Given that in the intersection of y = sin (ω x + ϕ) and y = 12, the distance between the nearest two points is π 3, then the minimum positive period of this function is () A. π3B. π2C. πD. 2π

Given that in the intersection of y = sin (ω x + ϕ) and y = 12, the distance between the nearest two points is π 3, then the minimum positive period of this function is () A. π3B. π2C. πD. 2π

∵ sin (ω x + φ) = 12, ∵ ω X1 + φ = 2K π + π 6, (1) ω x2 + φ = 2K π + 5 π 6, (2) (2) - (1) get: ω (x2-x1) = 2 π 3; ∵ | x2-x1 | = π 3, ∵ ω· π 3 = 2 π 3, ∵ ω = 2; ∵ period T = 2 π 2 = π
Given that in the intersection of y = sin (ω x + ϕ) and y = 12, the distance between the nearest two points is π 3, then the minimum positive period of this function is ()
A. π3B. π2C. πD. 2π
∵ sin (ω x + φ) = 12, ∵ ω X1 + φ = 2K π + π 6, (1) ω x2 + φ = 2K π + 5 π 6, (2) (2) - (1) get: ω (x2-x1) = 2 π 3; ∵ | x2-x1 | = π 3, ∵ ω· π 3 = 2 π 3, ∵ ω = 2; ∵ period T = 2 π 2 = π
Given that the distance between the nearest two intersections of the intersection of the image of the function f (x) = 2Sin (wx-3.14 / 5) and the line y = - 1 is 3.14/3, the minimum positive period of the function is obtained
3.14 means Pai online, please give a detailed answer
f(x)=2sin(wx-3.14/5)=-1
sin(wx-3.14/5)=-1/2=sin{w[x-3.14/(5w)]}
The distance between the nearest two intersections of y = sin (x) and y = - 1 / 2 is (- 3.14 / 6) - (3.14 * 5 / 6) = 6.28/3
Y = sin [x-3.14 / (5W)] is equivalent to the left-right translation of y = sin (x)
The distance between the nearest two intersections of y = sin [x-3.14 / (5W)] and y = - 1 / 2 is still 6.28/3
Y = sin (wx-3.14 / 5) is equivalent to y = sin [x-3.14 / (5W)] stretching to 1 / W times along the x-axis,
Then the distance between the nearest two intersections of y = sin (wx-3.14 / 5) and y = - 1 / 2 is (1 / W) * (6.28 / 3)
Yes (1 / W) * (6.28 / 3) = 3.14/3
W=2
Because y = - 1
So sin (Wx - π / 5) = - 1 / 2
For y = SiNx, y = - 1 / 2, the distance between the nearest two points is 2 π / 3
So (2 π / 3) / w = π / 3
So w = 2
So t = π
y=-1
sin(wx-π/5)=-1/2
Then Wx - π / 5 = 2K π + 2 π / 3 or = 2K π - 2 π / 3
x=(2kπ+13π/15)/w
Or x = (2k π - π / 15) / W
If two adjacent points are (2k π - π / 15) / W and (2k π + 13 π / 15) / W
Then (2k π + 13 π / 15) / W - (2k π - π / 15) / w = (14 π / 15) / W
If the two adjacent points are (2k π + 13 π / 1,...) expanded
y=-1
sin(wx-π/5)=-1/2
Then Wx - π / 5 = 2K π + 2 π / 3 or = 2K π - 2 π / 3
x=(2kπ+13π/15)/w
Or x = (2k π - π / 15) / W
If two adjacent points are (2k π - π / 15) / W and (2k π + 13 π / 15) / W
Then (2k π + 13 π / 15) / W - (2k π - π / 15) / w = (14 π / 15) / W
If two adjacent points are (2k π + 13 π / 15) / W and (2k π + 2 π - π / 15) / W
Then (2k π + 2 π - π / 15) / W - (2k π + 13 π / 15) / w = (16 π / 15) / W
Obviously, (2k π - π / 15) / W and (2k π + 13 π / 15) / W are closer
So (14 π / 15) / w = π / 3
w=14/45
T = 2 π / w = 45 π / 7 π
According to the meaning of the title:
Y = - 1
sin(wx-π/5)=-1/2
Then WX1 - π / 5 = 2K π + 7 π / 6; the angle of the third quadrant;
Wx2 - π / 5 = 2K π + 11 π / 6; the angle of the fourth quadrant.
So:
x1=(2kπ+41π/30)/w
Or x2 = (2k π + 61 π / 30) / W
According to the image, the distance between the two points is the smallest
x2-x1=π/3;
Out of 100 primary school grade six four operations. (out of more than three steps) specific: 30 decimal operations, 30 fractional operations, 40 mixed operations
Don't make it too difficult
1.3/7 × 49/9 - 4/3
2.8/9 × 15/36 + 1/27
3.12× 5/6 – 2/9 ×3
4.8× 5/4 + 1/4
5.6÷ 3/8 – 3/8 ÷6
6.4/7 × 5/9 + 3/7 × 5/9
7.5/2 -（ 3/2 + 4/5 ）
8.7/8 + （ 1/8 + 1/9 ）
9.9 × 5/6 + 5/6
10.3/4 × 8/9 - 1/3
11.7 × 5/49 + 3/14
12.6 ×（ 1/2 + 2/3 ）
13.8 × 4/5 + 8 × 11/5
14.31 × 5/6 – 5/6
15.9/7 - （ 2/7 – 10/21 ）
16.5/9 × 18 – 14 × 2/7
17.4/5 × 25/16 + 2/3 × 3/4
18.14 × 8/7 – 5/6 × 12/15
19.17/32 – 3/4 × 9/24
20.3 × 2/9 + 1/3
21.5/7 × 3/25 + 3/7
22.3/14 ×× 2/3 + 1/6
23.1/5 × 2/3 + 5/6
24.9/22 + 1/11 ÷ 1/2
25.5/3 × 11/5 + 4/3
26.45 × 2/3 + 1/3 × 15
27.7/19 + 12/19 × 5/6
28.1/4 + 3/4 ÷ 2/3
29.8/7 × 21/16 + 1/2
30.101 × 1/5 – 1/5 × 21
Four mixed operation exercises with parentheses or brackets (decimal, fractional, integer all to a point) only 10
45 × 2/3 + 1/3 × 15
7/19 + 12/19 × 5/6
1/4 + 3/4 ÷ 2/3
8/7 × 21/16 + 1/2
101 × 1/5 – 1/5 × 21
50＋160÷40 （58+370）÷（64-45）
120-144÷18+35
347+45×2-4160÷52
(58+37）÷（64-9×5）
95÷（64-45）
178-145÷5×6+42 420+580-64×21÷28
812-700÷（9+31×11） （136+64）×（65-345÷23）
85+14×（14+208÷26）
（284+16）×（512-8208÷18）
120-36×4÷18+35
3/7 × 49/9 - 4/3
8/9 × 15/36 + 1/27
12× 5/6 – 2/9 ×3
8× 5/4 + 1/4
6÷ 3/8 – 3/8 ÷6
4/7 × 5/9 + 3/7 × 5/9
5/2 -（ 3/2 + 4/5 ）
7/8 + （ 1/8 + 1/9 ）
9 × 5/6 + 5/6
3/4 × 8/9 - 1/3
7 × 5/49 + 3/14
6 ×（ 1/2 + 2/3 ）
8 × 4/5 + 8 × 11/5
31 × 5/6 – 5/6
9/7 - （ 2/7 – 10/21 ）
5/9 × 18 – 14 × 2/7
4/5 × 25/16 + 2/3 × 3/4
14 × 8/7 – 5/6 × 12/15
17/32 – 3/4 × 9/24
3 × 2/9 + 1/3
5/7 × 3/25 + 3/7
3/14 ×× 2/3 + 1/6
1/5 × 2/3 + 5/6
9/22 + 1/11 ÷ 1/2
5/3 × 11/5 + 4/3
45 × 2/3 + 1/3 × 15
7/19 + 12/19 × 5/6
1/4 + 3/4 ÷ 2/3
8/7 × 21/16 + 1/2
101 × 1/5 – 1/5 × 21
How to check decimal addition and decimal subtraction?
Addition is checked by subtraction,
Subtraction is checked by addition
Sum Sn = 1 / A + 2 / A ^ 2 + 3 / A ^ 3 +... + n / A ^ n
.Sn=1／a+2／a^2+3／a^3+...+n／a^n ,①（1/a)Sn= 1／a^2+2／a^3+...+(n-1)／a^n +n/a^(n+1),②①-②,（1-1/a)Sn=1/a+1/a^2+…… +1/a^n-n/a^(n+1)=[1/a-1/a^(n+1)]/(1-1/a)-n/a^(n+1),∴Sn=[a/(a-1)][(1-1/a^n)/(a-1...
Find 600 four mixed operation problems, including integers, fractions and decimals, about the level of grade 6
Or 300 equations, 300 operations
The four mixed operations of fractions, decimals and integers should have + - * / and use integers, fractions and decimals to help. It takes 300 channels
425 -（2.5+1.9）×(0.5-0.5) 425 -2.5+1.9×(0.5-0.5)
425 -2.5+1.9×0.5-0.5 [425 -(2.5+1.9×0.5)]-0.5
[425 -(2.5+1.9) ×((0.5-0.5) [425 -(2.5+1.9) ×0.5]-0.5
1213 -412 -214 -518 -12.5% 0.125×34 +18 ×8.25+12.5%
(78 +1316 )÷1316 2.5×37 ×0.4×213
15314 -2.25-734 89 ×[1516 +(716 -14 )÷12 ]
10×[(45 -0.5) ÷37 ](2.7-4.25×25 )÷2.8×47
1.25+114 ×7.4+125%÷ 58 10-4.68÷7.2+0.05
157 ×(5÷56 -56 ÷5) 18.09×[(1.5+223 )÷3.75-23 ]
0.84÷0.3÷(1.96×18.9) 56 -(0.15+920 ) ÷1.81325+540÷18×15
2.5÷8+9.5×18 +4×0.125 [2.1+7÷(3112 -1.625)] ×123
2.5×25 -2.1÷13 +9.63 (713 +713 ×2+713 )÷43.8+1314 +6.2+327
27 ×[(413 -3.5) ÷58 ] (234 +23 -156 )×122.5÷8+3.5×18 +0.125
(9.5+912 +912 +9.5) ×1212 313 -(157 +18 ÷134 )×125
[(0.05+14 )÷0.25-25 ]×125% 382+498 381382 498-116 5.35×0.25+2.65×14
(313 +34 -258 )÷(115 ÷80%) (4.2÷0.7+6×125 )×526
Title:
What is the difference between the reciprocal of 223 and the quotient of 114 divided by 13?
What is the quotient of the sum of 12 and 13 divided by their difference?
3. What's the product of reducing 125 by 12% and multiplying it by 311?
4. What is the result of the sum of 8 25's adding and removing 4 times of 5.3?
5. Three times of a number is three times more than 35 of 45
6. The sum of 13 and 40 of a number is exactly 120
7.  14 of a number plus 2.5 is equal to 13 of it
When the divisor is 25, the quotient is 4; when the divisor is 14, what is the quotient?
How many meters is 17 meters longer than 637 meters?
10. Number a is 25% more than number B. what percentage of number a is number B? What percentage of number B is less than number a? What percentage of number B is number a?
1.25 times of a number minus 2.5 equals 1212
12. How much is 316 divided by the quotient of 0.375 divided by the product of 15 and 25?
What is the quotient of subtracting the product of 0.4 and 3 from the reciprocal of 23 and dividing it by 6?
14.  a number is 10. Increase it by 20% and then decrease it by 20%. What percentage of the original number is the result?
15. 13 of a number is 12.5 less than 12. What's 20% of the number?
What is the product of the sum of 16.415 and 0.8 multiplied by the difference between 6.4 and 535?
What is the difference between 13 of 17.22.5 minus 4 divided by 0.4?
18. 720 of a number is 0.4 more than 114 times of 3.6. What's the number?
19. 47% of a number is 26.1 less than 82% of 105. What is 82% of this number?
20. 45 of a number is 7.5 more than 30% of 27
Practical questions
1. There are 45 male and 20 female teachers in a school. How many male and female teachers are there in this school?
2. The vehicle factory needs to produce 3000 tricycles. The original plan is to produce 60 tricycles per day, but the actual production is 25% more per day. How many days can the task be completed?
3. Young Pioneers collect waste batteries. The first team collected 160 waste batteries, 14 more than the second team. How many more waste batteries did the first team collect than the second team?
4. Two people produce a batch of parts together, which can be completed in 6 days. It is known that Party A produces 120 parts per day, which is 23 times of Party B's work efficiency?
5. The farm tools factory produced 1680 farm tools in March, and 20% of the output in April was equal to 13% of that in March. How many farm tools were produced in these two months?
6. A pile of red bricks, 35 of which are transported away, and the remaining ones are 360 more than the total number of 14. How many red bricks are there in this batch?
7. There is a manuscript that Li Hong can type with 30 points. When she scores 25 points, there are still 200 words left to type. How many words are there in this manuscript?
8. The car runs 58 times in 4.5 hours from station a to station B. at this speed, how many hours will it take to reach station B?
9. There is a batch of apples in the fruit shop. After selling 13, they are transported in 420 kg. At this time, the quality of the apples is 14 more than the original. How many kg are the original apples in the fruit shop?
10. A total of 60 kg of white sugar and brown sugar are transported into the store. It is known that the mass of brown sugar is 50% of that of white sugar. How many kg of the two kinds of sugar are there?
11. There are 960 kg of coal in the factory. After 18 kg of coal is used in the first day and some in the second day, there are 680 kg left. How many kg are used in the second day?
How to check decimal subtraction and addition?
On the other hand, if 18 + 3 = 21, the checking result is 21-3. If you want to be 18, you can prove that you are right,,, or 21-18