What is the sum of all the positive integers from square root 14 to square root 80
1 answer:
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Replace x with π/2 - x to get the equivalent integral
but the integrand is even, so this is really just
Substitute x = 1/2 arccot(u/2), which transforms the integral to
There are lots of ways to compute this. What I did was to consider the complex contour integral
where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be
which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit
and it follows that
Find sketch of parallelogram attached
Answer and explanation:
A parallelogram is a quadrilateral which is wider than it is long. A parallelogram has two sides parallel to the other. From the above, we are told the parallelogram PQRS has an angle QPS 120, with sides 10cm and 8cm, we use this to sketch the parallelogram
We find that angle QPS is 120 degrees hence angle RSP is 60 degrees since angle on straight line is 60 degrees from 180-120 in angle QPS and alternate angles are equal. Also opposite angles of a parallelogram are equal
