The direction of static friction on an object may be perpendicular to the direction of motion of the object. Who can explain? It's best to give an example

The direction of static friction on an object may be perpendicular to the direction of motion of the object. Who can explain? It's best to give an example

The simplest example:
You hold the cup (in the air) and shake it from side to side. The cup is moving from side to side, and the static friction between your hand and the book is in the vertical direction. If there is no static magic friction, you can't hold the cup

Given two fixed points a (- 3,5), B (2,15), and the moving point P on the line 3x-4y + 4 = 0, then the minimum value of | PA | + | Pb | is ()
A. 513B. 362C. 155D. 5+102

Let point a (- 3, 5) be a symmetric point a '(m, n) with respect to line 3x-4y + 4 = 0, then 3 × m − 32 − 4 × n + 52 + 4 = 05 − n − 3 − m × 34 = − 1, and the solution is m = 3N = − 3, that is, a' (3, - 3). Connecting a ′ B and line intersecting at point P, then the minimum value of | PA | + | Pb | is | a ′ B | = (3 − 2) 2 + (− 3 − 15) 2 = 513

The solution of the fractional equation 12x2 − 9 − 2x − 3 = 1x + 3 is ()
A. 3b. - 3C. No solution D. 3 or - 3

The two sides of the equation multiply (x + 3) (x-3) to get 12-2 (x + 3) = x-3, and the solution is x = 3. Test: substitute x = 3 into (x + 3) (x-3) = 0, that is, x = 3 is not the solution of the original fractional equation. Therefore, the original equation has no solution. So select C

Let the inequality x ^ 4 + 6x ^ 2 + a ＞ 4x ^ 3 + 8x hold for all real numbers X. try to determine the value range of the real number a, and use the derivative to do
How to solve it with derivative

x^4+6x^2+a>4x^3+8x
＝〉x^4-4x³+6x²-8x>-a
＝〉x^4-2x³-2x³+4x²+2x²-4x-4x+8>8-a
＝〉x³(x-2)-2x²(x-2)+2x(x-2)-4(x-2)>8-a
＝〉(x³-2x²+2x-4)(x-2)>8-a
＝〉[x²(x-2)+2(x-2)](x-2)>8-a
＝〉(x²+2)(x-2)²>8-a
∵x²+2≥2,(x-2)²≥0
The minimum value of (X & # 178; + 2) (X-2) &# 178; is 0,
In order to make the original inequality hold, it must be 8-A, which is smaller than the minimum value of (X & # 178; + 2) (X-2) &# 178;, that is, 8-a8

If x is a rational number which is not equal to 1, we call 1 / 2 of 1-x the difference reciprocal of X. for example, the difference reciprocal of 2 is 1-2 / 1 = - 1, and the difference reciprocal of - 1 is 1 - (- 1) 1 = 2 / 1. It is known that X1 = - 3 / 1, X2 is the difference reciprocal of x1, X3 is the difference reciprocal of X2, X4 is the difference reciprocal of X3, and so on?
Write down how to do it

X1 = - 1 / 3, X2 = 1 / (1-x1) = 3 / 4, X3 = 1 / (1-x2) = 4, X4 = / (1-x3) = - 1 / 3 = x1, so 2012 / 3 = 670.2, the remainder is 2, so x2012 = 3 / 4

The difference between the square + 3x of the square-4y of the polynomial 5x and the square + 3x + 7 of the square-x of the polynomial 2kx is known
Independent of X, find the value of the square of the algebraic formula 2K - [the square of 3K + (4k-5) + k]

The difference between the square of 5x - the square of 4Y + 3x and the square of polynomial 2kx - the square of X + 3x + 7
=5x²-4y²+3x-2kx²+x²-3x-7
=(6-2k)x²-4y²-7

Which of the following functions can't find zero by dichotomy?
1. F (x) = 3x-1 2. F (x) = x ^ 2 3. F (x) = x absolute value 4. F (x) = INX

Dichotomy for zero point requires continuous function
And the function values of two points should be greater than 0 and less than 0
So you can know
3. The absolute value of F (x) = x cannot be determined by dichotomy
Because the value of the function is always greater than or equal to 0

If y = ax & # 178; + BX + C and an intersection (- 1,0) of X axis, then a + C =?

∵ parabola y = ax & # 178; + BX + C and an intersection (- 1,0) of x-axis
∴a-b+c=0
∴a+c=b

The shape of the parabola is the same as that of the parabola y = - 3x & # 178, but the opening direction is opposite. When x = - 1, y has a minimum value of 2, then the analytical formula of the parabola is

Same shape, opposite opening
The vertex is (- 1,2)
So y = 3 (x + 1) ² + 2
That is y = 3x & # 178; + 6x + 5

（0.3+x)*2=8 7+5x=42 1.3x-x=18.6

（0.3+x)*2=8
0.3+x=8÷2
0.3+x=4
x=4-0.3
x=3.7
7+5x=42
5x=42-7
5x=35
x=35÷5
x=7
1.3x-x=18.6
0.3x=18.6
x=18.6÷0.3
x=62