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labwork [276]
2 years ago
15

Is my answer right to this problem ​

Mathematics
1 answer:
VLD [36.1K]2 years ago
7 0
Yes it’s right for this problem
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Let FS R be a finite set. (a) Prove that F is closed (b) Prove that every point in F is an isolated point.
Lorico [155]

Answer:

a) Suppose that F is ordered in ascending order: F = \{x_1,\ldots, x_n\}. Then, the complement of F can be written as

F^c = (-\infty,x_1)\cup (x_1,x_2)\cup (x_2,x_3)\cup \cdots \cup (x_{n-1}, x_{n})\cup (x_n,+\infty)

which is the union of a finite number of open intervals, then F^c is an open set. Thus, F is a closed subset of the real numbers.

b) Take an arbitrary element of F, let us say x_k. Now, choose a real number \epsilon such that

0 there are not other element of F, because \epsilon is less that the minimum distance between x_k and its neighbors.

In case that k=1 we only consider 0, and if k=n we only consider 0.

Then, all points of F are isolated.

Step-by-step explanation:

8 0
2 years ago
How many terms are there in a geometric series if the first term is 3, the common ratio is 4 and the sum of the series is 1,023
Olenka [21]
The sum of a geometric sequence is:

s(n)=a(1-r^n)/(1-r) in our case:

s(n)=3(1-4^n)/(1-4)

s(n)=-(1-4^n)

s(n)=(4^n)-1  and s=1023

(4^n)-1=1023

4^n=1024

n ln4=ln1024

n=(ln1024)/(ln4)

n=5
4 0
3 years ago
You owe 958.62 on a credit card at 9.7 percent apr the minimum payment is 105.00 how much goes toward principal if you make the
weqwewe [10]
APR stands for Annual Percentage Rate and in this problem, we are given APR is equal to 9.7%
Per month rate = 9.7% / 12 months = 0.808%

Total credit interest for 12 months = 958.62 *0.097 = $92.97
In one month = $92.97/12 = $7.7475
If you pay at the end of the first month:
Payment = 105.00
The amount goes to principal:
Amount =$105 - $ 7.7475
Amount = $142.25
7 0
3 years ago
18. Ms. Acosta works in the lab at a pharmaceutical company. She needs to make 21 liters of a 32% acid solution to
defon

Answer:

vbighughyuogytifvyigguhui

Step-by-step explanation:

3 0
3 years ago
Translate Δ A B C 6 units horizontally. How are the values in the ordered pairs affected by the translation?
snow_tiger [21]

Answer:

The x-coordinates are translated 6 units to the left or right while the y-coordinates are not affected.

Step-by-step explanation:

The given triangle has vertices at A(-4,1), B(-2,1) and C(-2,4)

The transformation rule for a horizontal translation by k units is

(x,y)\to (x\pm k,y)

In this case we have k=6

A(-4,1)\to A'(-4\pm6,1)

B(-2,1)\to B'(-2\pm6,1)

C(-2,4)\to C'(-2\pm6,4)

Therefore the x-coordinates are translated 6 units to the left or right while the y-coordinates are not affected.

See attachment

4 0
3 years ago
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