Math problems, please write the detailed process

Let the radius of circle a r, then the radius of circle c is (13 r)......According to the Pythagorean theorem, ac 13, since the two circles are inscribed, the sum of the radii of the two circles is the diagonal length of the rectangle Because b is inside the circle c, the radius of the circle c: 13 r is greater than the length of cd, i.e. 13 r>5 Because d is outside the circle c, the radius of the circle c: 13 r is less than the length of ab, i.e. 13 r<12 in summary1

Because ab=5 and bc=12, AC=13

Point D is inside the circle C and point B is outside the circle C.

Therefore, the radius of the circle c can be greater than 5 and less than 12

Therefore, the radius of the circle a can be greater than 1 and less than 8

The point AC=13D is 13-R>5 R<8 in the circle C

Point b is outside the circle c 13-r<12 r>1

1

1 connects the tangent points of the two circles A and C on AC, the range of the circle C is 5 r 12 and AC is 13, you can find it.

1ab=5 bc=12 so ac=13

If a circle centered on C is to include point D, then.

The smallest case of r is r=cd=5

Excludes point B.

The biggest case of r is r = bc = 12 (of course point b does not include cannot be taken), so r can be changed within 5-12.

Take ra+rc=13

So 1

According to the formula of the inner angles of the regular polygon, the sum of the internal angles = 180°(n-2), it can be seen that the sum of the internal angles of the regular polygon can be 180°, 360°, 540°, 720°, etc., and the inner angles of the regular polygon cannot be greater than 180°, so the sum of the internal angles of the regular polygon is 720°.

So the regular polygon is a regular hexagon.

Quite simply, the sum of the internal angles of a regular n-sided is 180*(n-2).

180*(n-2)*(n-1)/n=600n=5

The sum of the internal angles of a regular polygon is (n-2)*180

So 180(n-2)(n-1) n=600

The solution is n=6

600°/180°=3……60°

From the inner angle of the n-sided shape and the equation 180°*(n-2), it can be seen that

n-2)-1=3

So n=6

Because the sum of the inner angles of a regular polygon is (n-2)*180, that is, it should be a multiple of 180.

So the interior angle that is not calculated is 180-60 = 120 degrees.

Therefore, the sum of its internal angles is 600 + 120 = 720 degrees.

So the regular polygon is a regular hexagon.

It is a regular 12-sided shape, because, every three inner angles sum is 180°, and 180 4 = 720 (choose a number greater than 600, close to 600), and 600 is close, knowing that the other inner angle is 120°, visible. There are 3 4 = 12 inner corners.

To solve this problem, we must first understand a theorem! That is, when A2+B2>=2AB is taken as an equal sign if and only when A=B, that is, when the difference between A and B is zero, there is a maximum value of AB, then that is to say, when A+B is a fixed value, the smaller the difference between A and B, the greater the value of AB! Understand this theorem, and it will be solved!

Obviously, a+b=c+d, that is, the sum is a fixed value, then the smaller the difference, the larger its product, and all have cd>ab.

Verify the root number A + root number B, "Root number C + root number D, both sides square at the same time<==>A+B+2 root number AB< C+D+2 root number CD can be known from a+b=c+d, as long as 2 root number ab<2 root number cd is sufficient, and with the previous theorem, it can be seen that ab

Think of a and b, c and d as the length and width of two rectangles, respectively, because a+b = c+d

So, the circumference of the two rectangles is equal.

From the knowledge of area, it can be obtained that the difference between the length and width of two rectangles with equal circumference, the smaller the difference between length and width, the larger the area because a c d b, so ab cd

Root number ab root number cd and a+b = c + d so a + 2 root number ab + b c + 2 root number cd + d so (root number a + root number b) square positive number a, b, c, d

So the root number A + the root number B the root number C + the root number D

Replace x with -x, and you're wrong. Didn't do that.

Think of -x as a whole substitution for all the x's in the subformula. But it won't appear in the third formula you wrote.

……Instead of +2, *2 plus , the purpose is to eliminate f(1 x).

From the inscription, it can be seen that the fast train travels 8 meters more than the slow train per second (speed difference). The two trains marching in the same direction at the same time until the fast train overtakes the slow train can actually be understood as: the front of the fast train and the slow train go hand in hand until the fast train space leaves the slow train front of the process.

If you think of it as a person at the front of a slow train and a person at the front of a fast train, then the problem can be imagined as a person at the end of the fast train chasing the person at the front of the slow train, so the chasing distance between them is the length of the fast train: 12 seconds * 8 meters seconds = 96 meters.

In the same way, if the tail of two trains is in line with each other and driving in the same direction at the same time, the whole process is actually that the tail of the fast train and the slow train are at the same end to catch up with the front of the fast train, and you understand it as a person at the front of the slow train, a person at the end of the fast train, and the person at the end of the fast train chases the person at the front of the slow train, so the chasing distance between them is the length of the slow train: 9 seconds * 8 meters seconds = 72 meters.

If you don't understand anything, you can ask again, I hope you can understand it in this way. If you still don't understand, you can draw a picture according to my idea and you will suddenly understand).

In the head-to-head direction, the fast car overtakes the slow car at a relative speed and walks through its own length (because it is in the head-to-head, this can be drawn to help understand); Qi Wei is the commander of a slow train at a relative speed. So the fast train is 96 meters, and the slow train is 72 meters.

Design: fast train length x meters, slow train length y meters.

It can be seen that when moving forward at the same time: 18*12-10*12=x;

At the same time, when the tail is advancing in unison: 18*9-10*9=y;

In this way, we get x=96, y=72;

So the express train is 96 meters long. The slow train is 72 meters long.

Set: fast train length x, slow train length y

Analysis: Because it takes longer to overtake at the head than at the tail, it can be determined that the fast car is longer than the slow car, i.e., x>y. (Actually, this has nothing to do with solving the problem).

Together, exceeding, it can be determined that the express car is traveling more [the length of the express car itself], that is, X.

Qi tail, exceed, can be judged that the fast car travels more than the slow car [the length of the slow car], that is, y.

Solution: x=(18-10)x12 meters.

y=(18-10)x9 m.

x = 96 meters.

y = 72 meters.

A: ......It's said that there are points for check-in, right?

Express train length: (18-10)*12=96m

Slow train length: (18-10)*9=72m

The length of the express train is: (18-10)*12=96 (m).

The length of the slow train is: (18-10)*9=72 (meters).

Express car body length: 18*12-10*12=96 meters.

Slow train body length: 18*9-10*8=72 meters.

A train from the end to the overtaking to the whole train, in fact, the sum of the body length of the two trains, that is, 200 + 340 = 540 meters long, and the difference in speed is 32-20 = 12 meters per second, so to surpass, divide by these two numbers, 540 12 = 45 seconds. That's the result.

The calculation of the previous netizen was completely correct.

（2a-7b）x+(3a-8b）=8x+102xa-7xb+3a-8b-8x-10=0（2a-7b-8)x=10-3a+8b

To be true for a real number x, then.

2a-7b-8=0

10-3a+8b=0

This is equivalent to 0*x=0, and x can be taken as a real number.

So b=-4 5, a=6 5

(2a-7b)x+(3a-8b)=8x+10 to one real number x holds, so the coefficients and constant terms of x are equal.

So 2a-7b=8 (1).

3a-8b=10 (2)

a-b=2 (3)

5b=-4b=-4/5

a=2+b=6/5

According to the title, it can be known;

2a-7b=8,3a+8b=10

A system of binary linear equations is listed.

Solution, get; b=4/-37

a=134/37