Step-by-step explanation:
We are picking 6 numbers from the numbers 1,2,3,4,5,6,7,8,9,10. Since we care about numbers being next to each other, we might think of the 10 numbers as being distributed in 5 boxes (which you can think of as the holes):
| 1 2 | 3 4 | 5 6 | 7 8 | 9 10 |
So on the first box we have the numbers 1 and 2, on the second box we have the numbers 3 and 4, and so on. Since we are picking 6 numbers from those 10 numbers, that means we'll have to pick 6 boxes (and inside each box we pick a number), but we only have 5 available boxes, so by the pigeonhole principle, we'll have to pick 1 same box at least two times. Since on each picked box we'll need to pick a number, on this box which was picked two times, we will have to pick both of its numbers. And so those 2 numbers inside that box will be next to each other (meaning they're consecutive numbers).
Answer: It is A=-1<x<-6 is the domain
Answer:
i-its 4....
Step-by-step explanation:
It could be 22 tho. but its 4 ->-
Answer:
(a) First order linear separable differential equation
(b)
(c)
(d)
Step-by-step explanation:
(b) Solve for
The domain of y is:
So the lasrgest interval I on which the solution is defined is:
(c)
Differentiate y:
Evaluate this result into the differential equation:
Therefore, the solution is correct.
(d)
Simply evaluate the function y for x=0 and solve for C1:
Finally substitute into y:
Answer: 2/35
Step-by-step explanation: First you have to find the minimun common multiplier (MCM). 5 and 7 are prime numbers (only divisible by one and themselves), so they MCM is the product of both, resulting in 5 times 7 equals 35. Now you find the equavilent equation to 1/7 and 1/5 to make them in 5/35 and 7/35, respectively. Finally the clear difference is 2/35. (7/35 - 5/35)