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One quantity varies as a power of another: given one pair, find the value at another

This type of question, asked 4 times: CDS 1 2019, CDS 2 2020, CDS 2 2023, CDS 2 2024. All 4 questions below, oldest first.

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  1. Question 1

    CDS 1 2019

    75
    Given yy is inversely proportional to x\sqrt{x}, and x=36x = 36 when y=36y = 36. What is the value of xx when y=54y = 54 ?

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  2. Question 2

    CDS 2 2020

    42
    When a ball is allowed to fall, the time it takes to fall any distance varies as the square root of the distance and it takes 4 seconds to fall 78.40 m. How long would it take to fall 122.50 m ?

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  3. Question 3

    CDS 2 2023

    64
    The cube root of x varies inversely as the square root of y. x = 8 when y = 3. What is the value of x when y=33y = \sqrt[3]{3} ?

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  4. Question 4

    CDS 2 2024

    6
    pp varies directly as (x2+y2+z2)(x^2 + y^2 + z^2). When x=1x = 1, y=2y = 2, z=3z = 3, then p=70p = 70. What is the value of pp when x=−1x = -1, y=1y = 1, z=5z = 5 ?

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