Q: The coordinates of the point 1 A
2. Try to find the relationship between the movement of point P on OA line and the movement time of S.
2. The owner of a stationery retail store went to the wholesale market to buy two kinds of stationery, A and B. The wholesale prices were 12 yuan/piece and 8 yuan/piece respectively. If the daily sales volume y (pieces) and retail price x (yuan/piece) of two kinds of stationery in retail stores are described as linear functions (as shown in the figure).
(1) Find the functional relationship between y and x;
(2) The owner of our store plans to buy 100 pieces of stationery A and B this time, and the cost will not exceed 1000 yuan, hoping to make a profit of not less than 296 yuan after all of them are sold out. If the daily sales volume of stationery A is 4 pieces and each stationery B can make a profit, what kind of purchase plan does he have this time?
(3) If the retail price of stationery A is higher than that of stationery B by 2 yuan/piece, what is the retail price of two kinds of stationery, and the daily sales profit is the largest?
3. If the triangle area enclosed by the straight line y=-2x+b and the two coordinate axes is 9, then the value of b is ().
4. It is known that the image of the linear function y=kx+b intersects with the Y axis at point P through point A (-2,5), the straight line y= 1/2x+3 intersects with the Y axis at point Q, and the points Q and P are exactly symmetrical about the X axis, so as to find the linear resolution function.
At present, it is planned to transport Class A goods 1240t and Class B goods 840t to a certain place by one train. This train has two different carriages, A and B. The cost of using Class A carriage is 6000 yuan, and Class B is 8000 yuan.
1)。 Assuming that the total cost of the train transporting this batch of goods is Y yuan, this train is connected with X section of Type A train, and write the resolution function of Y about X (the range of independent variables is not required).
2)。 If each A-type vehicle can armor 35t Class A cargo and 15t Class B cargo at most, and each B-type vehicle can armor 25t and 35t Class B cargo at most, how many schemes are there to arrange the number of sections of Class A and Class B vehicles according to this requirement?
The answer: 1, the solution: 1, and the coordinates of point a are the solutions of equations y = x and y =-0.5x+6.
Solution: x=y=4
Therefore: a (4,4)
(2) b (6,0) can be obtained from y=-0.5x+6, so ob = 6.
A is AE⊥X axis, E is vertical foot, and PQ is in F.
Therefore: OE = AE = 4, therefore: OA = 4 √ 2.
Let the exercise time be x, then: OP = X, so: pa = 4 √ 2-x.
Because PQ‖X axis
Therefore: △APQ∽△AOB
Therefore: PA/OA=PQ/OB=AF/AE.
Therefore: PQ = 6-3 √ 2x/4; AF=4-√2x/2
Therefore: EF=√2x/2
When EF≤PQ, that is, √2x/2≤6-3√2x/4, that is, 0 < x ≤ 12 √ 2/5, s = PQ? EF = √ 2x/2 (6-3 √ 2x/4), that is, S = 3 √ 2x-3x? /4
When EF≥PQ, that is, 12 √ 2/5 ≤ X < 4 √ 2, S = PQ? =(6-3√2x/4)？
2. Solution: (1) According to the graph, let the functional relationship between y and x be y=kx+b and substitute it into points (10, 10) and (15,5).
10k+b= 10
15k+b=5
The solution is k=- 1 b=20.
So the functional relationship between y and x is y=-x+20.
(2) Since the daily sales volume of stationery A is 4 pieces, y=4 is substituted into the function, and 4=-x+20.
The solution is x= 16.
So the retail price of stationery A is 16 yuan per piece.
Because every piece of stationery B can make a profit, the retail price of stationery B in 2 yuan is 10 yuan.
Suppose the boss buys X pieces of stationery A, and then (100-x) pieces of stationery B.
12 * x+8 *( 100-x)≤ 1000①
( 16- 12)* x+( 10-8)( 100-x)≥296②
Simultaneous ① ② two formulas, the solution is 48≤x≤50.
Because the number of stationery is a positive integer, X can be 48, 49, 50.
Y is 52,565,438+0,50.
* * * There are three schemes.
3) If the retail price of stationery A is higher than that of stationery B by 2 yuan/piece, what are the retail prices of the two kinds of stationery respectively, and the daily sales profit is the largest?
Solution: According to the meaning of the question, if the retail price of stationery A is X yuan, then the retail price of stationery B is (x-2) yuan. X≥ 12 depends on the meaning of the question.
When the retail price of stationery A is X yuan, the daily sales volume is (20-x) pieces.
The retail price of stationery B is (x-2) yuan, so the daily sales volume is (22-x) pieces.
So the daily sales profit w = (x-12) (20-x)+(x-2-8) (22-x).
=-2(x-32)^2+52
Therefore, when the retail price of stationery A is 32 yuan and that of stationery B is 30 yuan, the daily sales profit is the largest.
,3, +—6,
4. y= 1/2x+3 intersects with Y axis at point Q, so the coordinate of point Q is (0,3), so the coordinate of point P is (0,3), so the function y=kx+b passes through points A and P, and the analytical formula is Y=-4X-3.
5, (1), Y=6000X (2), 1 Only use the A-type truck to load all the goods; Type 2 car is used to load all goods; 3- Two kinds of cars are used to load goods respectively.