
To solve for k, let us divide by 8 on both sides
[tex] \frac{23.99}{8}=\frac{8}{8} k [/tex]
2.99=[tex] \frac{1k}{1} [/tex]
k=3
Let us plug k=3, x=13 and y=22 to solve for z
[tex] z=3*\frac{13}{22} [/tex]
z=[tex] \frac{39}{22} [/tex]
z=1.77
Answer: z=1.77
The variable z is directly proportional to x, and inversely proportional to y,where k is the constant of proportionality. When, x=8 and y=18, z is 1.33.
So, plugging x,y and z in z=k\frac{x}{y} to get the value of k we get, To isolate, k let us multiply by 18 on both sides
1.33*18=k
23.99=k
So, 23.99=8k
To solve for k, let us divide by 8 on both sides. Let us plug k=3, x=13 and y=22 to solve for z.
z=1.77
Answer: z=1.77
