Choose the number equal to: 2/3 divided by (-3) A) -2 B)

Evaluate the summation from n equals 1 to infinity of the quotient of 3 and 2 raised the quantity n minus 1 power

Shalnov [3]

Answer:

3*∑ (1/2)^n = 6

Step-by-step explanation:

We have the summation from n = 1 to n = ∞, for:

∑ 3/(2)^(n - 1)

We know that the summation between k = 0, and k = N - 1 for:

∑ r^k = (1 - r^N)/(1 - r)

if we have the summation between k = 0 and k = ∞ - 1 = ∞

(here we used that ∞ is really big, then ∞ - 1 = ∞)

In the numerator we will have the term r^∞, if 0 < r < 1, then r^∞ = 0.

Then if we assume that 0 < r < 1 we can write:

∑ r^k = 1/(1 - r)

In our case, we can rewrite our summation as:

3*∑ (1/2)^n

for n = 0 to n = ∞

You can see that i changed the limits for n, this does not really matter because we are summing between a number and infinity, the only thing you need to take care is that now the power is n, instead of (n - 1)

Then we have r = (1/2) which is clearly smaller than 1.

then (1/2)

Then this summation is equal to:

3*∑ (1/2)^n = 3*( 1/(1 - 1/2)) = 3*( 1/( 2/2 - 1/2)) = 3*( 1/(1/2)) = 3*2 = 6

3*∑ (1/2)^n = 6

5 0

3 years ago

The opposite angles of a rhombus are equal. a. True b. False

Sergeu [11.5K]

The answer is a, all rhombuses have equal sides, if they have equal sides then day have equal angles.

5 0

3 years ago

Read 2 more answers

Mai had 5 candy bars she ate half of one candy bar and dicided to distribute the remaining bars between her two sisters and her

gogolik [260]

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━

So there are five candy bars.

Herself and two sisters equals 3 people in total.

This is a graph of 5 candy bars, each line being 1/2.

━ ━

If she ate half of one... the graph would become this.

━ ━

━

Now there are 9 halves. You need to split the 9 halves for 3 people. 9 divided by 3 is 3.

Each person gets 3 halves, or 1 and 1 half.

Mai: ━ ━ ━

Sister 1: ━ ━ ━

Sister 2: ━ ━ ━

Altogether that is 9 halves, AKA the number of halves Mai had after she ate 1/2.

The amount Mai ate in the first place: ━

9 halves plus 1 half, equals 10 halves. Each whole has 2 halves. 10 divided by 2 is 5, AKA the number of candy bars she had in the first place.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━

7 0

3 years ago

Zach wants to build a slanted skateboard ramp. He knows he wants the ramp to form a 15 degrees angle with the ground and be 4 fe

Fynjy0 [20]

Answer: The ramp would be 15.5 feet long.

Step-by-step explanation: Please refer to the attached diagram for details.

Angle C shows the angle to be formed by the ramp from the ground, which is 15 degrees. Also, from the ground, it’s going to be four feet tall, which is line AB. The top of the ramp is point A, which makes line AC the entire length of the ramp. Since we have a reference angle (angle C) and two sides, the opposite and the hypotenuse, we shall apply the trigonometric ratio.

SinC = opposite/hypotenuse

Sin 15 = 4/b

By cross multiplication we now have

b = 4/Sin15

b = 4/0.2588

b = 15.4599

Approximately b = 15.5

Therefore the length of the ramp would be 15.5 feet

6 0

3 years ago

HELP FOR BRAINLIEST ANSWER!!!!!

ss7ja [257]

i believe it would be: 1/2y = x

y = 2.5

7 0

3 years ago

Choose the number equal to: 2/3 divided by (-3) A) -2 B) - 2/9 C) 2/9 D) 2