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The distance between a and B is 540 km. The truck starts from a to B and travels 40 km per hour. At the same time, the car starts from B to a and travels 50 km per hour The two cars are facing each other. After meeting on the way, the two cars are opposite each other. When they arrive at their destination, they return immediately. How many hours does it take from departure to the second meeting?
It took three whole journey from starting to the second meeting
Time = 540 × 3 ÷ (40 + 50) = 18 hours
540/（40+50）=6
A: it takes six hours
Time = 540 × 3 ÷ (40 + 50) = 18 hours
69 times 99 and 68 out of 69
The answer is now
It's due tomorrow
Equal to 69 * (99 + 68 / 69) = 69 * (100-1) + 68 / 69 = 6900-69 + 68 = 6900-1 = 6899
Hope to adopt
69*(100-1/69)
=6900-1
6899 question: Thank you, but I want a more detailed process
A sequence of numbers
Function f (x) = a1 + A2 * x + a3 * (the square of x) + +An * (n minus 1 power of x). F (0) = 1 / 2, the sequence {an} satisfies f (1) = n square * an. Find the general term formula of {an}. There is no reward. Sorry
It doesn't matter if you don't have any points. Not everyone answers questions for virtual points and vanity level
1. F (0) = 1 / 2, then substituting into the expression of F (x), we can easily get A1 = 1 / 2
Substituting 1 into f (x) expression, f (1) = a1 + A2 +. + an
If f (1) = N2 * an, it is not difficult to obtain these two formulas simultaneously
An = (a1 + A2 +. + an-1) / (n2-1) = sn-1 / (n2-1), where sn-1 is the sum of the first n-1 terms
You can get A2 = 1 / 6, A3 = 1 / 12, A4 = 1 / 20 according to the value of A1 and the expression of an above. OK, you can guess whether an = 1 / N (n + 1). OK, the next step is mathematical induction
3. Suppose an = 1 / N (n + 1) is a general term formula
(1) For A1, the general formula is valid
(2) Suppose that the general term formula holds for an-1, where n-1 > 2, then substitute the formula obtained in 1
an=（a1+a2+.+an-1）/n2-1
Let a1 + A2 +. + an-1 = 1 / 1 * 2 + 1 / 2 * 3 +. + 1 / N (n-1)
=(1-1/2)+(1/2-1/3)+.(1/n-1-1/n)
=1-1/2+1/2-1/3.+1/n-1-1/n
=1-1/n
It is not difficult to substitute this result into the above formula
The general formula of an = 1 / N (n + 1) holds
That is to say, the general formula of an is an = 1 / N (n + 1)
The big truck starts from city a, traveling 60 kilometers per hour. After 70 kilometers, the car starts from city a to catch up with the big truck
How many hours can a car catch up with a big truck?
Let the car catch up with the truck in X hours
80x=70+60x
80x-60x=70
20x=70
x=70÷20
x=3.5
A: a car can catch up with a big truck in 3.5 hours
Calculation: (- 2) ^ 100 + (- 2) ^ 99
(-2)^100+(-2)^99
=-2×(-2)^99+(-2)^99
=(-2)^99×（-2+1）
=(-2)^99×（-1）
=-2^99×（-1）
=2^99
It is known that the sum of the first n terms of the sequence {an} is Sn, A1 = 3, and when n ≥ 2n ∈ n + satisfies that sn-1 is the median term of an and - 3. (1) find A2, A3, A4; (2) find the general term formula of the sequence {an}
(1) It is known that sn-1 is the mean of an and - 3. 2sn-1 = an-3, that is, an = 2sn-1 + 3 (n ≥ 2, n ∈ n *) A2 = 2S1 + 3 = 2A1 + 3 = 9A3 = 2s2 + 3 = 2 (a1 + A2) + 3 = 27a4 = 2s3 + 3 = 2 (a1 + A2 + a3) + 3 = 81 (6 points) (2) from an = 2sn-1 + 3 (n ≥ 2, n ∈ n *) (1) a
The truck and car run from a and B at the same time. The truck runs 60 kilometers per hour and the car runs one tenth of the whole journey per hour
When the car reaches 75% of the whole journey, how many kilometers does the truck travel?
75% △ 1 / 10 × 60 = 75% × 10 / 1 × 60 = 7.5 × 60 = 450 (km) a: the truck runs 450 km
Seventy five percent of the total travel time of a small car is 7.5 hours, so a large car travels 450 kilometers
Which is the closest number between 10.19.9 and 10.01
ten point zero one
A mathematical problem. About the sequence of numbers
In the sequence, s (n + 1) = 4A (n) + 2; A1 = 1; (1) let B (n) = a (n + 1) - 2A (n), find that B (n) is an equal ratio sequence?
(2) C (n) = a (n) / (the nth power of 2)
(3) Finding the general term of an
(1) S (n + 2) - A (n + 2) = s (n + 1) = 4A (n) + 2 = 4A (n + 1) + 2-A (n + 2) a (n + 2) - 2A (n + 1) = 2A (n + 1) - 4a (n), i.e. B (n + 1) = 2B (n), A1 = 1, S2 = 6 = 1 + A2, A2 = 5, B1 = 3, that is, BN = 3 * 2 ^ (n-1) (2) C (n + 1) - C (n) = (a (n + 1) - 2An) / 2 ^ (n + 1)
Big trucks and cars travel from the two places with a distance of 360 kilometers. Big trucks travel 60 kilometers per hour, and cars drive 1.5 hours later than big trucks
At the same time, finish the whole journey to a certain place, find the speed of the car
vehicle
Let the car speed be x, then
（360/x）+1.5=360/60
The solution is x = 80
The speed of a car is 80 km / h
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