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If r varies directly as the square of t and r is 20 when t is 2, find r when
t is 7

Sagot :

NataleighScottlynidn

Problem:

If r varies directly as the square of t and r is 20 when t is 2, find r when t is 7.

Solution:

A direct variation is a relationship between two variables, x and y, that can be written as y = kx where k ≠ 0.

The statement, "r varies directly as the square of t" translated into directly variation is r = kt² where k is the constant of variation.

Solve if r is 20 and t is 2. So, find the constant using the equation of a combined variation.

  • r = kt²
  • (20) = k(2)²
  • 20 = k(4)
  • 20 = 4k
  • 4k/4 = 20/4
  • k = 5

The constant of the variation is 5. In equation of variation.

  • r = 5t²

Find r when t is 7. Substitute the equation using the constant of the variation that you obtained.

  • r = 5t²
  • r = 5(7)²
  • r = 5(49)
  • r = 245

Answer:

∴ Therefore, the value of r is 245 to the directly variation.

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