Math masters, please come in, in a hurry

The positional relationship is vertical.

The quantitative relationship is equal.

Proof ab=cd

bc = de angle b = angle d = 90

Therefore, it can be seen that the two triangles are congruent.

Hence ac=ce

acb=ced

ced+ecd=acb+ecd=90

Therefore ace=90

i.e. two straight lines perpendicular.

AC perpendicular CE, first of all, through the corner edge theorem to prove that ABC and CDE are congruent triangles, so the angle ACB is called angle 1, angle ace is angle 2, angle ECD is angle 3, so, angle A = angle 3, angle 1 = angle E, and because angle A + angle 1 = 90, angle 3 + angle e = 90, so angle 1 + angle 3 = 90, so angle 2 = 180 - (angle 1 + angle 3) = 90, so angle 2 = 90, so AC perpendicular CE.

It's not easy to use... You can't even pass two mathematical symbols.

AC CE is because of two identical triangles, so spelled, it must be 90 degrees.

9 There is a uniform solution to this type of problem, discovered by a mathematician, and can be used for all odd squares, or us.

Elementary School Mathematics. Competition. The following rules apply.

Fill in 1 in the middle of the first line

Fill in the numbers later in order, like the right diagonal top.

If it is above the square, fill in the number to the bottom of the column where it should be, if it goes out to the right of the square, fill in the number to the leftmost box of the row where it should be, if there is a number on the right.

Or go out to the upper right of the phalanx (i.e., in the diagonal direction).

then fill in the numbers.

Because the quadratic trinomial formula x 2+2ax+b 2 and x 2+2cx-b 2 have a common factor, so the equation x 2+2ax+b 2=0 and the equation x 2+2cx-b 2=0 have a common root, let the common root of these two equations be x, then there is x 2+2ax+b 2=x 2+2cx-b 2, so 2b 2=2(c-a)x, so x=b 2 (c-a), substitute x=b 2 (c-a) into x 2+2ax+b 2=0, [b 2 (c-a)] 2+2a[b 2 (c-a)]+b 2=0, so b 4 (c-a) 2+2ab 2 (c-a)+b 2=0, so b 4 + 2ab 2(c-a)+b 2(c-a) 2=0, both sides divided by b 2 to get b 2+2a(c-a)+(c-a) 2=0, so b 2+2ac-2a 2+c 2-2ac+a 2=0, So B 2-A 2+C 2=0, so B 2+C 2=A 2, so the triangle ABC must be a right triangle.

The outer angles of a triangle are equal to the sum of the two inner angles that are not adjacent to it.

Cross the point D to make a parallel line of BC.

The isotope angles are equal.

The inner misalignment angles are equal.

You can prove it.

The indefinite integral result is not the only derivative, and the verification should be able to improve the computational power of the differential calculation.

Sorry to bother. Digital empire GG flooded but is a calculator web page.

Solution: f(x)=sinx+ 3 cosx

That is, f(x)=asinx+bcosx is formalized into f(x)=asin(wx+q), and the first step is to extract (a 2+b), a 2+b 2)[a (a 2+b 2)sinx+b (a 2+b 2)cosx]; In the second step, let cosq=a (a 2+b 2), sinq=b (a 2+b 2); Then f(x) = (a 2 + b 2) sin(x+q). Therefore, f(x)=sinx+ 3cosx=2(1 2 sinx+ 3 2 cosx)=2(sinxcos 丌 3+cosxsin丌 3)=2sin(x+丌 3), t=2丌 |w丨=2丌, f(x) max=丨a丨=2, f(x) min=-丨丨a丨=-2

Periodic of the function of type such as f( )=asin x ten bcos x type, the maximum value problem, the commonly used auxiliary angle formula:

f(ⅹ)=asinωx+bcosωx

(a +b )sin( where tan =b a, minimum positive period: t=2 丨 丨, the maximum value is obtained from the boundedness of the function.

Find the period, maximum and minimum values of y=sin + 3cosx.

Solution: y=sinx+ 3cos

2 (1 2·sinx + 3 2·cosx) = 2 (sin cos 3 + cosxsin 3) = 2sin ( + 3), minimum positive period: t = 2 = 2 , period is: 2k +2 , (k z), -1 sin(x+ 3) 1, -2 2sin( + 3) 2, the maximum value is 2, the minimum value is -2.

This is the basic property of sinusoidal functions, see the fourth compulsory course in the high school mathematics textbook.

1.First, make sure that f(x) is a function of the second degree.

f(x)+g(x) is the odd function Note the definition of the odd function, so f(x)=-x 2+ax+3 The opening is downward.

Assuming =-1 is the minimum value of a under verification.

Assuming = 2 is calculated first before the value of a is verified.

Calculate a=1, so f(x)=-x2+x+3

It's very simple.

Note: Odd and even, increasing and decreasing, once and twice, etc., can be solved.

If there are still questions, add 422822998

Do x 2 and m 2 mean squared? I don't know the math symbols on the keyboard that I can't type! As long as you understand the concept of defining a domain and the concept of parity functions, these questions are actually quite simple!

1.2x+2(x-3)=26 is easy to obtain x=8, so the length is 8, and the width is 5)2 100m/81

3.800 [Let the ticket ** be x, the equation can be obtained: (30-20)*4.]

4997,4999, 5001, 5003 (Let the first of this consecutive odd number be 2n+1, and the equation can be obtained: 2n+1+2n+3+2n+5+2n+7=20000, i.e., n=2498;.)A simpler algorithm is to divide 20,000 by 4, and then find 2 odd numbers before and after 5000).

5.[The formula is: principal = principal and interest (1+12*monthly interest) year [power]; The calculation can be simplified as: principal = principal and interest (1 + year * 12 * monthly interest); This question is:

a-5）2+（√b-4 -1）2+ |Root number (c-1)-2|＝0a=5 b=4 c=3

Right-angled triangle.

You make it into two perfectly squared formulas, plus an absolute value.