As shown in the figure, the straight line y = kx-1 intersects the x-axis and y-axis at two points B and C respectively, Tan ∠ OCB = 12 (1) Find the coordinates of point B and the value of K; (2) if point a (x, y) is a moving point on the line y = kx-1 in the first quadrant, try to write out the functional relationship between the area s of △ AOB and X when point a moves; (3) explore: under the condition of (2): ① when point a moves to what position, the area of △ AOB is 14; ② if it holds, whether there is a point P on the X axis So that △ POA is an isosceles triangle? If it exists, please write the coordinates of all P points that meet the condition; if not, please explain the reason

(1) ∵ y = kx-1 and y-axis intersect at point C, ∵ OC = 1; ∵ Tan ∠ OCB = 12 = OBOC, ∵ ob = 12; ∵ B coordinates are: (12, 0); substituting B coordinates as: (12, 0) into y = kx-1 to get k = 2; (2) ∵ s = 12 · ob | y | y = kx-1, ∵ s = 12 × 12 (2x-1); ∵ s = 12x-14; (3) when s = 14, 12x-14 = 14, ∵ x = 1, y = 2x-1 = 1; when a coordinates are (1, 1), the area of △ AOB is 14 The coordinates of all P points meeting the conditions are: P1 (1,0), P2 (2,0), P3 (2,0), P4 (- 2,0). (12 points) (Note: only one solution is given for each question, if there are different solutions, please refer to the scoring opinions for points)

As shown in the figure, it is known that the bottom edge Ao of the trapezoid ABCO is on the x-axis, BC ‖ Ao, ab ⊥ Ao, the hyperbola passing through point c y = KX intersects ob with D, and OD: DB = 1:2. If the area of △ OBC is equal to 3, then the value of K is___ ．

Let C (x, y), BC = A. then AB = y, OA = x + A. through D point, let de ⊥ OA be at e point. ∵ od: DB = 1:2, de ∥ AB, ∥ ode ∥ oba, the similarity ratio is od: OB = 1:3, ∥ de = 13ab = 13y, OE = 13oa = 13 (x + a); ∵ D point is on the image of inverse scale function, and D (13 (x + a), 13y), ∥ 13y · 13 (x + a) = k, that is, XY + Ya = 9K, ∥ C point is on the image of inverse scale function, then xy = K Therefore, the answer is: 34

As shown in the figure, P is any point on the x-axis, Pb is perpendicular to the x-axis, intersection line y = 0.5x, y = KX at two points a and B, BC ⊥ Pb intersection line y = 0.5x at point C, CD ⊥ BC intersection line y = KX at point D

(1) Let the coordinates of point p be (x, 0), ∵ A and B on the straight line y = 0.5x and y = KX, the coordinates of point a and point B be (x, 0.5x), (x, KX),.. PA = 0.5x, Pb = KX, ∵ papB = 0.5x, KX = 0.5K respectively. (2) let the coordinates of point p be: (T, 0) ∵ Pb perpendicular to the X axis, and point B on the straight line y = KX

The price of two story books and three science and technology books is 24.3 yuan. The price of three story books and two science and technology books is 23.2 yuan. What is the unit price of story books and science and technology books?

The price of 5 story books and 5 Science and technology books is: 24.3 + 23.2 = 47.5 (yuan). The price of 1 story book and 1 science and technology book is: 47.5 △ 5 = 9.5 (yuan). The unit price of each story book is: 23.2-9.5 × 2 = 23.2-19 = 4.2 (yuan). The unit price of each science and technology book is: 9.5-4.2 = 5.3 (yuan) or: 24.3-9.5 × 2 = 24.3 -

For a project, Party A and Party B work together for eight days. If Party A works for two days first, and Party B works for 11 days alone, just 5 / 8 of the project will be completed. If Party B works alone, how many days will it take?
For a batch of parts, it takes a quarter more time for Party A to work alone than for Party B. If two people work together, Party A will finish the task 40 times less than Party B. how many parts are there in this batch?
It takes 60 days for Party A to finish a job alone, and two people work together. Party A doesn't do it for 3 days, and takes a day off. Party B takes a day off for every 5 days. What day is it to finish all the work?

A does it for 2 days, B does it for 11 days = A and B cooperate for 2 days, B does it alone for 9 days
B speed: (5 / 8-2 / 8) / 9 = 1 / 24, then B alone need 1 / (1 / 24) = 24 days
It takes 1 / 4 more time for Party A to do it alone than for Party B to do it alone, indicating that the speed ratio of Party A and Party B is (1 + 1 / 4) / 1, that is, 4 / 5
So, the total number is 9 * 40 = 360
3. It will take 60 days for a and B to finish the task separately
60 / 19 = 3 (the remaining 3 days)
So finish all the work at noon on day 3 * 12 + 2 = 38

The length of the same object is measured with four kinds of straightedge with division value of 1m, 1dm, 1cm and 1mm respectively, and the number of digits after the decimal point is the most in the recorded data ()
A. Results measured with millimeter ruler B. results measured with decimeter ruler C. results measured with centimeter ruler D. results measured with meter ruler

Similarly, record the data in meter: A. measure with millimeter ruler, the division value is 1 mm, and the result retains 4 decimal places; B. measure with decimeter ruler, the division value is 1 DM, and the result retains 2 decimal places; C. measure with centimeter ruler, the division value is 1 cm, and the result retains 3 decimal places; D. measure with meter ruler, and the division value is 1 m, and the result retains 1 decimal place; so select a

Chinese Grade 6 Volume 2 Lesson 18 across a hundred years of beauty
() () winding

This article uses flashback to praise Madame Curie's perseverance in scientific research and the quality of regarding fame and wealth as dirt

12. Least common multiple of 18 and 20 least common multiple of 15, 12 and 10

12=2x2x3
18=2x3x3
20=2x2x5
So the least common multiple of 12, 18 and 20 = 2x2x3x3x5 = 180
15=3x5
12=2x2x3
10=2x5
So the least common multiple of 15, 12 and 10 = 2x2x3x5 = 60

Because two thirds of X is equal to three eighths of Y, is x proportional to y? If so, is it positive

2x/3=3y/8
x=9y/16
X is proportional to y
In proportion

If a, B and C are used to represent rational numbers a, B and C respectively, and 0 is the origin, as shown in the figure. We know that a < C < 0, b > 0. (1) simplify | a-c | + | B-A | - | - C-A |;; (2) simplify | - A + B | - | - C-B | + | - A + C | (3) simplify 2C + | a + B | + | - C-B | - | - C-A |

(1) This is the combination number axis, which is the combination number axis, \\\124;a-a-c-0, B-A \|a-c-a ||124\124\\\124\124\\\\\\\\\124\124\\124\\\\\124\\124\\\\(3) combined with the number axis, ∵ a < C < 0, b > 0, ∵ a + B < 0, C-B < 0, C-A > 0, ∵ 2C+ |a+b|+|c-b|-|c-a|=2c-a-b-c+b-c+a=0．