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Direct, inverse or joint variation: find the constant, then the new value

This type of question, asked 5 times: 19 Jul 2023 S1, 26 Jul 2023 S4, 9 Sep 2024 S2, 19 Sep 2024 S2, 25 Sep 2024 S3. All 5 questions below, oldest first.

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  1. Question 1

    19 Jul 2023 S1

    70
    A varies directly as (B + 18) and A = 108 when B = 36. Find the value of A when B = 68.

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  2. Question 2

    26 Jul 2023 S4

    58
    The force (in pound-force) needed to keep a car from skidding on a curve varies directly with the weight of the car (in pounds) and the square of its speed (in miles per hour [mph]) and inversely with the radius (in feet) of the curve. Suppose 6125 pound-force is required to keep a 2750 pound car, travelling at a speed of 35 mph, from skidding on a curve of radius 550 feet. How much pound-force is then required to keep a 3600 pound car, travelling at a speed of 50 mph, from skidding on a curve of radius 750 feet?

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  3. Question 3

    9 Sep 2024 S2

    72
    If x varies inversely as y and x = 2 when y = 6, then the value of y when x = 3 is:

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  4. Question 4

    19 Sep 2024 S2

    58
    At a school building, there is an overhead tank. To fill this tank 50 buckets of water are required. Assume that the capacity of the bucket is reduced to two-fifth of the present. How many buckets of water are required to fill the same tank?

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  5. Question 5

    25 Sep 2024 S3

    58
    ‘x’ varies directly with the cube of ‘y’, and inversely with the square of ‘z’. If x=136x = \frac{1}{36} when y=2y = 2 and z=3z = 3, then what is the value of 800x800x when y=3y = 3 and z=5z = 5?

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