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mmm119
21.06.2021 •
Mathematics
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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Ответ:
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
T² =![\frac{18a^3}{d^2}](/tpl/images/1380/1727/84960.png)
Step-by-step explanation:Few things to note:
i. direct variation: 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. inverse variation: When a variable x varies inversely with another variable y, we write it in this form;
x ∝![\frac{1}{y}](/tpl/images/1380/1727/2d67c.png)
This can then be written as;
x = k(
)
Where;
k = constant of proportionality or variation
iii. combined variation: 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
From the question;
The square of T varies directly with the cube of a and inversely with the square of d.
Note that
square of T = T²
cube of a = a³
square of d = d²
Therefore, we can write;
T² ∝![\frac{a^3}{d^2}](/tpl/images/1380/1727/a430a.png)
=> 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 =![\frac{144}{8}](/tpl/images/1380/1727/b40e4.png)
k = 18
Now substitute the value of k back into equation (i);
T² = 18 (
)
T² =![\frac{18a^3}{d^2}](/tpl/images/1380/1727/84960.png)
Therefore, the general formula that describes the variation is;
T² =![\frac{18a^3}{d^2}](/tpl/images/1380/1727/84960.png)
Ответ:
25% would be the answer
Step-by-step explanation: