Math puzzles are urgent, fast, math puzzles, urgent

First, the time for the correspondent to chase the leader from the end of the line is x hours, and the time for returning from the head of the line to the back of the line is y hours. Separate equations:

7x-5x= 7y+5y=

Solve them separately and get: x=hour), y=hour).

The total time required is: x+y=hours) = 21 (minutes).

This is extremely bad with equations, let's use arithmetic:

At the beginning, it is a catch-up problem, dividing the distance by the speed difference, time.

When you come back, it's a matter of encounter, divide the distance by the speed and the total time is: hours.

Solution: Set up a chase to the front of the row to x

2x= x=.

Set to catch up with the first row A hour and return to the bottom of the row B hour.

Catch up with the top of the line and subtract the speed of traveling in the same direction.

Go back to the end of the row and add the speed in the opposite direction.

The solution is a+b=

When setting up x, the tail of the team walked 5x kilometers and the communicators traveled 7x kilometers.

Now it's a matter of distance.

5x+7x=600

12x=600

x=50

Let A be x years old, then x+(x+4)+one-half (x+2)+2x+4=36

So x=6 so the four people are 6, 10, 4, 16 years old, and the youngest is Ding, 4 years old.

Passing the point d to the x-axis Hu Xiaokong as a perpendicular line segment de, another |de|=xSelect|eo|=x so |ea|=x+1

By the triangle DEA is a right triangle can be listed.

de +ea = da cherry blossoms.

where da=ac=root number 2

So (x+1) +x =2

The solution gives x=(root number 3-1) 2

or x=(-root, number, 3-1) 2

So the coordinates of point d are ((-root number 3+1) 2, (root number 3-1) 2).

At 3 o'clock, the minute hand is 90 degrees from the hour hand, and after X minutes, the minute hand and the hour hand form a second angle of 30 degrees.

6°x-(3*60+x)*

x=240/11

At 3:21 and 9 11 minutes, the minute hand and the hour hand form an angle of 30° Note: The minute hand goes around 360°, and it takes 60 minutes, so the minute hand goes 6° in one minute; It took 60 minutes for the hour hand to go one big block at 360° 12=30°, so the hour hand traveled 30° 60=

1) Because APD, APE, and ABC are equilateral triangles, AP AD, Angle ADP = Angle APE 60 degrees, Angle DAP Angle PAE Angle BAC 60 degrees, Angle DAP Angle DAP-Angle MAP 60 Degrees-Angle MAP Angle BAC-Angle MAP Angle.

pan, defined by congruent triangles (two corners sandwiched on one side), adm and apn congruence, then am an

Rely on yourself, you don't have to ask about the exam!

Use sin(x+y) = sin(x)cos(y)+cos(x)sin(y).

It can be seen that f(x)=2+sin(3x+ 12+x+6)=2+sin(4x+ 4).

1) The center of symmetry is ((- 4+k) 4,2 and the closest to the origin is (- 16,2).

The axis of symmetry is y=( 4+k ) 4 The closest to the y axis is y= 4(2) and the minimum positive period is pi 2

By plotting, you can see that the number of roots of the equation is 3

The formula of the first sine sum deforms the original function to f(x)=sin(4x+4)+2, and then according to this, the directional displacement is -16

So the closest center of symmetry to the origin is (- 16,2) and the closest axis of symmetry to the y-axis is x=7 16

The second problem is still from the deformed formula to get the minimum positive period of 2 4, that is, 2 deform the equation of the second problem to f(x)=x+1, and then set g(x)=x+1, to be true, that is, the function image of f(x) and g(x) has an intersection point, and after roughly making the image of f(x) and g(x), it can be obtained that there is an intersection point, so the equation has 1 root.

Using the sum angle formula: f(x)=2+sin(4x+4), the center of symmetry (k 4- 16,2) k is an integer, the axis of symmetry: x=k 4 + 8, k is an integer.

The closest center of symmetry to the origin (-16,2), the closest axis of symmetry to the y-axis x = 8.

The minimum positive period of f(x) is 2

f(x)=2+sin(3x+π/12)cos(x+π/6)+cos(3x+π/12)sin(x+π/6)

2+sin(3x+π/12+x+π/6)=2+sin(4x+π/4)

Center of symmetry = k 4- 16 coordinates of the closest center of symmetry to origin o (2, - 16).

Axis of Symmetry = k 4 + 16 Equation for the axis of symmetry closest to the y axis x= 16

The last two products can be turned into sin(4x+v4), the answer is ( v16 ,2) the period is v2 to draw by myself, I have to turn off the lights.