Known: as shown in the figure, ∠ mon = 90 °, points a and B move on ray OM and on respectively, AC bisects ∠ OAB, BD bisects ∠ ABN, AC and DB intersect at point C. try to guess: as points a and B move, does the size of ∠ ACB change? Prove your conclusion

The size doesn't change with it
prove:
＜ABD＝1／2＜ABN＝1／2（＜O＋＜OAB）＝1／2＜O＋1／2＜OAB
1 / 2 < OAB = < cab
So ＜ abd = 1 / 2 ＜ o ＋＜ cab
Also: < abd = < C + < cab
So: < C = 1 / 2 < o = 1 / 2 * 90 = 45
That is, the angle c is always 45 degrees

It is known that, as shown in the figure, ∠ mon = 90 ° points a and B move on the ray on and OM respectively,
Be is the bisector of ∠ ABM, and the reverse extension of be intersects with the bisector of ∠ Bao at point C. if it changes with the movement of points a and B, find out the range of change. If it remains unchanged, please explain the reason
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The size of C remains unchanged
∵∠ ABN = 90 ° + ∠ OAB, AC bisection ∠ OAB, BD bisection ∠ ABN,
∴∠ABD=12∠ABN=12（90°+∠OAB）=45°+12∠OAB,
That is ∠ abd = 45 °+ ∠ cab,
And ∵ ∠ abd = ∠ C + ∠ cab,
∴∠C=45°,
Therefore, the size of ∠ ACB does not change, and it always keeps 45 degrees

Figure 1-9 shows the schematic diagram of a space probe, P1, P2, P3 and P4 respectively. What motion will they do if they are started separately? If four engines can produce the same size space probe
Thrust, what motion will the detector make when it starts at the same time?

(1) When P1 is opened separately, the force is along the - X direction, so it makes a uniform deceleration linear motion; when P3 is opened separately, it makes a uniform acceleration linear motion; when P2 or P4 is opened separately, it makes a uniform velocity curve motion
(2) When P2 and P3 are activated at the same time, the external force is closed along the direction of 45 ° with + X and + y, and the detector moves in a constant speed curve
(3) Start four engines at the same time, then do uniform linear motion
(4) When P2 is turned on, the detector moves uniformly in the first quadrant of the coordinate system, while when P4 is turned on, it moves uniformly in the fourth quadrant

As shown in the figure, flip the OAP of the equilateral triangle with the side length of 1 continuously along the positive direction of the x-axis for 2010 times, and point P falls on point P1, P2, P3 , p2010, then the coordinate of point p2010 is______ ．

The abscissa of P1 and P2 is 1, that of P3 is 2.5, that of P4 and P5 is 4, and that of P6 is 5.5 By analogy, the abscissa of P2005 and p2006 is 2005, the abscissa of p2007 is 2006.5, and the abscissa of P2008 and P2009 is 2008

Suppose there are 10, 5 and 7 resources of a, B and C in the system, and there are processes of P 0, p 1, P 2, P 3 and P 4
Max Allocation Need Available
A B C A B C A B C A B C
p0 7 5 3 0 1 0 7 4 3 3 3 2
p1 3 2 2 2 0 0 1 2 2
p2 9 0 2 3 0 2 6 0 0
p3 2 2 2 2 1 1 0 1 1
p4 4 3 3 0 0 2 4 3 1
Q: (1) is the system safe at t0? If so, the security sequence is given
(2) if there is a request, request1 = [1,0,2], can it be allocated? Why?
(3) after (2), there is a new state. Can request0 = [0,2,0] be allocated? Why?

(1) There is a security sequence {P1, P3, P4, P2, P0} at T0, so security (2) is checked according to banker's algorithm: ① request 1 (1,0,2) ≤ need 1 (1,2,2) ② request 1 (1,0,2) ≤ available (3,3,2), so resources can be allocated immediately, the same as (2) can be allocated

As shown in the figure, flip the square OAPB with side length of 1 for 2 & nbsp; 010 times in the positive direction of x-axis, and point P falls on point P1, P2, P3, P4 , p2010, then the abscissa of p2010 is x2010=______ ．

The abscissa of P1 is 1, the abscissa of P2 is 2, the abscissa of P6 is 6, the abscissa of P10 is 10, and the abscissa of p14 is 14. Starting from the third rotation, every four times, the abscissa is equal to the number of rotations 2, so the abscissa of p2010 is equal to 2010 in the 2010 flip, so the answer is: 2010

The OAPB of the square with side length of 1 was flipped continuously for 2006 times along the positive direction of x-axis, and point P fell on point P1, P2, P3, P4 , p2006,
Then the abscissa x2006 of p2006 =?

So p2004 (2005,1), so
P2005(2006,0),P2006(2006,0).

Find all prime numbers of 4N ^ 2 + 1, such as P1 = 5, P2 = 17, P3 = 37, P4 = 101
Is a prime number P below 1000 000

#include
bool IsPrime(int x)
{
if(x==2)return true;
for(int i=2;i*i

Satisfy P1

P1 of known three prime numbers

p1=2；
p22+p32=2234
p22

Known: as shown in the figure, ∠ mon = 90 °, points a and B move on ray OM and on respectively, AC bisects ∠ OAB, BD bisects ∠ ABN, AC and DB intersect at point C. try to guess: as points a and B move, does the size of ∠ ACB change? Prove your conclusion