Formula
l×w×h=volume
12×5×9=v
540=v
Is it? I would say it is not.
The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
The angle of rotation for a regular polygon is 360/number of sides.Here, it is 360/20=18 degrees.
Given:
Consider the below figure attached with this question.
The table represents a proportional relationship.
To find:
The missing value from the table.
Solution:
If y is proportional to x, then
...(i)
Where, k is a constant of proportionality.
The relationship passes through the point (-3,-1). Substituting 
in (i), we get
Putting 
in (i), we get
...(ii)
We need to find the y-value for 
.
Substituting in (ii), we get
Therefore, the missing value in the table is -4. Hence, option D is correct.
