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Find the constant of proportionality k k if z=3600 z = 3600 when y=3 y = 3 and x=5 x =5 .

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Full solution

Q. Find the constant of proportionality k k if z=3600 z = 3600 when y=3 y = 3 and x=5 x =5 .
  1. Understand Relationship Between Variables: Understand the relationship between the variables. In a direct variation with three variables, the relationship can be expressed as z=kxyz = kxy, where kk is the constant of proportionality.
  2. Substitute Given Values: Substitute the given values into the direct variation equation.\newlineWe know that z=3600z = 3600, y=3y = 3, and x=5x = 5. Substitute these values into the equation z=kxyz = kxy to find kk.\newline3600=k×3×53600 = k \times 3 \times 5
  3. Solve for Constant kk: Solve for the constant of proportionality kk. To find kk, divide both sides of the equation by the product of xx and yy. k=3600(3×5)k = \frac{3600}{(3 \times 5)} k=360015k = \frac{3600}{15}
  4. Calculate Value of k: Calculate the value of kk. Perform the division to find the value of kk. k=240k = 240

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