If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

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  1. answer :-

    Step 1 : Write the correct equation. Combined variation problems are solved using a combination of variation equations. In this case, you will combine the direct and inverse variation equations, use f, g, and h instead of x, y, and z, and notice how the word “square” changes the equation.

    Y = KX/Z --» F = KG/H^2.

    Step 2 : Use the information given in the problem to find the value of k. In this case, you need to find k when f = 20, g = 50, and h = 5.

    20 = K(50)/5^2.

    20 = 2K.

    10 = K.

    Step 3 : Rewrite the equation from step 1 substituting in the value of k found in step 2.

    F = 10G/H^2.

    Step 4 : Use the equation found in step 3 and the remaining information given in the problem to answer the question asked. In this case, you need to find f when g = 18 and h = 6.

    F = 10(18)/6^2.

    Therefore , F = 5.

  2. answer:   x = 3 + √11     and     x = 3 - √11

    step-by-step explanation:

    x² - 6x + 9 = 11

    (x - 3)² = 11

    x - 3 = ±√11

        x = 3 ± √11

    x = 3 + √11     and     x = 3 - √11

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