Verified answer

✒ COMBINED VARIATION

• if m varies directly as n inversely as a and m=6 when n=3 and s =4 find m when n=6 and s =8

»Since k is the constant of variation, expressed as the formula to find the value of k.

» Now substitute the values, n = 6 and s = 8 to the equation

the value of m is 6 when n = 6 and s = 8.

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Problem:

If m varies directly as n inversely as s and m = 6 when n = 3 and s = 4 find m when n = 6 and s = 8.

Solution:

To translate into variation statement a relationship involving combined variation between two quantities.

The statement, "m varies directly as n inversely as s" translated into combined variation is m = kn/s where k is the constant of variation. Now, write an equation of a combined variation.

Solve if m is 6 when n is 3 and s is 4. So, find the constant using the equation of a combined variation.

• m = kn/s
• 6 = k(3)/4
• 6 = 3k/4
• 24/3 = 3k/3
• 8 = k or k = 8

The constant of the variation is 8. In equation of variation.

• m = 8n/s

Find m when n is 6 and s is 8. Substitute the equation using the constant of the variation that you obtained.

• m = 8n/s
• m = 8(6)/(8)
• m = 48/8
• m = 6

Answer:

∴ Therefore, the value of m is 6 to the combined variation.

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