Answer:
Step-by-step explanation:
The ratio of the side lengths (AB) and (BC) is given. One is also given an expression for the side lengths of each of these sides. Set up a proportion to describe this scenario, then solve using cross products;
Substitute,
Cross products,
Inverse operations,
Answer:
4 acres of wheat and 4 acres of rye.
Step-by-step explanation:
Given: Farmer has only 7 acre, he has plant at least 7 acres.
Farmer has only $1200 to spend.
Each acre of wheat will cost $200 and rye will cost $100.
Planting time is only 12 hours
Wheat planting take 1 hour per hour and rye take 2 hours per acre.
Profit on wheat is $500 per acre and rye $300 per acre.
As to find out maximum profit, we need to plant maximum wheat.
While dividing number of acres of land for wheat and rye for plantation, we need to keep two constraint in the mind; Constraint of cost and time as given.
Lets assume few number considering these constraint to get maximum profit.
First assumption, 5 acres of wheat and 2 acres of rye
Time taken=
Total time taken 7 hours
Amount spent=
Total cost is $ 1200.
Profit=
Maximum profit= $3100.
Second assumption, 4 acres of wheat and 4 acres of rye.
Times taken=
Total time taken is 12 hours
Amount spent=
Total cost is $1200.
Profit=
Maximum profit= $3200.
∴ By using hit and trail method, we can see that we are getting maximum profit when farmer is planting 4 acres of wheat and 4 acres of rye.
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