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Neporo4naja [7]
3 years ago
14

(1) In Section 1.4 we used the Axiom of Completeness (AoC) to prove the Archimedean Property of R (Theorem 1.4.2). Show that the

Monotone Convergence Theorem can also be used to prove the Archimedean Property without making any use of AoC.
(2) Use the Monotone Convergence Theorem to supply a proof for the Nested Interval Property (Theore 1.4.1) that doesn't make use of AoC. These two results suggest that we could have used the Monotone Con- vergence Theorem in place of AoC as our starting axiom for building a proper theory of the real numbers

Mathematics
1 answer:
serious [3.7K]3 years ago
3 0

Answer:

Both Answers are in the following attachment (a) and (b)

Step-by-step explanation:

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Solve for x: 1 over 3 (2x − 8) = 4. (1 point)
garik1379 [7]

Answer:

x=6

Step-by-step explanation:

2x - 8 = 4 \\ 2x = 4 + 8 \\ 2x = 12 \\ x =  \frac{12}{2}  \\ x = 6

6 0
2 years ago
Abcd is a rectangle if DB=26 and DC=24 find bc
Anettt [7]
Let's solve this problem step-by-step.

STEP-BY-STEP EXPLANATION:

Let's first establish that triangle BCD is a right-angle triangle.

Therefore, we can use Pythagoras theorem to find BC and solve this problem. Pythagoras theorem is displayed below:

a^2 + b^2 = c^2

Where c = hypotenus of right-angle triangle

Where a and c = other two sides of triangle

Now we can solve the problem by substituting the values from the problem into the Pythagoras theorem as displayed below:

Let a = BC

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

a^2 + 24^2 = 26^2

a^2 = 26^2 - 24^2

a = square root of ( 26^2 - 24^2 )

a = square root of ( 676 - 576 )

a = square root of ( 100 )

a = 10

Therefore, as a = BC, BC = 10.

If we want to check our answer, we can substitute the value of ( a ) from our answer in conjunction with the values given in the problem into the Pythagoras theorem. If the left-hand side is equivalent to the right-hand side, then the answer must be correct as displayed below:

a = BC = 10

b = DC = 24

c = DB = 26

a^2 + b^2 = c^2

10^2 + 24^2 = 26^2

100 + 576 = 676

676 = 676

FINAL ANSWER:

Therefore, BC is equivalent to 10.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3
7 0
2 years ago
Hector has 3/4 hour to spend his homework. He wants to spend 1/3 of this time on math homework, 10 minutes of his time on readin
DENIUS [597]

Answer:

20 minutes

Step-by-step explanation:

Remember that

1\ h=60\ mi

we know that

Hector has 3/4 hour to spend his homework

Convert to minutes

\frac{3}{4}(60)=45\ min

so

1) He wants to spend 1/3 of this time on math homework

To find out the time on math homework, multiply 45 minutes by 1/3

45(\frac{1}{3})=15\ min

2) He wants to spend 10 minutes of his time on reading homework

3) He wants to spend the remaining time on science homework

The time spend on math homework plus the time spend reading homework, plus the time spend on his science homework must be equal to 45 minutes

Let

x ----> the time spend on his science homework

15+10+x=45

Solve for x

25+x=45\\x=45-25\\x=20\ min

3 0
2 years ago
What value of n makes the equation true?<br> 1/2 (n + 4) = 6<br> A. 8<br> B. -1<br> C. 2<br> D. 4
Black_prince [1.1K]
1/2 (8+4)= 6
1/2(-1+4)= 1.5
1/2 (2+4)= 3
1/2 (4+4)= 4

So the correct answer would be A(8)
7 0
3 years ago
Find the distance between A(2,3,5) and B(6,7,-2)<br> (pictures of the answer above)
scoray [572]

Answer:

I think it's B (Sorry if im wrong)

3 0
2 years ago
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