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the quantity y varies directly as x and inversely as z. when x is 10 and z is 4, y is 15. what is y when x is 20 and z is 6? 1) 6 2) 20 3) 27 4) 30

Verified Answer :

Answer:

Option 2nd is correct

y = 20

Step-by-step explanation:

Joint variation says that:

if \(y \propto x\) and \(y \propto \frac{1}{z}\)

⇒\(y \propto\frac{x}{z}\)

then;

equation is in the form of :

\(y = k \cdot \frac{x}{z}\) where, k is the constant of variation.

As per the statement:

the quantity y varies directly as x and inversely as z.

then by definition we have;

\(y = k \cdot \frac{x}{z}\)         .....[1]

When x = 10, z = 4 and y = 15

Substitute these in [1] we have;

\(15 = k \cdot \frac{10}{4}\)

⇒\(15 = 2.5k\)

Divide both sides by 2.5 we have;

6 = k

or

k = 6

then;

\(y = 6 \cdot \frac{x}{z}\)    

we have to find y, when x = 20 and z = 6

Substitute these we have;

\(y = 6 \cdot \frac{20}{6}= 20\)

⇒y = 20

Therefore, the value of y = 20

ashishdwivedilVT

When x is 20 and z is 6, then the value of y will be 20.

What is Proportionality Constant?

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.

Here, according to question

y α x/z

y = kx/z

when, y = 15, x = 10 and z = 4

then, 15 = k.10/4

         k = 15 X 4 / 10

         k = 6

Now, y = 6x/z

at, x = 20 and z = 6

y = 6 X 20 / 6

y = 20

Thus, when x is 20 and z is 6, then the value of y will be 20.

Learn more about Proportionality constant from:

https://brainly.com/question/8598338

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