Use the solution of the equation to write the quantitative relationship (equivalent relationship) on both sides of a large paper : a 32 page textbook is printed on both sides of a large piece of paper. After folding it five times, the area of each page is 344.875 square centimeters. What is the area of the large paper used to print textbooks? What else can you find when you look at the copyright page of textbooks? Write the quantitative relation (equivalent relation) with the solution of equation

Set the area of large paper as x square centimeter
x/32=344.875
x=12236

There are 24 pages in Brain Twister and 32 pages in little Copernicus. If the two books are printed on the same thick paper and folded at the same height, at least how many are each?

24 = 2 × 2 × 2 × 3, 32 = 2 × 2 × 2 × 2, the least common multiple of 24 and 32 is: 2 × 2 × 2 × 2 × 3 = 96, 96 △ 24 = 4 (Ben), 96 △ 32 = 3 (Ben). A: at least 4 copies of brain twists and 3 copies of little Copernicus

Divide an equilateral triangle into 12 triangles of the same size and shape!

In the plane, if a graph is moved along a straight line, a new graph will be obtained. Every point in the new graph is obtained by moving a point in the original graph. The two points are (), the line segments connecting the corresponding points () and ()

Corresponding parallel and equal

The square of x minus 6x = 9 times the square of x minus 9 =?
... minus 6x + 9

First multiply 9 on both sides to get: 9x ^ 2-54x = x ^ 2-81, then 8x ^ 2-54x + 81 = 0, and then factor (4x-9) (2x-9) = 0 to get x = 4 / 9, or x = 9 / 2

Let a be a matrix of order n, and a be a n-dimensional column vector. If AA ≠ 0, but a & # 178; a = 0, it is proved that the vector group A and AA are linearly independent

Let k1a + k2aa = 0 (*)
The left of both sides of the equation is multiplied by A
k1Aa + k2A^2a = 0
From a ^ 2A = 0 to k1aa = 0
From AA ≠ 0, we know that K1 = 0
Substituting (*) formula, k2aa = 0
Similarly, K2 = 0
So K1 = K2 = 0
So the vector group A, AA is linearly independent

As shown in the figure, in △ ABC,

Certification:
∵CD⊥AB
∴∠BFD+∠ABE=90º
∵BE⊥AC
∴∠A+∠ABE=90º
∴∠BFD=∠A
∵∠ABC=45º
The ∧ BCD is an isosceles right triangle
∴BD=CD
And ∵ BDF = ∠ CDA = 90 & # 186;
∴△BDF≌△CDA（AAS）
∴BF=AC

The known function f (x) = 1 / 2 * x ^ 2-A ^ 2lnx, a > 0
Finding the minimum value of function f (x)
When X & gt; 2a, it is proved that f (x) - f (2a) / x-2a & gt; 3A / 2

f'(x)=x-a^2/x
Let f '(x) = (x ^ 2-A ^ 2) / x = 0
x^2=a^2,(x>0,a>0)
Then there is x = a
x> A, f '(x) > 0,
x2a
f'(x)>3a/2
That is to say, the unloading rate at any point of the curve on the right side of (2a, f (2a) is more than 3A / 2
∴f(x)-f(2a)/x-2a>3a/2

How to use vector to calculate line surface angle and build system to calculate line surface angle

Only the normal vector of the surface and the vector of the straight line are required, and then the angle between the two straight lines can be calculated by using the formula of the product of the two vectors. The angle between the line and the plane is its residual angle?

It is known that, as shown in the figure, in △ ABC, ad and AE are the bisectors of height and angle of △ ABC respectively. If ∠ DAE = 10 ° and ∠ C = 50 °, the degree of ∠ B can be calculated

∧ ad ⊥ BC, ∧ ADC = 90 °, ∧ DAE = 10 °, ∧ AED = 90 ° - DAE = 90 ° - 10 ° = 80 °, ∧ C = 50 °, ∧ DAC = 90 ° - 50 ° = 40 °, ∧ EAC = 40 ° + 10 ° 50 °, ∧ AE bisection ∧ BAC, ∧ BAE = ∧ EAC = 50 °, ∧ B = ∧ AED - ∧ BAE = 80 ° - 50 ° = 30 °