Math High School! Ball Analysis! I!!!

1.Let the set u=, the set a=, then cua=?

cua= 2.The function y= (2-|.)x|What is the definition domain?

2-|x|≥0 ==> |x|≤2==>-2≤x≤2

Define the domain as [-2,2].

3.If one of the equations x 2-3ax+2a 2=0 is less than 1 and the other is greater than 1, then what is the range of values for the real number a?

Constructing f(x)=x 2-3ax+2a 2 requires only f(1)<0

i.e. 2a 2-3a + 1<0 ==> a (1 2,1).

4.What is the domain of the function y= (log2 3(3x-2)))?

log2/3(3x-2)≥0==>0<3x-2≤1 ==>2/3 a=0,b=1 ==>ab=0

6.Knowing that f(x)=x+1(x>0) and (x=0) and x 2(x<0), if f(x0)=3, then x0=?

x0>0,x0+1=3 ==> x0=2

x0<0,x0^2=3 ==> x0=-√3

7.Find the value of (lg2) 2+lg2 lg5+(log3 5) (log3 10).

The formula for changing the bottom (log3 5) (log3 10)=lg5,lg 2+lg2 lg5+lg5=lg2*(lg2+lg5)+lg5=lg2+lg5=1

where LG2+LG5=LG(2*5)=LG10=1).

1 Finding the complement is the set of all the elements in u that are left by removing a, i.e.

2 2-|x|≥0 |x|≤2 -2≤ x≤2

3 f(x)=x 2-3ax+2a 2 One is less than 1 and the other is greater than 1, and f(1)<0 can be deduced from the image

4 log2 3(3x-2) 0 and (3x-2)>0 meet their respective defined domains.

5 f(-x)+f(x)=0 f(0)=0 You can choose to substitute special values such as 1 to find the values of a and b.

6 x>0,f(x)=x+1=3,x0=2

x<0 f(x)=x^2=3 x0= -√3

7,(log3 5)/(log3 10)=lg5,，（lg2）^2+lg2×lg5+lg5=lg2*(lg2+lg5)+lg5=lg2+lg5=1

lg2+lg5=lg(2*5)=lg10=1

1.The complement is what A doesn't have in U.

2. [2,2] 2-|x|Not less than 0

3.(1 2,1) denote f(x)=x 2-3ax+2a 2, then f(1)<0

4. [1,+00) log2/3(3x-2)>=0，3x-2>=1，x>=1

5.0 f(x)=-f(-x)=2x 3-ax 2-b+1, contrast coefficient value, a=0, b=1

6.2 or - 3 piecewise functions, discuss x0

7.1 First, use the formula (log3 5) (log3 10)=LG5,(LG2) 2+LG2 LG5+LG5=LG2*(LG2+LG5)+LG5=LG2+LG5=1 (where LG2+LG5=LG(2*5)=LG10=1).

cua represents a set u, when it does not belong to set a, so cua=

Define the domain as -2

Because ab is parallel to the projection plane, ab is the same as a'b'Parallel. Even AA'，bb'，oo', there is AA'||bb'||oo'

So ao bo=a'o'/b'o'=m：n

(1) The rectangular plot should be x meters long and y meters wide.

x*y=1800, since the circumference of the rectangular plot cannot exceed 220 meters, so x+y"110, therefore, x+1800 x"110, solve 20"x"90(2) The area of the fish pond is the area of three small rectangles, which can be listed by the title, s=2(x-6) 2*+(x-4)*(y-6) 3, because x*y=1800

Simplification can be obtained.

s=1832-6(1600/x+x)

3) If and only if, 1600 x = x, that is, x = 40, the area is the largest, and the maximum area is s=1832-6*80=1352

There is indeed a knowledge point, that is, periodicity.

f(x+4)=f(x) indicates that f(x) is a periodic function and 4 is its period.

That is, there is f(7) = f(3) = f(-1).

And because f(x) is an odd function on r.

So f(x)=-f(-x) and because when x belongs to (0,2), f(x)=2x 2

So f(7)=f(3)=f(-1)=-f(1)=-2 if in doubt, you can hi me.

Because f(x+4)=f(x), the function has a period of 4 and is a periodic function.

So f(7) = f(3) = f(-1).

Or you think so, because f(x+4)=f(x), let x=3, give f(7)=f(3), let x=-1 get.

f(3）=f（-1）

Establish a Cartesian coordinate system, B is the origin, PB is the Z axis, BC and AB are the X axis and Y axis, respectively.

a( 0,3,0 ),b( 0,0,0 ),d( 3,3,0 ),p(0,0,3 )

Easy to get e(0,2,1).

The method on the first floor can be as follows if it is a multiple-choice question, that is, if p is the center of the circle (x-2) 2+(y-3) 2=1, and at this time a=2, b=3, then q(0,1) is the center of the circle (x-2) 2+(y-3) 2=1 about the circle symmetrical with a straight line l.

Therefore, the equation is derived.

But if it's a problem, how can you make a=2, b=3?

To solve the problem, you can set the center point of pq to w(x',y'), then x'=(3+a-b)/2, y'=(3+b-a) 2, the slope of l is -1, and after the point w, let its equation be y=-x+m, and substitute the coordinates of w to obtain, m=3.

The equation for l is: y=-x+3

Let the center of the circle be n(x'',y''Then n is symmetrical with the point (2,3) with respect to l, using y''+3=-(x''+2)+6 and (y''-3)/(x''-2) = 1 to get x''=0,y''=1, the radius of the circle is also 1, so the equation is: x 2+(y-1) 2=1.

Use substitution: here let a=2, b=3

Then the coordinates of the symmetrical point (3-b,3-a) = (0,1) Since l bisects the line segment pq, the perpendicular bisector between (2,3) and (0,1) must also be l

So, the equation for the resulting circle is x 2+(y-1) 2=1

If the coordinates of two different points p and q are (a,b),(3-b,3-a), then the slope of the perpendicular bisector l of the line segment pq is -1, and the equation for the circle (x-2) 2+(y-3) 2=1 for a circle symmetrical with a straight line l is .

Solution: Let p(a,b); q(3-b, 3-a), p, q symmetrical with respect to l. There are many, many such p,q,According to the topic,Of course I can choose。

choose a=2, b=3In this way, the center of the symmetrical garden is quickly found to be (0,1), and the equation for the desired garden is quickly obtained:

x²+(y-1)²=1.Whether it's a multiple-choice or math-based question, you can do that! Friends on the second floor are a bit sloppy.

(1)2x-3=0 y+2=0

x= y=-2

xy=-32)5x-2=mx+21

5x-mx-23=0

x(5-m)-23=0

m=4 or m=-18 Supplement:

Are you sure it's 2 to 1? Not 1 2?This is a quotient, just an integer, e.g. 8 5 = 1

3)|x-2\1|-1=0 This is divided by all things that need to be managed e.g. 8 5=

x-2 = +1 or -1

x=3 or x=1

x = 3 substitution (m+1) x = 2 (m+x) x = 1 substitution (m+1) x = 2 (m+x).

3m+3=2m+6 m+1=2m+2

m=3 -m=1

m=-1, so m=3 or m=-1

1, to make the sum of the two absolute values equal to 0, then the two absolute values must be 0, then we can get x=3 2, y=-2, then, xy=3

2, 4, 6, or when (5-m) is an integer multiple of 23.

3, the third question, what is the meaning of the " " in the absolute value sign at the end, I don't understand.

1。If x,y are rational numbers, and satisfy |2x-3|+|y+2|=0, then xy=2x-3=0 x=3 2

y+2=0 y=-2

xy=-32.The equation for x, 5x-2=mx+21, has an integer solution 5x-2=mx+21 (5-m)x=23x=23 (5-m) when m takes what integer

5-m=23 5-m=-23

m=-18 m=28

3.(m+1)x=2(m+x) satisfies |x-2|-1=0x=3 x=1

m-1)x=2m

m=-1 m=3

1 Question 3

2 questions -18 or 4

2 1, I haven't learned, what do you mean.