Detailed solutions to math problems, detailed solutions to math problems

1. The value range of a is greater than 0 degrees, less than or equal to 45 degrees; (using the triangle corner relation formula).

2、π/2；(In MATLAB, use **x=:5; y=(sin(x)).4+(cos(x)).2;plot(x,y);grid on;Graphing, we can see that the minimum positive period is. ）

3. Choice: a. Isosceles triangle (using Veda's theorem).

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Detailed explanation of mathematical problems: Mathematics is a discipline that studies the concepts of quantity, structure, change, space and information, and belongs to a kind of formal science from a certain point of view. In the historical development and social life of mankind, mathematics plays an irreplaceable role, and it is also an indispensable basic tool for learning and researching modern science and technology.

Detailed explanations of math problems.

Teacher, how to do these three questions, can the process be answered in more detail?

Hello dear <>

Mathematics is a discipline that studies concepts such as quantity, structure, change, space, and information, and belongs to a kind of formal science from a certain point of view. In the historical development and social life of mankind, mathematics plays an irreplaceable role, and it is also an indispensable basic tool for learning and researching modern science and technology.

Extended Material: Mathematics is a universal means of rigorous description of the abstract structure and spine patterns of things, and can be applied to any problem in the real world, and all mathematical objects are inherently artificially defined. In this sense, mathematics belongs to the formal sciences, not the natural sciences.

Different mathematicians and philosophers have a range of opinions on the exact scope and definition of mathematics. <>

Okay. Teacher, take a look.

According to the cosine theorem, there is a file jujube: cos c = a 2 + b 2 - c 2) 2ab) in the substitute state detached into a = 3, b = 3, closed c = 2 3, obtain: cos c = 3 2 + 3 2 - 2 3) 2) 2 3 3).

Simplified: cos c = 3 + 3 - 12) 6 3) cos c = 1 2 3) cos c = 3 6

Because the noisy C is an acute angle, there are: sin c = 1 - cos 2 c) substituted cos c = 3 6, obtain: sharp fluid sin c = 1 - 3 6) 2) sin c = ascending base bridge (1 - 3 36) sin c = 33 36) sin c = 11 2

Because the lost finger infiltrates sin c > 0, c is in the first or second quadrant. Cha Chi again because of c

Kiss. Hello, this is the solution to (2), oh <>

Can the teacher write it by hand, I don't understand what you posted.

This is the meaning of the change.

If you don't understand this, you can ask the teacher.

How does the teacher do this question?

Okay. 1) According to the theorem of Gouzi Concealment Stocks, when A=5, B=12, C=13, the conditions of a right-angled triangle are met, that is, the three-object hand angle ABC is a straight-covered Qiqi angle triangle.

The second thing that does not satisfy the Pythagorean theorem is that ordinary triangles.

The modulus length of the vector mn is a=root number[(10+2) +2-7)]15, because the modulo pn=2pm, so the modulo of pn is 10 and pm is 5; Set p(x,y) then (x+2) +y-7) =5 ,(10-x) +2-y) =10. And -2 choose c: the distance from the outer center to the three vertices is equal.

The sum of the three vectors, starting from the center of gravity and ending at the three vertices of the triangle, is equal to the zero vector.

The product of the two parts of each high line is equal.

1) Let y=0 x1-x2=root number under discriminant formula 1=root number under (k+2) 2-4(2k-1)=2

k^2+4k+4-8k+4=4

k1=k2=2

k=2a（0，3）

2) Find b(1,0).

Find the ab analytic formula y=-3x+3

Because Pb is a circle of diameter, it is tangent to AB at the point B

pb ab set pb to y=kx+b

k*(-3)=-1 (high school knowledge, it is useful to remember, otherwise you have to use similar triangles to push slowly).

k = 1 3 and b(1,0).

So y=1 3x-1 3

Because y=1 3x-1 3

y=x^2-4x+3

x=1 (rounded) or x=10 3, so y=7 9

p（10/3，7/9）

Hope it helps.

Solve the equation first. b=

c = since a intersects c equals the empty set.

So A does not contain the elements in C.

b intersection c = a intersection b is not equal to an empty set.

So A contains elements B.

So a contains 3 elements.

3 is brought into the equation in a.

x^2-ax+a^2-19=0

9-3a+a^2-19=0

a^2-3a-10=0

a=5 or -2

Validation: A=5.

A=Not eligible, A, C, is empty.

a= -2.

a=conforms so a= -2

b=,c=It stands to reason that a c will not be empty... There should be an A in C, right?

Calculate a, because a b≠, 2 or 3 or both belong to or a 2-3a-8 = 0. Solve a and then the elimination method, the problem is less conditional and cannot be solved.

Because the ball must be an integer, first decompose 42, 42 = 2 3 7, that is, the integer divided by 42 has 1, 2, 3, 6, 7, 14, 21, 42

According to the title, you can rule out the possibility of 1, 14, 21, and 42 boxes.

1) If there are 2 boxes, one with 20 and the other with 22, it is obviously not in line with the title after analysis;

2) If there are 3 boxes, arrange them according to the equal difference sequence, put 13, 14, 15 balls in turn in the three boxes, take out 1 of the three boxes respectively, put 3 balls into 13, get 15, and the remaining two boxes have 13, 14 balls, rearrange them, meet the requirements, so the 3 boxes are in line with the theme;

3) If there are 6 boxes, put the number of balls in turn is 5,6,7,7,8,9, take 1 each, a total of 6 put into 5, get 10, and the rest of the boxes are left with 5,6,6,7,8, which does not meet the theme;

4) If there are 7 boxes, put the number of balls in turn is 4,5,6,7,8,9,10, take 1 for each a total of 7 and put it into 4, get 10 balls, and the rest of the boxes are left with 4,5,6,7,8,9 balls, rearrange them, meet the requirements, so 7 boxes also meet the theme.

So, there are 3 or 7 boxes in total.

3 pieces of 13, 14 and 15 balls respectively.

4 Contains 9, 10, 11, 12 balls, 7 Contains 9, 8, 7, 6, 5, 4, 3 balls Details: There are x boxes The box with the least balls was originally filled with m balls, so there are m+x-1 balls in the box with the most balls (since the number of balls in the box has not changed after rearrangement, it means that there is only a ball between adjacent boxes).

m+(m+1)+(m+2)+.m+x-1)=42 is sorted out: 1 2x 2+(m-1 2)x=42 As long as x, m is a positive integer is the answer.

There are 7 boxes in total, and the quantities in the 7 boxes are 3,4,5,6,7,8,9

The original is replaced by x 2 + (3 2) x - 1 2 = 0. Based on the coefficients, the results of a+b and ab are obtained. (a+b)^2=a^2+b^2+。I understand it this way. I use two to denote it.

Known 3 x 4

The left and right sides of the equation are squared, and the equation is solved to obtain the relationship between the increase and decrease of the equation when 3 to 4, and the extreme value can be taken.

Determine the definition domain, i.e., 3<=x<=4. Then f(x) is squared.

Organize the contents of the root number, and then consider the boundary situation of defining the domain, and find it yourself.

The maximum value is 4 and the minimum value is 3