Use the distributive property to remove the parentheses. -5(6y - u - 2)
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I think you meant to say
and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.
Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives
Note that when x = 0 and y = 1, we have dy/dx = 3.
Differentiate both sides again with respect to x :
No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get
No, it is not.
That specific question is named the Delian Problem, where supposedly, Apollo, the Greek god, had asked for his altar to be doubled in size to stop a plague going around. The builders only had a compass and straightedge, but they couldn't figure out how to double the volume. The reason they couldn't was because there was no way to construct multiples of , which was what was needed to double the volume.
This problem is one called the impossible problems from antiquity, or problems the ancient Greeks could not solve with only a compass and a straightedge. Another example of one of these problems is how to trisect an angle.