Respuesta :
Answer:
Value of x = 400
Step-by-step explanation:
Joint variation states that describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them.
Given: x varies directly with y and z.
i.e [tex]x \propto y[/tex] and [tex]x \propto z[/tex]
then we have the joint variation as;
[tex]x = k yz[/tex] ......[1] where k is the constant variation.
Substitute the value of x =1200 when y =20 and z = 30 to solve for k;
[tex]1200 = k (20)(30)[/tex]
Simplify:
[tex]1200 = 600k[/tex]
Divide both sides by 600 we get;
[tex]k = 2[/tex]
Now, substitute k =2 , y =10 and z = 20 to find x;
Using [1] we have;
[tex]x = 2 \times (10)(20) = 2 \times 200[/tex]
Therefore, the value of x is, 400
Answer:
x = 400
Step-by-step explanation:
given that x varies directly with y and z the the equation relating them is
x = kyz ← k is the constant of variation
to find k use the given condition x = 1200 when y = 20 and z = 30
k = [tex]\frac{x}{yz}[/tex] = [tex]\frac{1200}{20(30)}[/tex] = 2, thus
x = 2yz is the direct variation equation
when y = 10 and z = 20, then
x = 2 × 10 × 20 = 400
