1. If x varies directly as y and inversely as z, and x=10 when y=5 and z=3, for what value of z will x=3 and y=4?
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1. If x varies directly as y and inversely as z, and x=10 when y=5 and z=3, for what value of z
1. If x varies directly as y and inversely as z, and x=10 when y=5 and z=3, for what value of z will x=3 and y=4?
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Answer:
To find the value of z when x = 3 and y = 4, we can use the concept of direct and inverse variation.
First, let's set up the proportion based on the given information:
x/y ∝ 1/z
Now, let's substitute the initial values:
10/5 ∝ 1/3
Simplifying the proportion, we get:
2 ∝ 1/3
To find the value of z when x = 3 and y = 4, we can set up the new proportion:
3/4 ∝ 1/z
Now, let's solve for z:
(3/4) * z = 1
z = 4/3
Therefore, when x = 3 and y = 4, the value of z would be 4/3.