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Question:</h2>
Write a general formula to describe each variation.
The square of T varies directly with the cube of a and inversely with the square of d; T = 4 when a = 2 and d = 3
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Answer:</h2>
T² =
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Step-by-step explanation:</h2>
Few things to note:
i.<em> direct variation</em>: When a variable x varies directly with another variable y, we write it in this form;
x ∝ y.
This can then be written as;
x = ky
Where;
k = constant of proportionality variation.
ii.<em> inverse variation</em>: When a variable x varies inversely with another variable y, we write it in this form;
x ∝
This can then be written as;
x = k()
Where;
k = constant of proportionality or variation
iii. <em>combined variation</em>: When a variable x varies directly with variable y and inversely with variable z, we write it in this form;
x ∝ ()
This can then be written as;
x = k ()
Where;
k = constant of proportionality or variation
<em>From the question;</em>
<em>The square of </em><em>T</em><em> varies directly with the cube of </em><em>a </em> and inversely with the square of <em>d.</em>
<u><em>Note that</em></u>
square of T = T²
cube of a = a³
square of d = d²
Therefore, we can write;
T² ∝
=> T² = k () -------------------(i)
Since;
T = 4 when a = 2 and d = 3
We can find the constant of proportionality k, by substituting the values of T=4, a = 2 and d = 3 into equation (i) and solve as follows;
(4)² = k ()
16 = k ()
8k = 16 x 9
8k = 144
k =
k = 18
Now substitute the value of k back into equation (i);
T² = 18 ()
T² =
Therefore, the general formula that describes the variation is;
T² =