Operation exercises of integral

Operation exercises of integral

1. Simplification: 3 (a + 5b) - 2 (B-A)
2. There is such a question: "calculate the value of (2x ^ 3-3x ^ 2y-2xy ^ 2) - (x3-2xy ^ 2 + y ^ 3) + (- X3 + 3x ^ 2y-y ^ 3), where x = 1 / 2, y = - 1". Student a wrongly copied "x = 1 / 2" into "x = - 1 / 2", but the result of his calculation is also correct. Try to explain the reason and work out this result

Someone rides a bicycle at a constant speed of V2 = 4m / s. at a certain moment, a car in the same direction at the speed of V1 = 10m / s starts to turn off the engine at x = 7m in front of him, and advances at a constant deceleration at the acceleration of a = 2m / s2. How long does it take for the person to catch up with the car?

The time when the car stops: T1 = V1a = 5 & nbsp; s, the displacement during this period is: X1 = v212a = 25 & nbsp; M. during this period, the displacement of the bicycle is: x2 = v2t1 = 20 & nbsp; m ＜ (25 + 7) m, so the bicycle will catch up after the car stops, so the time when the bicycle catches up with the car: 2 = X1 + xv2 = 25 + 74s = 8s

In the known sequence {an}, A1 = 12, and the sum of the first n terms is Sn, satisfying Sn = n2an, (n ∈ n *) (1) find out the values of A2, A3, A4, and generalize the general term formula of an; (2) prove the inequality: an > an + 1 by the conclusion of (1)

(1) From Sn = n2an, A1 = 12, we get: when n = 2, S2 = 4a2, that is, a1 + A2 = 4a2, A2 = 16. When n = 3, S3 = 9A3, that is, a1 + A2 + a3 = 9A3, A3 = 112. When n = 4, S4 = 16a4, that is, a1 + A2 + a3 + A4 = 16a4, A4 = 120. We conclude that an = 1n (n + 1) (n ∈ n *) (2) suppose an ≤ an + 1, then 1n (n + 1) ≤ 1 (n + 1) (n + 2), that is, 1n ≤ 1n + 2 N + 2 ≤ n, i.e. 2 ≤ 0, is contradictory. The hypothesis is not true, so an > an + 1 is true, and the inequality is proved

A car brakes at an initial speed of 5 m / s and moves in a straight line with uniform deceleration. The acceleration is 0.5/s
When a car brakes at an initial speed of 5m / s, it decelerates and moves in a straight line. The acceleration is 0.5/s. (1) the speed of the car after 6S. (2) how long does it take for the car to stop. (3) how long does the car slide when it stops?
This is a physics problem, please write down the calculation process.

Let V 0 = 5 m / s, a = - 0.5 m / S ^ 2, (1) t = 6 s, V, v = V 0 + at = 5-0.5 * 6 = 2 m / S (2) V T = 0, t = (V T-V 0) / a = (0-5) / (- 0.5) = 10 s (3) the final velocity is 0, and the displacement is calculated. According to the formula 2A s = V ^ 2-V 0 ^ 2, s = (0-5 ^ 2) / (- 1) = 25 M

Xiao Ming and Xiao Gang do morning exercises around a 400 meter runway. If they walk from the same place at the same time, they will meet in two minutes,
If two people walk in the same direction from the same place at the same time, they will meet in 20 minutes. If Xiao Ming's speed is faster than Xiao Gang's, what are the speeds of Xiao Ming and Xiao Gang?
I found the answer on the Internet, but I can't understand it. Don't just give me a formula

It takes two minutes for two people to run 400 meters together
At the same place and in the same direction, they can meet each other at least one circle faster than the slower
Xiaoming a m / min, Xiaogang B M / min; 2A + 2B = 400, a + B = 200m; 20A = 20b + 400m; 2A + 2B = 400, a + B = 200m;
The results show that a = 110m; b = 90m

15°25′34〃×3=?
38 ° 24 ′ 36 ″ =? Degrees, 39.28 ° =? Seconds

15°25′34〃×3=15°*3+25′*3+34〃*3=45°+75′+[(102〃)/60]=45°+75′+1.7′=45°+76.7′=45°+(76.7′/60)≈45°+1.2783°=46.2783°38°24′36〃=38°+24′+(36〃/60)=38°+24′+0.6〃=38°+24.6′=38°+(24.6...

The distance between a and B points on the number axis from the origin is 2 and 3 respectively, then the distance between ab points is______ ．

∵ the distance between a and B points on the number axis from the origin is 2 and 3 respectively. We can get that point a represents ± 2 and point B represents ± 3. When points a and B are on the same side of the origin, ab = | 3-2 | = 1; when points a and B are on different sides of the origin, ab = | - 2-3 | = 5

There is a hat. As shown in the figure, the top part of the hat is cylindrical, and the brim part is a ring, which is also made of the same cloth. The radius and height of the hat top are known
The width of the eaves is one decimeter. How many decimeters of cloth should I use to make this hat

At least:
　　1²×3.14 + 1×2×3.14×1  + 【（1+1）²-1²】×3.14
　　=3.14+6.28+9.42
　　=18.84dm²

First grade mathematics [integral addition and subtraction] problem, the best answer before 7:30 tonight, the answer must be correct, "simplified evaluation" problem steps! Upload photos
[Note: 1 / 3 is one third, 2 / 5 is two fifths, and so on, please pay attention]
Completion
1】 Given 2x-y = 3, then the value of the algebraic formula (y-2x) &# 178; - 2 (- y + 2x) + 5 is?
choice question
1】 This is a multiple choice question: if the value of 4Y & # 178; - 2Y + 5 is 7, then the value of 2Y & # 178; - y + 1 is equal to? Option: [a] 2 [b] 3 [C] - 2 [D] 4
2】 A polynomial minus X & # 178; - Y & # 178; is equal to X & # 178; + Y & # 178;, and this multinomial value is? Option: [a] 2x & # 178; [b] - 2x & # 178; [C] 2Y & # 178; [D] - 2Y & # 178; [C] 2Y & # 178; [D] - 2Y & # 178;
3】 The value of the algebraic formula (XYZ & # 178; + 4xy-1) + (- 3xy + XYZ & # 178; - 3) - (2xyz & # 178; + XY)? Options: [a] has nothing to do with X, y, Z, [b] has something to do with the size of X, y, Z, [C] only has something to do with the size of X, [D] only has something to do with the size of X, y
4】 The following is the wrong choice in the following brackets: the [a] is [a] the [a] 2x & \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\35;178; - B & #178;
The problem of "simplification before evaluation"
1】 Note: only this question is simplified, not evaluated: (3x & # 178; - 5xy-6y & # 178; - 1 / 2 (- Y & # 178; - 4xy + 4x & # 178;)
2】 Find the value of the algebraic formula 5x & # 178; - [3x-2 (2x-3) + 7x & # 178;], where x = 1 / 2, simplify X / 2-2 [(X-Y & # 178 / 3) - 1 / 6 (Y & # 178; - 9 / 2x)], and find the value when x = - 3, y = - 3 / 2
3】 It is known that a and B are opposite to each other, C and D are reciprocal to each other, x = 3 (A-1) - (a-2b), y = C & # 178; D + D & # 178; - (D / C + C-2), find the value of (2x-y) / 3 - (3x + 2Y) / 6
Kneel down for answers. If you use photos to answer questions, please write neatly. If you take photos with camera, please avoid blurring. If I finish answering questions within the specified time, I can add 15 wealth value in return. If I finish answering questions after time, but today, I will add 10 wealth value. If the steps are clear and careful, I will add 5 wealth value. If I finish answering questions after time, or if the handwriting is scribbled or skip steps, I will not add additional wealth value

Fill in the blanks
1】 Given 2x-y = 3, then the value of the algebraic formula (y-2x) &# 178; - 2 (- y + 2x) + 5 is?
The answer is: (y-2x) &# 178; - 2 (- y + 2x) + 5 = 3 & # 178; - 2 * 3 + 5 = 9-6 + 5 = 8
choice question
1】 This is a multiple choice question: if the value of 4Y & # 178; - 2Y + 5 is 7, then the value of 2Y & # 178; - y + 1 is equal to? Option: [a] 2 [b] 3 [C] - 2 [D] 4
The answer is: from 2 (2Y & # 178; - y + 1) = 4Y & # 178; - 2Y + 2 = (4Y & # 178; - 2Y + 5) - 3 = 4, so 2Y & # 178; - y + 1 = 2, choose a
2】 A polynomial minus X & # 178; - Y & # 178; is equal to X & # 178; + Y & # 178;, and this multinomial value is? Option: [a] 2x & # 178; [b] - 2x & # 178; [C] 2Y & # 178; [D] - 2Y & # 178; [C] 2Y & # 178; [D] - 2Y & # 178;
The answer is: (X & # 178; - Y & # 178;) + (X & # 178; + Y & # 178;) = 2x & # 178;, choose a
3】 The value of the algebraic formula (XYZ & # 178; + 4xy-1) + (- 3xy + XYZ & # 178; - 3) - (2xyz & # 178; + XY)? Options: [a] has nothing to do with X, y, Z, [b] has something to do with the size of X, y, Z, [C] only has something to do with the size of X, [D] only has something to do with the size of X, y
The answer is: (XYZ & # 178; + 4xy-1) + (- 3xy + XYZ & # 178; - 3) - (2xyz & # 178; + XY) = 2xyz & # 178; - 2xyz & # 178; + 4xy-4xy-4 = - 4, choose a
4】 The following is the wrong choice in the following brackets: the [a] is [a] the [a] 2x & \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\35;178; - B & #178;
The answer is: C A & # 178; - 4 (- A + 1) = A & # 178; + 4a-4
The problem of "simplification before evaluation"
1】 Note: only this question is simplified, not evaluated: (3x & # 178; - 5xy-6y & # 178;) - 1 / 2 (- Y & # 178; - 4xy + 4x & # 178;)
The answer is: (3x & # 178; - 5xy-6y & # 178;) - 1 / 2 (- Y & # 178; - 4xy + 4x & # 178;)
Original test = 3x & # 178; - 5xy-6y & # 178; + 1 / 2Y & # 178; + 2xy-2x & # 178;
=3x²-2x²-5xy+2xy-6y²+1/2y²
= x²-3xy-11/2y²
2】 Find the value of the algebraic formula 5x & # 178; - [3x-2 (2x-3) + 7x & # 178;], where x = 1 / 2
Simplify X / 2-2 [(X-Y & # 178 / 3) - 1 / 6 (Y & # 178; - 9 / 2x)] and find the value when x = - 3, y = - 3 / 2
（1）5x²-[3x-2(2x-3)+7x²]=5x²-[3x-(4x-6)+7x²]=5x²-（3x-4x+6+7x²）=5x²-3x+4x-6-7x²
=-2x²+x-6,
When x = 1 / 2, the original formula = - 2 * (1 / 2) & # + 1 / 2 - 6 = - 6
（2）x/2-2[(x-y²/3)-1/6(y²-9/2x)]=x/2-2（x-y²/3-1/6y²+1/6×9/2x)=x/2-2（x-y²/2+3/4x)
=x/2-2（-y²/2+7/4x)=x/2+y²-7/2x=-3x+y²
When x = - 3, y = - 3 / 2, the original formula = - 3 × (- 3) + (- 3 / 2) &# 178; = 9 + 9 / 4 = 45 / 4
3】 It is known that a and B are opposite to each other, C and D are reciprocal to each other, x = 3 (A-1) - (a-2b), y = C & # 178; D + D & # 178; - (D / C + C-2), find the value of (2x-y) / 3 - (3x + 2Y) / 6
A + B = 0, CD = 1, d = 1 / C, a + B = 0, CD = 1 / C, CD = 1 / C, CD = 1 / C, CD = 1 / C, CD = 1 / C,
So x = 3 (A-1) - (a-2b) = 3a-3-a + 2B = 2A + 2b-3 = 2 (a-b) - 3 = - 3
y=c²d+d²-(d/c+c-2)=cd*c+d*1/c-d/c-c+2=c+d/c-d/c-c+2=2
So (2x-y) / 3 - (3x + 2Y) / 6 = (4x-2y-3x-2y) / 6 = (x-4y) / 6 = (- 3-4 * 2) / 6 = - 11 / 6

VFP design program fixed number of loop statements in the range of 0-999 to find out the number output that meets the following conditions: the value of the number = the sum of the cube of each digit in the number

set talk off
Clear & clear screen
C = 0 & & count, clear, if you don't need to count, delete this sentence
For I = 0 to 999
G = mod (I, 10) & take the number
S = mod (int (I / 10), 10) & take ten
B = int (I / 100) & take hundreds
If I = B ^ 3 + S ^ 3 + G ^ 3
I & & print if conditions are met
C = C + 1 & & count, satisfy a condition, add 1, correspond to C = 0, do not need to count, delete this sentence
endif
endfor
"In the range of 0-999: the value of the number = the sum of the cubes of the digits in the number: + alltrim (STR (c)) +"
return