need help ASAP!!!
Find the sum of each infinite geometric series, if it exists​

Need Help ASAP!!!Find The Sum Of Each Infinite Geometric Series, If It Exists

Answers

Answer 1

The first series diverges because each successive term is getting multiplied by -3, so the common ratio is larger than 1 in magnitude.

Assuming the second series is

3 - 3/2 + 3/4 - 3/8 + ...

then it converges because the common ratio between terms is -1/2, which is less than 1 in magnitude.

To find the value of the sum, let S denote the n-th partial sum, i.e. the sum of the first n terms in the series:

S = 3 - 3/2 + 3/4 - 3/8 + ... + 3(-1/2)^(n - 2) + 3(-1/2)^(n - 1)

Multiply both sides by -1/2:

(-1/2) S = -3/2 + 3/4 - 3/8 + 3/16 - ... + 3(-1/2)^(n - 1) + 3(-1/2)^n

When we subtract S and (-1/2) S, we see all the middle terms canceling, and we can solve for S:

S - (-1/2) S = 3 - 3(-1/2)^n

S/2 = 3[1 - (-1/2)^n]

S = 6[1 - (-1/2)^n]

As n gets larger, the (-1/2)^n term will converge to 0, leaving us with

lim (n -> infinity) S = 6

so that the series converges to 6.


Related Questions

which expression is equivalent to 7/12?

Answers

if i understand correctly what you mean by this question the answer could be

14/24

28/48

you can just keep multiplying the top and the bottom by the same number to get an equivalent fraction

im sorry if i understood the question wrong, i hope this helped a little bit

Disclaimer: The options are missing. The options to the question are:

A.7x1/12; B.7/7x12/12; C.1/7x7/12; D.12x1/7

The expression equivalent to 7/12 is 7x1/12. So, option A. is the right choice.

What are equivalent fractions?

Two fractions are said to be equivalent fractions when they both give the same value in their reduced or simplest form.

How do we solve the given question?

We are asked to find the expression equivalent to 7/12 from the given options.

To solve the question, we reduce all the options to their simplest form. The option = 7/12 will be our answer.

A. 7 * 1/12 = 7/12B. 7/7 * 12/12 = 1*1 = 1C. 1/7 * 7/12 = 1/12D. 12 * 1/7 = 12/7

As we can see only option A. 7 * 1/12 = 7/12 in its simplest form, so it is the right option.

Learn more about equivalent fractions at

https://brainly.com/question/875439

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Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.

Answers

Answer:

The product of these slopes is [(d-b)/(c-a)] × [(c-a)/(-d+b)] = -1

Proved: This product shows that the slopes are negative reciprocals

Question:

The complete question as seen on brainly ( question ID = 13270010):

Determine the missing information in the paragraph proof.

Given: Line PQ is rotated 90° counterclockwise to form line P’Q’. The lines are perpendicular. Line PQ contains the points (a, b) and (c, d). Line P’Q’ contains the points (–b, a) and (–d, c).

Prove: The slopes of perpendicular lines are negative reciprocals.

The slopes of lines PQ and P’Q’ can be determined using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction

The product of these slopes is ________. This product shows that the slopes are negative reciprocals. It is given that the lines are perpendicular and we have shown that the slopes of the lines are negative reciprocals.

Step-by-step explanation:

Line PQ contains the points (a, b) and (c, d)

Line P’Q’ contains the points (–b, a) and (–d, c)

The two lines are said to be perpendicular.

For two lines are said to be perpendicular, the product of the slope of the two lines must be equal to -1.

Let's determine if it's true for this two lines.

Find attached the the diagram and explanations.

The product of these slopes is [(d-b)/(c-a)] × [(c-a)/(-d+b)] = -1

This product shows that the slopes are negative reciprocals

Answer:5

Step-by-step explanation:

Four different positive integers have a product of 110.
What is the sum of the four integers?

Answers

Answer:32.09

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

To Find Out What are the four Positive Integers, Let's Prime Factorize 110:

110 = 1 × 2 × 5× 11

This means these are the four positive integers by multiplying which results in 110.

Now, The sum of these integers:

=> 1+2+5+11

=> 19

Find the area of the shaded region. Can I have the steps explained please?

Answers

Answer:

76.3 cm²

Step-by-step explanation:

step 1

area of circle= πr²= 3.14*5²= 78.6 cm²

step 2

area of 60° sector= 60/360*area of circle= 1/6*78.6= 13.1 cm²

step 3

Area of equilateral triangle = √3/4a²= √3/4*5²= 10.83 cm²

step 4

Area of circle - area of sector + area of triangle=  78.6 - 13.1 + 10.8= 76.3 cm²

Simplify square root of c^2d^6 / square root of 4c^3d^-4
a. d^2 / 2 square root c
b. d^5 / 2 square root c
c. d^5 / 2-c
d. d^2 / 4c

Answers

Answer: B on ed, i just took my test

Step-by-step explanation:

Answer:

on edge 2021

Step-by-step explanation:

just took the test :)

Suck at maths! HELP!

Answers

Answer:

Step-by-step explanation: you can use a protractor if you have 1 or seeing as the bottom left is 65, the bottom right will be the same, mostly a guess but half 65 and try that.

A=50
Explanation as it is an isosceles triangle it ads up to 180
65+65=130
180-130=50

What’s the answer to this ??

Answers

Answer:

Option C

Step-by-step explanation:

zero's are

(2, 0) and (0, -2)

y= x-2, x<3

(3, 2) and (4,3)

y=x-1, x≥3

These are covered in Option C

What is the vertical asymptote for the reciprocal of y=8x-4

Answers

Answer:

The vertical asymptote for the reciprocal of y=8x-4 is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given Equation : [tex]y = 8x-4[/tex]

Reciprocal of given equation =[tex]\frac{1}{y}=\frac{1}{8x-4}[/tex]

Now to find the vertical asymptote

[tex]\frac{1}{y}=\frac{1}{8x-4}[/tex]

Equate denominator to 0

8x-4=0

8x=4

[tex]x=\frac{4}{8}[/tex]

[tex]x=\frac{1}{2}[/tex]

So, The vertical asymptote is[tex]\frac{1}{2}[/tex]

Hence the vertical asymptote for the reciprocal of y=8x-4 is [tex]\frac{1}{2}[/tex]

If h(x)=x-7and g(x)=x^2, which expression is equivalent to(g*h)(5)?

Answers

Answer:

(g*h)(5) is g(h)=x

Step-by-step explanation:

because if h(x)=x-7 and g(x)=x^2.

How many inches are in a square foot?

Answers

Answer:

144 inches.

Step-by-step explanation:

One foot = 12 inches

One square foot = 144 inches.

Answer:

144

Step-by-step explanation:

Foot=12 inch

Square foot= foot times foot

Square foot= 12 inch times 12 inch

Square foot= 144 square inch.

Can somebody help me with this ?? :)

Answers

Answer:

(-3, -4)

Step-by-step explanation:

6 units down from point F will be x: 2, y: -4

5 units left from there will be x: -3, y: -4

which expression is equivalent to: -9x^-1y^-9/-15x^5y^-3

Answers

Answer:

3 / 5x^6y^6

Step-by-step explanation:

= -9x^-1y^-9/-15x^5y^-3

= -9y-9 / -15x^6y^-3

= -9 / -15x^6y^6

= 3 / 5x^6y^6

Answer:

b on edge

Step-by-step explanation:

Gisele worked as a carpenter for how many hours and worked as a blacksmith for how many hours last week? please help

Answers

Answer: She worked as a carpenter for 12 hours and a blacksmith for 18 hours.

Step-by-step explanation:

18*25 = 450

12*20 = 240

240 + 450 = 690

12 + 18 = 30.

Help pls! I ended up getting the wrong answer, so an explanation would help! (:

Answers

Answer:

4p squared - 28pq

Step-by-step explanation:

4p(p−7q)

=(4p)(p+−7q)

=(4p)(p)+(4p)(−7q)

=4p squared −28pq

Apply the distributive property.
4
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Tap for more steps...
4
p
2
+
4
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4
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Rewrite using the commutative property of multiplication.
4
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Which expression is equivalent to -36 – 8?
Choose 1 answer:

A.36 + 8
B.-36 + (-8)
C.8 – 36
D.-8+36

Answers

Answer is B I got it right on the test :)

Answer:B

Step-by-step explanation:

-36 – 8=-44

36+8=44

-36 + (-8)=-44

8 – 36=-28

-8+36=28

As you can see only B equals -44 just like the expression given,

Hope my explanation helps

The diameter of a bicycle wheel is 50 cm. How many complete rotations does it make over a distance of 3km?

Answers

Answer:

47.12388

Step-by-step explanation:

Wheel Diameter = Wheel 2 x Radius; 50 cm / 2 = 25 cm.

For one rotation of the wheel, the distance travelled = circumference of the wheel.

Circumference = 2 x pi x radius = 2 x 3.1415926858 x 25 cm = 157.07 cm approx.

Distance travelled with 30 turns of the wheel = 30 x 157.07 = 4712.39cm approx.

Distance in meters = 4712.39cm / 100 = 47.12388 meters approximate (1 cm = 1/100th of a meter).

hope it helps you

The requried bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.

What is the circumference?

The circumference of the bicycle wheel is equal to its diameter multiplied by π (pi).

Here

Circumference = diameter x π = 50 cm x 3.14 ≈ 157 cm

To find the number of rotations, we need to divide the distance traveled by the circumference of one rotation:

Number of rotations = Distance ÷ Circumference

Number of rotations = 300000cm ÷ 157 cm = (3000 m ÷ 157 cm) ÷ (100 cm ÷ 1 m) = 1910.82

Therefore, the bicycle wheel makes approximately 1910 complete rotations over a distance of 3 km.

Learn more about circumference here:

brainly.com/question/6465134

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Please help ASAP! Correct answer only! I need to finish this assignment today.
There are 9 college students running for student government class president. The candidates include 5 biology majors.
If 5 of the candidates are randomly chosen to give the first 5 speeches, what is the probability that exactly 3 of the chosen candidates are biology majors?

Write your answer as a decimal rounded to four decimal places.

Answers

Answer:

  0.4762

Step-by-step explanation:

There are 9C5 = 126 ways to choose 5 candidates to give speeches. There are (5C3)(4C2) = 60 ways that 3 of those candidates can be biology majors (and the other two can be non-biology majors). The probability of interest is ...

  60/126 ≈ 0.4762

__

nCk = n!/(k!(n-k)!)

YEAR 9 MATHS- PLEASE HELP
The shape A has been reflected on the line drawn to give shape B.
State the equation of the line.

Answers

Answer:

y=2

Step-by-step explanation:

since the line is horizontal, on the point 2 on the y axis, the equation is 2. If, however the line were to be diagonal, it would have been different, as would it if the line were vertical(in which case, the equated would start x =)

Hope this helps

Answer: y =2

Step-by-step explanation:

factorise 32 x cube minus 8 y square​

Answers

Answer: [tex]8(4x^3-y^2)[/tex]

Step-by-step explanation:

[tex]32x^3-8y^2[/tex]

[tex]8(4x^3-y^2)[/tex]

how to find the distance from a velocity-time graph?

Answers

Answer:

Calculating the distance travelled

Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.

Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.

½ × base × height.

½ × 6 × 2 = 12 m 2

(10 – 6) × 2 = 8 m 2

Answer:

Calculate the total distance travelled by the object - its motion is represented by the velocity-time graph below.

Here, the distance travelled can be found by calculating the total area of the shaded sections below the line.

½ × base × height.

½ × 4 × 8 = 16 m 2

(10 – 4) × 8 = 48 m 2

Step-by-step explanation:


I need help .... can y’all help me

Answers

6. C.

7. B.

8. B.

9. B.

10. C

-7/10+7/15+1/-20+-9/10+11/15+11/-20
what is the answer please help me .....!!!!

Answers

Answer:

-1

Step-by-step explanation:

-7/10+7/15+1/-20+-9/10+11/15+11/-20

= -7/10 + -9/10 + 7/15 + 11/15 + 1/-20 + 11/-20

= -16/10 + 18/15 + 12/-20

= -8/5 + 6/5 + -3/5

= (-8+6-3)/5

= -5/5

= -1

How are the equations of a parabola, ellipse, and hyperbola created?

Answers

Answer:

ellipses and hyperbolas as a simple form has the x-axis as principal axis and the origin (0,0) as center. If it's a circle, c = 0 so a2 = b2. And for the parabola, the standard form has the focus on the x-axis at the point (a, 0) and the directrix the line with equation x = −a.

(I'm sorry I got most of this from google) :(

If g(x)=2x-1 and h(x)= swuare root x, find (g o h) (9)

Answers

Answer:

5

Step-by-step explanation:

To evaluate (g ○ h)(9), evaluate h(9) , then use this value to evaluate g(x)

h(9) = [tex]\sqrt{9}[/tex] = 3, then

g(3) = 2(3) - 1 = 6 - 1 = 5

The day after her birthday party 1/3 of Emma’s birthday cake is left is the remaining cake is shared equally among Emma her brother Owen and their mother and father what fraction of the original Kikoo each of them get

Answers

Answer:1/4

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

1/3 ÷ 4

1/3 x 1/4 = 1/12

cos (x/2) = -sqrt2/2 in (0,360) looking for two values ?? Can someone please help me I can’t seem to figure out how to solve this problem, I’m looking at other examples but I’m still confused please help

Answers

Answer:

135° and 225°

Step-by-step explanation:

basically you want to find the value of x between 0 and 360 in this equation

cos x/2 = -(√2)/2

assume x/2 as n, so

cos n = -(√2)/2

n = 45°

then remember the quadrant system

0-90 1st quadrant, all is POSITIVE

90-180 2nd quadrant, only SIN has positive value

180 - 270 3rd quadrant, only TAN has positive value

270 -360 4th quadrant, only COS positive here.

so if you try to find negative value look into 2nd and 3rd quadrant that related 45° to x-axis (0°or 180°)

so the value of x is

180 - 45 = 135° (2nd quadrant) and

180 + 45° = 225° (3rd quadrant)

The names of 5 boys and 5 girls are in a hat. What is the probability of first drawing a girl’s name and then a boy’s name from the hat?

Answers

Answer:

9/20

Step-by-step explanation:

The probability of drawing a girl's name is 0.5, since there are 5 girls in 10 kids here.  If that girl's name is not replaced, then the probability of drawing a boy's name is 5/9, since there are still such names but the total number of names is now 9.

Thus, the probability of this joint event is (0.5)(9/10) = 4.5/10 = 9/20

Answer:

so drawing a girls name from the hat would be 5/10 since 5 girls are there out of 10 students in total. After, you pick the girls name the total number of student names would become 9 and since there are 5 guys, you get a 5/9 probability

Dr.Chavez drew a rectangle on a coordinate plane to estimate the size of a lake. Each unit represents 1 mi. The coordinates of the rectangle are the origin, (0,7.65), (12.8, 7.65) and (12.8,0). Based on the information, what is the perimeter of the lake?

Answers

Answer:

40.9 mi

Step-by-step explanation:

The four points will make the rectangle, and each pair of points in sequence will create a side of the rectangle. So, to find the length of each side, we need to find the distances between each pair of points in sequence:

distance between (0,0) and (0, 7.65) -> |7.65 - 0| = 7.65 mi

distance between (0,7.65) and (12.8, 7.65) -> |12.8 - 0| = 12.8 mi

distance between (12.8, 7.65) and (12.8, 0) -> |0 - 7.65| = 7.65 mi

distance between (12.8, 0) and (0, 0) -> |0 - 12.8| = 12.8 mi

So the perimeter is 7.65 + 12.8 + 7.65 + 12.8 = 40.9 mi

Answer:

40.9 mi

Step-by-step explanation:

will make it simple and short

in a surveying measurements with coordinates, we always take it from the Zero. So each coordinates must be subtracted from Zero to get the length of each point.

therefore the perimeter = 0 + 7.65 + 12.8 + 7.65 + 12.8 + 0 = 40.9 mi

The interior angles of a triangle are 42°,56° and 2x°. Find the value of x.

Answers

Answer:

41 degrees

Step-by-step explanation:

Since the sum of the interior angles of a triangle will always be 180 degrees:

42+56+2x=180

2x=82

x=41

Hope this helps!

Answer:

X=41°

[tex]solution \\ 42 + 56 + 2x = 180(sum \: of \: angle \: in \: triangle) \\ or \: 98 + 2x = 180 \\ or \: 2x = 180 - 98 \\ or \: 2x = 82 \\ or \: x = \frac{82}{2} \\ x = 41[/tex]

hope this helps...

Good luck on your assignment...

Mary is paid 7.5% commission on all of her sales. She had sales of $2300 for the month of December. How much commission did Mary make?

Answers

Answer: $172.50

Step-by-step explanation:

$2300 x 0.075 = $172.50

You can double check quickly because you know 10% of 2300 is $230, so 5% is $115.  The answer is halfway between the 5% and 10% numbers, so you know it is reasonable.

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