Chris can make 8 shoes per hour on a good day. If a customer needs 24 shoes, how long will it take him to make the shoes?
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
Answer:
A
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
- 12 ÷ - 3 = - 48 ÷ - 12 = - 192 ÷ - 48 = 4
this indicates the sequence is geometric with nth term
= a₁
where a₁ is the first term and r the common ratio
here a₁ = - 3 and r = 4 , then
a₈ = - 3 × = - 3 × 16,384 = - 49,152