A glass is
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The triangle below has a perimeter of 27\text{ cm}27 cm27, start text, space, c, m, end text.
What is the length of one side of the triangle?
All 333 sides are the same length.
Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.
so.. that'd be the V(x) for such box, now, where is the maximum point at?
now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.
so, the volume will then be at
so.. that'd be the V(x) for such box, now, where is the maximum point at?
now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.
so, the volume will then be at
The slope of the tangent line to at
is given by the derivative of
at that point:
Factorize the numerator:
We have approaching -1; in particular, this means
, so that
Then
and the tangent line's equation is