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3 years ago

Test for convergence

Mathematics

1 answer:

natita [175]3 years ago

5 0

Since $\frac{1}{2^{n}}$ is a geometric series, for a series like this to converge, its ratio has to be less than 1.

The ratio is $|\frac{1}{2}| < 1$ , thus, we can conclude that $\sum_{n=1}^{\infty} \frac{1}{2^{n}}$ will converge (ie has a limiting sum)

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How do I find each measure? Please I need answers ASAP it's due at 1:50

Norma-Jean [14]

Answer:

Angle CAD is 44 degrees

Angle ACD is 44 degrees

Angle ACB is 136 degrees

Angle ABC is 22 degrees

Explanation:

29. Triangle ADC is an isosceles triangle because it has two equal sides.

If segments AD and DC are congruent, then segment AC is the base and the base angles of an isosceles triangle are equal.

Let x be angle CAD.

Let's go ahead x;

$\begin{gathered} 92+x+x=180\text{ (sum of angles in a triangle)} \\ 92+2x=180 \\ 2x=180-92 \\ 2x=88 \\ x=\frac{88}{2} \\ \therefore x=44^{\circ} \end{gathered}$

Therefore, measure of angle CAD is 44 degrees.

30. Measure of angle ACD is 44 degrees (Base angles of an isosceles triangle are equal)

31. Let angle ACB be y,

Let's go ahead and find measure of angle ACB;

$\begin{gathered} 44+y=180\text{ (angles on a straight line)} \\ y=180-44 \\ \therefore y=136^{\circ} \end{gathered}$

So measure of angle ACB is 136 degrees.

32. Let angle ABC be z.

Triangle ACB is also an isosceles triangle so the base angles are the same.

Let's go ahead and find z;

$\begin{gathered} 136+z+z=180_{}\text{ (sum of angles in a triangle)} \\ 138+2z=180 \\ 2z=180-136 \\ 2z=44 \\ z=\frac{44}{2} \\ \therefore z=22^{\circ} \end{gathered}$

So measure of angle ABC is 22 degrees.

3 0

1 year ago

Use elimination to solve the system of equations:

zhenek [66]

4
x
+
y
−
2
z
=
0
4
x
+
y
-
2
z
=
0
,
2
x
−
3
y
+
3
z
=
9
2
x
-
3
y
+
3
z
=
9
,
−
6
x
−
2
y
+
z
=
0
-
6
x
-
2
y
+
z
=
0
x
+
2
y
=
4
x
+
2
y
=
4
,
2
x
+
4
y
=
8
2
x
+
4
y
=
8
3
x
+
y
=
4
3
x
+
y
=
4
,
6
x
−
7
y
=
2

8 0

3 years ago

Find each indicated product <br>1) 2s(s-4) <br>2) (w+7) (w+3)<br>3) (x+9) (x-2) 4) (2t-1) (t+5)

Andrej [43]

Answer:

1) 2s(s-4

Ans:

$2(−4)$

$22−8$

2)(w+7) (w+3)

Ans:

$(+7)(+3)$

$(+3)+7(+3)$

$2+3+7(+3)$

$2+3+7+21$

$2+10+21$

4 0

3 years ago

Which number line shows point A at 3, point B at −1.5, point C at , and point D, which is the opposite of point A?

Oduvanchick [21]

Step-by-step explanation:

We have that point A is at 3.

This is 3 units to the right of 0 on the number line.

The point that is opposite of A should be 3 units to the left of 0.

That point will be at -3.

Therefore you have to choose the point that is on -3.

It should be similar to one in the attachment.

6 0

3 years ago

How do you solve -1/12 - (-11/12)

valentinak56 [21]

-1/12 - (-11/12) would change into -1/12 + 11/12 because a double negative (bold print) would become a positive. The answer to the new problem would be 10/12 or 5/6 (depending on if it says to simplify).

7 0

4 years ago