Fill in the table using this function rule
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Given that the rate of change of y with respect to x is inversely proportional to y². Its equation can be written as :-
where 'k' is the proportionality constant, it can take any real value.
We can solve it by integrating the above equation with respect to x.
Rewriting and rearranging the terms of above equation :-
y²·dy = k·dx
Integrating both sides :-
∫ y²·dy = ∫ k·dx
= k·x
y³ = 3·k·x + C
where C is the constant of integration.
So, y³ = 3·k·x + C is the final answer.
<span>The volume of a rectangular prism is:</span>
<span>
</span>
Where
l=lenght,
w=width
h=height
So, as this prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches, the volume is calculated as follows: