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Assoli18 [71]
3 years ago
9

Give an example of each of the following, or argue that such a request is impossible.

Mathematics
1 answer:
Masteriza [31]3 years ago
3 0

Answer and Step-by-step explanation:

Solution:

(a) Let (bn) be a bounded sequence of (an) then, Bolzano- Weierstrass theorem,

(bn) contains a subsequence that is converges.

(b) The sequence :

Xn = 1 + (-1) n / 2 + 1/n

Clearly, (xn) does not contain 1 or 0.

If we take sequence (x2n), then it converges to 1 and when we take sequence (x2n+1),

Then it converges to 0.

(c) The sequence:

1

1,1/2

1, 1/2, 1/3

1, 1/2, 1/3, 1/4

i.e

(xn) = (1,1/2, 1, 1/2, 1/3, …)

Then, the subsequence (xn) that is identically ½ in second column and 1/3 is third column and so on.

It has sub sequence that converges to every point in infinite set {1, 1/2, 1/3, 1/4, 1/5…}.

(d) The sequence

{1, 1/2, 1/3, 1/4, 1/5…}

if we take sequence of given set, then, this set converges to zero. This is not contained in it.

If (xn) converges to every point in set {1, 1/2, 1/3 …} then there exists subsequence which converges to 0. And 0 does not belong to given set.

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Please Show your work.
lukranit [14]

Answer:

Equation: y = 2.5x

Answer: 43.75 drawers

Step-by-step explanation:

Equation: 10 - 7.5 = 2.5 and when you subtract 2.5 until the Number of Drawers (x) is 0, then you get 0 for Total Volume (y), so y =2.5x+0 or y = 2.5x

Answer: Substitute 17.5 into x.

y = 2.5(17.5)

y = 43.75 drawers

5 0
2 years ago
the box that contains the salt lick is 1 1/4 feet by 1 2/3 feet 5/6 feet.how many cubes of salt lick fit in the box?explain or s
irakobra [83]

Answer:

24

Step-by-step explanation:

24 cubes. Reasoning varies. Sample reasoning: The length of the box

can fit or 5/4 : 5/12 =3 cubes. The width of the box can fit or 5/3 : 5/12 = 4 cubes.  The height of the box can fit 5/6 : 5/12 = 2 cubes. The box can fit

or 24 cubes.

8 0
3 years ago
Read 2 more answers
Given that the product of 22 integers is equal to 1, prove that their sum is not equal to 0.
Kay [80]

1. If the product of these integers is to be 1, then all of them must be either 1 or -1.

2. Since the product is positive (+1), it must be that there are an *even* number of negative ones (-1), if any.

3. If the sum were 0 it would mean that the number of +1's must equal the number of -1's. So that means there would have to be exactly 22/2=11 of each.

4. But if there were 11 of each, that means the number of -1's would be *odd* and there's no way the product could be +1 (as stated in 2 above).

Hence, the sum is never 0, if the product of 22 integers is equal +1.

4 0
3 years ago
Read 2 more answers
Please help I can’t do this
worty [1.4K]
Answer to a1=6.8
a2= 0.5
mean is 6.78
i don’t know the rest sorry
4 0
2 years ago
What are the coordinates of the endpoints of the segment
Vsevolod [243]

Answer:

A) T'(-3, 6) and V'(0, 3)

Step-by-step explanation:

In the picture attached, triangle TVW is shown.

Transforming points T and V according to the rule (x,y) -> (3/4x, 3/4y), we get:

T(-4, 8) -> (-4*3/4, 8*3/4) -> (-3, 6) which corresponds to T'

V(0, 4) -> (0*3/4, 4*3/4) -> (0, 3) which corresponds to V'

6 0
2 years ago
Read 2 more answers
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