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The numbers corresponding to two points a and B on the number axis are - 8 and 4. A and B move on the number axis at a certain speed The velocity of point a is 2 units per second (1) Find the distance of ab (2) Point a and point B start at the same time, face each other, meet at the origin, and find the velocity of point B (3) A and B start at the same time with the speed in (2) and move in the positive direction of the number axis. In a few seconds, the distance between them is 6 units of length?
(1) The distance of AB = 4 - (- 8) = 4 + 8 = 12,
(2) Velocity of point B = 8 / (2 × 4) = 1 (unit / s)
(3) After x seconds, the distance between them is 6 units,
There are two situations,
A is on the left side of B, 4 + X - (2x-8) = 6, and the solution is x = 6
A is on the right side of B, 2x-8 - (4 + x) = 6, and the solution is x = 18
So, after 6 seconds or 18 seconds, they are 6 units apart
(1)4+8=12
(2)t=8/2=4, v=S/t=4/4=1
(3)VB*t+12-VA*t=6
t=6s
If the velocity of two points is opposite to that of B in the direction of A-12, and the velocity of two points is opposite to that of B in the direction of A-12?
-3-t=-(12-4t)
t+3=12-4t
5t=9
t=1.8s
The position of rational number AB on the number axis is shown in the figure below, simplifying | a + B | - 2 | a-b|
| A+B| -2|A-B|=-（A+B）-2(B-A)=-A-B-2B+2A=A-3B
The known function f (x) = asinx * cosx - √ 3acos & sup2; X + √ 3 / 2A
When x belongs to [0, π / 2], the minimum value of F (x) is - √ 3. Find the sum of all the independent variables X in the interval [- π, π] when the function f (s) reaches the maximum value
F (x) = asinx * cosx - √ 3acos & # 178; X + √ 3 / 2A = a [(1 / 2) sin2x - (√ 3 / 2) cos2x] = asin (2x - π / 3) when x belongs to [0, π / 2], 2x - π / 3 belongs to [- π / 3,2 π / 3], so the minimum value is f (0) = a * (- √ 3 / 2) = - √ 3, a = 2, so f (x) = 2Sin (2x - π / 3) (1) minimum value f (s) = - √ 3, x =
f(x)=asinx*cosx-√3acos²x+√3/2a
＝a/2*sin2x-√3/2-√3/2cos2x+√3/2a
=1/2*√（a^2+3)*sin(2x-m)-√3/2(1-a)
Where COSM = A / √ (a ^ 2 + 3), sinm = √ 3 / √ (a ^ 2 + 3),
a> When 0, 0
If the function f (x) = a ^ 3x-x ^ 2-x + 1 is a decreasing function on (1,2], then the value range of real number a is
Using the method of separating parameters
If f (x) = ax ^ 3-x ^ 2-x + 1 is a decreasing function on (1,2], then f '(x) = 3ax ^ 2-2x-1 ≤ 0 is constant on (1,2], that is, 3ax ^ 2-2x-1 ≤ 0 is constant on (1,2], that is, 3ax ^ 2 ≤ 2x + 1 is constant on (1,2], that is, 3a ≤ 2 / x + 1 / x ^ 2 is constant on (1,2], that is, 3a ≤ (1 / x + 1) ^ 2-1 is constant on (1,2]
Given function f (x) = asinx * cosx - √ 3cos square x + √ 3 / 2A + B (a is greater than 0)
Given the monotone decreasing interval of the function f (x) = asinx * cosx - √ 3cos square x + √ 3 / 2A + B (a is greater than 0), let x belong to the closed interval from 0 to π / 2, the minimum value of F (x) is - 2, and the maximum value is √ 3 to find the real number ab
Is there a missing a
It is proved that the function f (x) = 2x ^ 3 + 3x ^ 2-12x + 1 is a decreasing function in the interval (- 2,1)
Let x, y ∈ (- 2,1), let x > y. then f (x1) - f (y) = 2 (x ^ 3-y ^ 3) + 3 (x ^ 2-y ^ 2) - 12 (X-Y) = 2 (x ^ 3-y ^ 3) + [3 (x + y) + 12] (X-Y) because x > y, and X, y ∈ (- 2,1), the above formula is constant negative, that is, f (x) y. the monotone decreasing is proved by the definition
If we know that the function y = the square of cosx + the square of asinx-a + 2A + 5 has the maximum stop two, we can find a
Y = (cosx) ^ 2 + asinx-a ^ 2 + 2A + 5 = 1 - (SiNx) ^ 2 + asinx-a ^ 2 + 2A + 5 = (sinx-a / 2) ^ 2-3a ^ 2 / 4 + 2A + 61) - 2 ≤ a ≤ 2, - 3A ^ 2 / 4 + 2A + 6 = 23a ^ 2-8a-16 = 0 (3a + 4) (A-4) = 0a1 = - 4 / 3, A2 = 4 (rounding) 2) a > 2, SiNx = 1 has the maximum value of 0 + A-A ^ 2 + 2A + 5 = 2A ^ 2-3a-3 = 0a1 = (...)
If the image of the quadratic function y = - x2 + MX-1 has two different intersections with the line AB whose two ends are a (0,3), B (3,0), then the value range of M is______ .
It is known that the equation of line segment AB is y = - x + 3 (0 ≤ x ≤ 3). Because there are two different intersections between quadratic function image and line segment AB, the equations y = − x2 + MX − 1y = − x + 3, 0 ≤ x ≤ 3 have two different real solutions. The elimination result is: X2 - (M + 1) x + 4 = 0 (0 ≤ x ≤ 3), Let f (x) = X2 - (M + 1) x +
Let f (x) = cosx, cos (PAI, 6-x), then f (1 degree) + F (2 degree) + +The value of F (60 degrees) is equal to
I hope as soon as possible,
It belongs to [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2
Any meeting will do,
For example, f (1 degree) = cos1 / 29, f (59 degree) = cos59 / - 29F (1 degree) + F (59 degree) = (cos1 + cos59) / cos29cos1 + cos59 = cos (30-29) + cos (30 + 29) = 2cos30cos29, which is equal to 2cos30 = radical 3, the same as 2 degrees and 58 degrees, 3 degrees and 57 degrees
RELATED INFORMATIONS
- 1. a. B is a rational number. The positions of a and B on the number axis are shown in the figure, which is simplified as | a + B | - | a-b|=______ .
- 2. A. B are two points on the number axis, the number corresponding to a is - 10, and the number corresponding to B is 90. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (1) please write the number corresponding to m point whose distance is equal to a and B. & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; (2) If the electron ant P starts from point B and moves to the left at a speed of 3 units per second, and the other electron ant Q starts from point a and moves to the right at a speed of 2 units per second, how long does it take for the two electron ants to be 35 units apart on the number axis?
- 3. Given the position of a and B on the number axis as shown in the figure, if point P is on the number axis and PA + Pb = 6, find the corresponding position of P
- 4. O asks one between a and B; PA =] Pb =] two; does there exist a point P on the number axis so that PA + Pb = 5? 3、 Point P moves to the right from point o at the speed of one unit length / min, while point a moves to the left at the speed of 5 units / min, and point B moves to the right at the speed of 20 units / min. in the process of movement, m and N are the midpoint of AP and ob respectively. Please explain why the value of AB op / Mn changes
- 5. As shown in the figure, given the line AB = 80cm, M is the midpoint of AB, P is on MB, n is the midpoint of Pb, and Nb = 14cm, find the length of PA
- 6. It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively, and point P is a moving point on the number axis, and its corresponding number is X 1) If the distances from point P to point a and point B are equal, find the number corresponding to point p; (point a is - 1, point O is 0, point B is 3, point P is the point between point 1 and point 2) (2) Whether there is a point P on the number axis, so that the sum of the distances from point P to point a and point B is only 6. If there is, we can find the value of X. if not, we can explain the reason
- 7. It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively It is known that the numbers corresponding to two points a and B on the number axis are - 1 and 3 respectively, and point P is a moving point on the number axis, and its corresponding number is X (1) If the distances from point P to point a and point B are equal, find the number corresponding to point P; (2) Whether there is a point P on the number axis, so that the sum of the distances from point P to point a and point B is 5? If there is, ask for the value of X; if not, explain the reason; (3) When point P moves to the left from point o at a speed of 1 unit per minute, point a moves to the left at a speed of 5 units per minute, and point B moves to the left at a speed of 20 units per minute. Ask them to start at the same time. In a few minutes, are the distances from point P to point a and point B equal?
- 8. a. The position of B and C on the number axis is shown in the figure, and a = C, simplify a - B + A + B-C + C + C + C + a=______ .
- 9. The representation of inequality on the number axis
- 10. Can we say "rational numbers correspond to the points on the number axis one by one"? The real number corresponds to the point on the number axis one by one. This sentence is right, but what about the above sentence?
- 11. A. The position of two points B on the number axis is shown in the figure. Now two points a and B move to the left at the speed of 1 unit / s and 4 units / s respectively. (1) after a few seconds, the origin is just in the middle of two points? (2) A few seconds later, OA: OB = 1:2?
- 12. If the function f (x) = x ^ 2-2mx is a decreasing function on X ≤ 1, find the range of M
- 13. If the function f (x) = x & # 178; + (4a + 1) x + 2 is a decreasing function in the interval 0 (- ∞, 1), then the value range of a is
- 14. If y = xsquare - 2mx + 1 is a decreasing function on (negative infinity, 2], then the range of M is
- 15. Y = f (x) is a decreasing function in [- 2,1], and f (A & # 178; - 1) > F (1-A) is the range of A
- 16. F (x) = 2x * 3-3 (A-1) x * 2 + 1, find the monotone interval and extremum of the function
- 17. The monotonicity interval (1) f (x) = x Λ 2 + 2X-4 (2) f (x) = 2x Λ 2-3x + 3 (3) f (x) = 3x + X Λ 3 is obtained （4）f(x)=x∧3+x∧2-x
- 18. Given the function FX = (PX ^ 2 + 2) / (q-3x), find the monotone interval of the function Please look at the title, The analytic expression is FX = (2x ^ 2 + 2) / (- 3x)
- 19. If a, B, x, y satisfy ax + by = 3, ax + by = 7, ax + by = 16, the fourth power of AX + the fourth power of by = 42, find the value of the fifth power of AX + the fifth power of by
- 20. Ax + BX = 3, ax ^ 2 + by ^ 2 = 7, ax ^ 3 + by ^ 3 = 16, ax ^ 4 + by ^ 4 = 42, find ax ^ 5 + BX ^ 5