On the number axis, the distance from point a to the origin is 3, and the distance from point B to the origin is 4

On the number axis, the distance from point a to the origin is 3, and the distance from point B to the origin is 4

On the number axis, the distance from point a to the origin is 3, and the distance from point B to the origin is 4
A is 3 or - 3, B is 4 or - 4
Ψ line AB = │ 4-3 │ = 1
Or line AB = │ 3 - (- 4) │ = 7
Point a is on the left side of the origin on the number axis, and is 2 units of length from the origin. The distance from point B to the origin is 3 units of length. Find the distance between two points ab
1 or 5
According to the meaning of the title
A is - 2
B is - 3 or 3
So the distance between AB is 1 or 5
Point a is on the left side of the origin on the number axis and is 2 units of length from the origin,
Then a is - 2
If the distance from point B to the origin is 3 units of length, then B
3 or - 3
Then AB distance is: 3 - (- 2) = 5 or: (- 2) -(- 3) = 1
We call a () which defines the origin, positive direction and unit length as the number axis a line B line c-ray D line
We call a (d) that defines the origin, positive direction and unit length as the number axis
Line a, line B, line C, line D
C-ray
A point on a number axis that represents an integer is called an integral point. The unit length of a certain number axis is 1 cm. If you draw a line AB with the length of 2012 cm randomly on the number axis,
Then the number of integral points covered by line AB is? A: 2010 or 2011 B: 2011 or 2012 C: 2012 or 2013
D: Who knows which to choose in 2013 or 2014,
Please tell me why
Let's look at a simple example. What if it's a 1 cm line segment?
If the end point coincides with the whole point, two points are covered. If not, only one point can be covered,
Therefore, we can think of 2012 cm can cover 2012 or 2013 points
C: why?
Calculating divisor is the division of decimals. First, convert () into an integer, and then divide according to the calculation method of (). This applies the law of () (to be simple)
Calculating divisor is the division of decimals. First, convert (divisor) to integer, and then divide according to the calculation method of (integer division). This applies the law of (constant quotient)
Y = x + | sin2x | determine monotone interval of function
Method 1
Y = x + | sin2x | is equivalent to
y=x+sin2x kπ≤x≤kπ+π/2
y=x-sin2x kπ+π/2≤x≤(k+1)π
The derivative of the curve equation is obtained
y'=1+2cos2x kπ≤x≤kπ+π/2
y'=1-2cos2x kπ+π/2≤x≤(k+1)π
When y '> - 0, the function increases monotonically
1+2cos2x>0 kπ≤x≤kπ+π/2
1-2cos2x>0 kπ+π/2≤x≤(k+1)π
That is ± cos2x > - 1 / 2
When k π ≤ x ≤ K π + π / 2, if and only if K π ≤ x ≤ K π + π / 3,
Cos2x > Cos2 π / 3, namely cos2x > - 1 / 2
When k π + π / 2 ≤ x ≤ (K + 1) π, if and only if K π + π / 2 ≤ x ≤ K π + 5 π / 6,
cos2x-1/2,
So y = x + | sin2x | monotone increasing interval is [K π, K π + π / 3] u [K π + π / 2, K π + 5 π / 6],
The monotone decreasing interval is [K π + π / 3, K π + π / 2] u [K π + 5 π / 6, K π + π]
Method 2
It's a little complicated. The key is the sum function of Y1 = x and y2 = | sin2x | to judge the monotonicity, we need to use the derivation. (y 'of the derivation of function y is equal to the slope of Y)
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The idea is to divide y into two parts, Y1 = x must be monotonically increasing, and the slope of the line is 1
The period of y2 = | sin2x | is π / 2, and the shape of a single period is an arc above the x-axis
So just consider the case in [0, π / 2], and the rest is repeated
In [0, π / 2], y2 = sin2x, where y2 = sin2x in [0, π / 4] is increasing, but in [π / 4, π / 2], y2 = sin2x is decreasing, and its slope is changing all the time, so the increase or decrease of y can not be judged directly. Therefore, we need to determine whether y = Y1 + Y2 is increasing or decreasing to the bottom by calculating the slope of trigonometric function
The slope of Y2 is K2 = (sin2x) '= 2 * cos2x
So the slope k of Y is the slope 1 of Y1 plus the slope K2 of Y2,
That is, k = 1 + 2 * cos2x, the range of X is [0, π / 2]
After a simple calculation, it can be concluded that:
When x belongs to [0, π / 3], k > 0, that is, y increases monotonically;
When x = π / 3, k = 0 (critical point);
When x belongs to (π / 3, π / 2], K ＜ 0, that is, y decreases monotonically
It is extended to R
When x belongs to [M π / 2, π / 3 + m π / 2], y increases monotonically;
When x belongs to [π / 3 + m π / 2, π / 2 + m π / 2], y decreases monotonically
Of course, don't forget to write that M belongs to Z (usually K belongs to the integer Z, because the K in front of me is used to represent the slope, so I use M instead)
Why is the result different, which is right and why?
In fact, the following interval with M is the combination of the above interval with K
How to express the formula of time distance in letters
What is v equal to? What is s equal to? What is t equal to
What does s = VT mean
V is speed, s is distance, t is time
In engineering, s is also the code of time "second"; t is for "ton"
Divisor is the division of decimals. First, the divisor and the divisor are expanded by the same multiple at the same time, so that the divisor becomes an integer, and then the decimal division of () is used
Divisor is the division of decimals. First, the divisor and the divisor are expanded by the same multiple at the same time, so that the divisor becomes an integer, and then it is calculated according to the decimal division (divisor is an integer)
Monotone decreasing interval of function y = sin2x, X ∈ [0, π]
Because x ∈ [0, π], so 2x ∈ [0, 2 π],
When 2x ∈ [π / 2,3 π / 2], i.e. x ∈ [π / 4,3 π / 4], the function y = sin2x is a decreasing function, i.e
The monotone decreasing interval of the function y = sin2x, X ∈ [0, π] is [π / 4,3 π / 4]
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On the letter of speed in Physics
Our teacher said that all velocities are expressed in V, but in addition to the speed of light, the speed of light is expressed in C, but he also said that the speed of light in vacuum is expressed in C, but the speed of light in other substances is also expressed in V (for example, glass, water, etc.),
But the teacher before us said that as long as the speed of light is in any matter, it is represented by C,
Which statement is right?
C is the speed of light in vacuum, so the speed of light in other media is usually expressed as v