① What is the average unit price of feed purchased by Party A and Party B?
(2) Whose purchase method is more reasonable?
Solution:
(1)∫A 1000kg each time, the unit price of feed purchased twice is m yuan /kg and n yuan /kg respectively.
∴ Party A pays (1000m+ 1000n) to purchase twice,
Buyer B is in 800 yuan every time he spends money, no matter how much feed he buys.
∴ Party B buys (800/ m3 +800/ m3) kilograms in two times,
∴: The average unit price of feed purchased by Party A twice is (1000 m+1000 n)/2000? =(m+n)/2 yuan/kg,
∴ The average unit price of feed purchased by Party B twice is 2/(1/m+1/n) = 2mn/(m+n)? Yuan/kg;
(2) according to the meaning of the question? (m+n)/2-2mn/(m+n)=[(m+n)^2-4mn]/(2mn)=(m_n)^2/(2mn)
∫m, n is a positive number, m≠n,
∴(m-n)^2>0，
∴(m_n)^2/(2mn)>0，
∴(m+n)/2>； 2mn/(m+n)，
The average price of feed purchased twice by B is low, and the second way is reasonable.
As shown in the figure, it is known that in △ABC, AB=AC, ∠ BAC = 90, the straight lines passing through B and C respectively are vertical lines, and the vertical feet are E and F respectively, so I draw my own diagram.
(1) verification: △ Abe △ caf;
(2) When the straight line passing through A does not intersect with the hypotenuse BC, try to explore the relationship among the three line segments EF, BE and CF;