Find the measure of angle

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

Masteriza [31]

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.

3 0

3 years ago

If x and y satisfy both 9x+2y=8 and 7x+2y=4, then y=?

Alex

Answer:

The value of y is -5

Step-by-step explanation:

we have

$9x+2y=8$ ------> equation A

$7x+2y=4$ ------> equation B

we know that

If x and y satisfy both equations, then (x,y) is the solution of the system of equations

Using a graphing tool

Remember that

The solution of the systems of equations is the intersection point both graphs

The intersection point is (2,-5)

therefore

The solution of the system of equations is the point (2,-5)

The value of y is -5

7 0

2 years ago

Evaluate the following expression when b = -2.4<br><br> 2 x 5x =

Illusion [34]

Are you sure it’s b or is it x?

3 0

2 years ago

What is the value of x?

Phantasy [73]

Answer:

value of x = 5.8 mm

Step-by-step explanation:

We have given,

Two right triangles EDH and EDG.

In right triangle EDH, EH = 56mm , DH = 35 mm

Using Pythagoras theorem we can find ED.

i.e EH² = ED²+DH²

56²=ED²+35²

ED²=56²-35²

ED = √(56²-35²) = 7√39 = 43.71 mm

Now, Consider right triangle EDG

Here, EG=44.8mm , GD = x+4 and ED = 7√39

Again using Pythagoras theorem,

EG² = ED² + DG²

44.8²= (7√39)²+ (x+4)²

(x+4)² = 44.8² - (7√39)²

x+4 = √(44.8² - (7√39)²)

x+4 = 9.8

or x = 9.8 - 4 = 5.8 mm

Hence we got the value of x = 5.8 mm

6 0

3 years ago

The price of all rail season tickets to London increased by 4%. The price of a rail season ticket from Cambridge to London incre

kirill115 [55]

Percentage increase in the rate of all rail season tickets to London = 4%
Price of the rail ticket from Cambridge to London increased by = 121.60
Let us assume the price before the increase in the fare = x
Then
4% * x = 121.60 dollars
(4/100) * x = 121.60 dollars
x/25 = 121.60 dollars
x = 25 * 121.60 dollars
= 3040 dollars
So the price of the ticket from Cambridge to London before the increase in price was 3040. I hope the procedure is simple enough for you to understand.

8 0

2 years ago

Find the measure of angle​

Find the measure of angle