2. In △ABC, AB=8, ∠ ABC= 30, AC=5, then BC=? This question is very classic. Answer 4, number 3-3 or 4, number 3+3.
3. Xiao Ming, a student in the east-west direction of Jiang Yan Road, measured that the lighthouse in the river was 60 due east-north at B and 30 due east-north at 400m east of A. So what's the distance from P lighthouse to Jiang Yan Road? Answer the root number 3 of 200.
4. The sales of a commercial building this year 1 month was 600,000, which decreased by 65,438+00% in February due to poor management. After that, the management was improved, which greatly stimulated the enthusiasm of all employees, and the monthly sales increased significantly. By April, sales had soared to 960,000 yuan. What is the average monthly growth rate in March and April? (accurate to 0. 1%)
[Solution]
Thinking: This is a question of growth rate. First, calculate the sales in February, and then let the average growth rate in March and April be X, indicating the sales in April.
Solution: Let the average monthly growth rate in March and April be X, depending on the meaning of the problem.
60( 1- 10%)( 1+x)2 = 96。
The solution is. x 1 = 1/3，x2 =-7/3。
Since the percentage increase cannot be negative, it is irrelevant and discarded.
That is. x = 1/3 = 33.3%。
A: In March and April, the average monthly sales growth rate of commercial buildings was 33.3%.
Summary: The basic formula of growth rate is: a (1 x) n, where a is the cardinal number, x is the growth rate or decline rate, and n represents the number of months that have passed.
5. As shown in the figure, A, B, C and D are four vertices of a rectangle, AB= 16cm, AD=6cm, and the moving points P and Q start from point A and point C respectively. Point P moves to point B at 3cm/s until point B, and point Q moves to point D at 2 cm/s. 。
Q: When (1) point P and point Q start for a few seconds, the area of quadrilateral PBCQ is 33cm2?
(2) When P and Q start for a few seconds, the distance between P and Q is 10cm?
[Analysis] Idea: (1) Because the quadrilateral PBCQ is trapezoidal and the height CB=6cm, the equation can be listed only by expressing the length of the upper and lower base sides;
(2) Because of the distance between two points of PQ, it is not easy to express the unknown by algebraic expression. It is necessary to construct the basic geometric figure-right triangle with auxiliary lines and solve it with Pythagorean theorem.
Solution: (1) Let the area of quadrilateral PBCQ be 33cm2 when two points p and q start for x seconds, then AP=3x, Pb = 16-3x and CQ = 2x. According to the area formula of trapezoid, the solution is x = 5.
Answer: The area of quadrilateral PBCQ is 33cm2 when P and Q are 5 seconds away from departure.
(2) Let the distance from point P to point Q be 10cm. From departure to y seconds.
As shown in the figure, if Q intersects with QH⊥AB and AB intersects with H, then AP=3y, CQ=2y, and pH = 16-3y-2y. According to Pythagorean Theorem, (16-3y-2y) 2 = 102.
Answer: The distance from point P to point Q is 10cm. From departure to 8/5 seconds or 24/5 seconds.
6. When a shopping mall sells a brand-name shirt, it can sell an average of 20 pieces a day, and each piece will make a profit in 40 yuan. In order to expand sales, increase profits and minimize inventory, the mall decided to take appropriate price reduction measures. After investigation, it is found that if each shirt is reduced by 1 yuan, the mall can sell 2 shirts on average a day. If the average daily profit of the mall is 1200 yuan, how much will each shirt be reduced?
[Analysis] Idea: Every time the price is reduced by 1 yuan, each piece earns (40- 1) yuan, and (20+2) pieces can be sold every day. Therefore, if the price of each shirt is reduced by X yuan, each shirt will earn (40-x) yuan and sell (20+2x) pieces every day.
Solution: If the price of each piece is reduced by X yuan, then each piece will make a profit of (40-X) yuan, and (20+2x) pieces can be sold every day. According to the meaning of the question, the equation can be formulated.
(40-x)(20+2x)= 1200
The sorted x2-30x+200 = 0.
The result is x 1= 10, x2=20.
Because we need to reduce the inventory as much as possible, the more we reduce the price, the faster the sales will be, so we have to reduce the price of each piece by 20 yuan.
A: Every shirt will be reduced in price, 20 yuan.