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*Use identity sinxcosx = 1/2sin2x

=5/2sin2x + 5cosx

*then use simple integration gives

=(-5/2 x1/2)cosx + 5sinx + c

= =5/4cosx +5sinx + c

5 + 5√ 2 - √ 8 - √ 16    (Break up all terms in terms of square roots of 2)

5 + 5√ 2 - √ 8 - 4

5 + 5√ 2 - 2 √ 2 - 4 

1 + 3√2

For this question, one would sum the algebraic lengths of the rectangle, creating a result of 4x + 16.

This is the algebraic perimeter of the rectangle which must be equated to the numerical value ...

Sinx differentiates to give cosx.

We then multiply this by the differential of "2x."

Which equals 2.

Our answer therefore is "2cos(2x)."

First, we must evaluate what is given in the question. As it can be seen, the expression indicates that the problem consists of a first-order differential equation. We are also given the values of x and t...