(answer with formula and analysis) 1. There are four workshops in a factory. The number of people in the first workshop is one third of the total number of people in the other workshops. The number of people in the second workshop is one fourth of the total number of people in the other workshops. The number of people in the third workshop is one fifth of the total number of people in the other workshops. There are 460 people in the fourth workshop? 2. Grandfather Zhang climbs a mountain every day. It takes 20 minutes to walk every 100 meters up the mountain. It takes 5 minutes to walk every 40 meters down the mountain. Grandfather Zhang always takes a rest in a pavilion one hour after climbing the mountain. He just arrives at the pavilion one hour down the mountain. How many meters does he have to walk every day for exercise?

(answer with formula and analysis) 1. There are four workshops in a factory. The number of people in the first workshop is one third of the total number of people in the other workshops. The number of people in the second workshop is one fourth of the total number of people in the other workshops. The number of people in the third workshop is one fifth of the total number of people in the other workshops. There are 460 people in the fourth workshop? 2. Grandfather Zhang climbs a mountain every day. It takes 20 minutes to walk every 100 meters up the mountain. It takes 5 minutes to walk every 40 meters down the mountain. Grandfather Zhang always takes a rest in a pavilion one hour after climbing the mountain. He just arrives at the pavilion one hour down the mountain. How many meters does he have to walk every day for exercise?

1. The first workshop accounts for 1 / (1 + 3) = 1 / 4 of the total number, the second workshop accounts for 1 / (1 + 4) = 1 / 5 of the total number, the third workshop accounts for 1 / (1 + 5) = 1 / 6, the fourth workshop accounts for 1-1 / 4-1 / 5-1 / 6 = 23 / 60, the total number of people: 460 △ 23 / 60 = 1200, the climbing speed: 100 △ 20 = 5m / min, the distance from the mountain to the pavilion: 60 * 5 = 300

Applied mathematics problems (Grade 6) (top student)
A middle school enrolled 750 students last year. This year, the number of male students increased by 1.6, while the number of female students decreased by 1.5?

Boys increased by 1 / 6,
If the number of female students also increases by 1 / 6, the total number of female students will also increase by 1 / 6
750 * (1 + 1 / 6) = 875
Now the number of girls is reduced by 1 / 5, compared with the increase of 1 / 6;
1/6+1/5=11/30
875-710 = 165
So last year girls were:
165 / (11 / 30) = 450
This year, the number of female students: 450 * (1-1 / 5) = 360
This year, the number of boys is 710-360 = 350

There are signs everywhere on the expressway to remind drivers to keep a reasonable distance. Try to estimate the distance according to the following data: the car is driving on the expressway at the speed of 120km / h, and the car is in front of the road
When the car stops on the road due to a fault, it takes 0.6s for the driver to brake immediately when he finds out the situation. After the emergency braking, the acceleration of the car sliding forward is 0.6m/s2, which can be regarded as uniform deceleration movement?

According to the data in the question, it can be calculated as follows:
S=（120/3.6)*0.6+(120/3.6)*(120/3.6)/2/0.6
=945.9m
I feel that the acceleration is a little small! Is there something wrong with the data!
It doesn't matter! If it's not the acceleration, just replace 0.6 with the correct one!

On the clock face, the minute hand rotates 360 degrees. How many degrees does the hour hand need to rotate?

Minute hand 360 is an hour, clock 30 degrees

Shanghai Nanjing Expressway is 274 kilometers long. A bus leaves from Shanghai and runs at 95 kilometers per hour. After a period of time, there are 84 kilometers left in Nanjing

Let the bus travel time be t
The result is: 95t + 84 = 274
95t=274-84
95t=190
T = 2 hours
The bus runs for 2 hours

If n is an integer, a ^ 2n = 2, find the value of (2a ^ 3n) ^ 2-3 (a ^ 2) ^ 2n

(2a^3n)^2-3(a^2)^2n
=4a^6n-3a^4n
=a^4n(4a^2n-3)
=(a^2n)^2(4a^2n-3)
Because a ^ 2n = 2, so:
Original formula = 2 ^ 2 (4x2-3) = 20

The roads and railways between a and B are parallel. Trains travel 60 kilometers per hour, cars 40 kilometers per hour, and trains from a to B
2 hours less than the car. How many kilometers is the distance between a and B?

Set the distance to x km
x/40-x/60=2

If (m-1) x ^ m ^ 2 is a quadratic monomial about X, y, then M=__ And its coefficient is___ ?

If (m-1) x ^ m ^ 2 is a quadratic monomial about X, y, then M=_ √2_ And its coefficient is_ （√2）-1__ Pro, please adopt. Your adoption is my motivation. Thank you

There was a batch of cement on the construction site. More than 40% of the total amount of cement was used in 20 bags. Later, 280 bags were transported in. This is because the number of cement bags increased by 25% compared with the original. There were 20 bags on the construction site
How many bags?

There were x bags on the construction site
x-(x*40%+20)+280=x(1+25%)
0.6x+260=1.25x
260=0.65x
x=400
A: there were 400 bags on the construction site

Let a (x1, Y1), B (X2, Y2) be functions f (x) = (1 / 2) + log2 (x / 1-x), and OM = (1 / 2) (OA + OB)
(1) Calculate the ordinate value of point M;
(2) Find S2, S3, S4 and Sn;
(3) Given an = 1 / (Sn + 1) (Sn + 1 + 1), where n ∈ n *, and TN is the sum of the first n terms of the sequence {an}, if TN ≤ λ (Sn + 1 + 1) holds for all n ∈ n *, try to find the minimum positive integer value of λ
The abscissa of point m is 1 / 2, and Sn = f (1 / N) + F (2 / N) + +F (n-1 / N), where n ∈ n * and N ≥ 2,

S (n) = (n-1) / 2 + log (1 / N) - log (n-1) / N) + log (2 / N) - log (n-2) / N) + log (3 / N) - log (n-3) / N) +. Log (n-1 / N) - log (1) / N). Obviously log (1 / N) - log (n-1) / N) + log (2 / N) - log (n-2) / N) + log (3 / N) - log (n-3) / N +. Log (n-1 / N) - log (1) / N) = 0, so s (n) = (n -