Urgent (10 21:51:23) Find the maximum value of the function f (x) = the square of X + the square of 2A (a is a constant) in the interval [2,4]? Note: if you can't type a square, you use words

f(x)=x²+2a²x+a^4-a^4-1
=(x+2a²)²-a^4-1
Axis of symmetry x = - 2A & sup2;, opening upward
Because - 2A & sup2;

High school mathematics urgent, please answer in detail, thank you! (14 21:51:55)
It is known that f (x) and G (x) are odd and even functions on (- A, a) respectively. It is proved that f (x) · g (x) is odd function on (- A, a)
step

f(-x)·g(-x)=-f(x)·g(x)
So it's an odd function

There is a mathematical problem: given that the product of two numbers is 180, the greatest common factor of the two numbers is 15, what are the two numbers?

180=2×2×3×3×5
15=3*5
The product of these two numbers must be a multiple of 15 × 15 = 225
Because 180 is not a multiple of 225, such two numbers do not exist

What problems should be paid attention to when using discriminant method to find the range of quadratic fraction function?
What problems should be paid attention to when using discriminant method to find the range of quadratic function (a, D are not all zero) with the form of y = (AX ^ 2 + BX + C) / (DX ^ 2 + ex + F)?

For the fractional function y = f (x) = (AX ^ 2 + BX + C) / (DX ^ 2 + ex + F): for any real number y, if and only if the equation y = (AX ^ 2 + BX + C) / (DX ^ 2 + ex + F) about X has a real solution, the problem of "finding the range of F (x)" can be transformed into "the equation about X is known"

Simple calculation: 23 × 62-6 × 31

23×62-6×31
=46×31-6×31
=（46-6）×31
=40×31
=1240

The derivation process of the formula of the relationship between displacement and velocity of the uniform speed change linear motion
Derivation process of vt2-v02 = 2As

Kinetic energy theorem: 1 / 2mvt ^ 2-1 / 2mv0 ^ 2 = ma * s
Vt2-v02 = 2As

In the space rectangular coordinate system o-xyz
(1) Find a point P on the z-axis so that its distance to point a (4,5,6) is equal to that to point B (- 7,3,11);
(2) Given that the distance from point a to the origin of coordinates is equal to 2, the root sign is 3, and its coordinate components are equal, the coordinates of the point can be obtained
(3) Say the trajectory equation of a point with a distance of 4 from the origin

1) If point P is on the z-axis, then the coordinates of point P are (0,0, z1)
If the distance from point P to point a is equal to point B, there is a formula for the distance between two points in space
(4-0)²+(5-0)²+(6-z1)²=(-7-0)²+(3-0)²+(11-z1)²
The solution is Z1 = 10.2
So the coordinates of point P are (0,0,10.2)
2) The coordinate components of the point m are equal, that is, x = y = Z
Let its coordinates be (x, x, x)
Then the distance from it to the origin is 2 √ 3
That is 3x & # 178; = 12
The solution is x = 2 or x = - 2
So the left side of the point is (2,2,2) or (- 2, - 2, - 2)
3) The coordinates of the point with a distance of 4 to the dot are set to G (x, y, x)
Then there is X & # 178; + Y & # 178; + Z & # 178; = 16
So the trajectory is a ball

The volume of water decreased by 112 after ice formation and increased by 111 after ice formation______ ．

After water forms ice, its volume increases by 111

Analysis of physical pulley formula
There are two formulas: 1) f = g / n
② F = wtotal / S = GH / NHg
Under what circumstances are these two formulas used?

The first is the force problem, in the pulley block, the force on each rope is 1 / N; the second is the work problem, the force multiplied by the work distance is equal to the work, the latter formula is wrong

Urgent (10 21:51:23) Find the maximum value of the function f (x) = the square of X + the square of 2A (a is a constant) in the interval [2,4]? Note: if you can't type a square, you use words