for n prove by
[tex]3 + 3 {}^{2} + 3 {}^{3} ... + 3 {}^{n} = \frac{3(3 {}^{n} - 1) }{2} [/tex]
thank you​

Answers

Answer 1

Answer:

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Step-by-step explanation:

Given

[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]

Required

Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]

The above shows the sum of a geometric series and this will be calculated as shown below;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]

Where

a = First term;

[tex]a = 3[/tex]

r = common ratio

[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]

[tex]r = 3[/tex]

Substitute 3 for r and 3 for a in the formula above;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes

[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]

[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]

Hence;

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Answer 2
12 5 that is the answer for your question

Related Questions

Pls answer I need help please give me an answer and a explanation

Answers

Answer:y=4x

Step-by-step explanation:

Answer:

4x = y

Step-by-step explanation:

Since we see that "X" multiplied by 4 is "Y" in every pattern,

we get the equation that 4 times of x (4x) is equal to the corresponding y.

and Thus we have the final answer of 4x = y.

Hope this helps!

Find the slope of this graph

Answers

The answer is 3/2 you use rise over run , rise up 3 run 3, remember to pick 2 even points no points that look like they could be fractions . Whole numbers.
Option A. 3/2 is the slope of the graph

Sam can paint the house in 7 days by himself, while Betty can paint the same house in 42 days. How long would it take Sam and Betty to paint the same house together?

Answers

Answer:

It would take 6 days for Sam and Betty to paint the same house together.

Step-by-step explanation:

Let x represent the time it takes ( in days ) to complete painting the house working together. Our approach here is to add the rates of the two people, equal to the total rate, or 1 / 7.

Sam's rate = 1 / 7 ( 7 days to paint 1 house ),

Betty's rate = 1 / 42 ( 42 days to paint 1 house )

1 / 7 + 1 / 42 = 1 / x - now let us solve for x, our solution

1 / 7 + 1 / 42 = 1 / x ( multiply either side by 42x )

7x = 42,

x = 42 / 7 = 6 days

I believe you would divide 42 by 7 and you would get 6

A state highway department uses a salt storage enclosure that is in the shape of a cone, as shown above. If the volume of the storage enclosure is 48π m3, then what is the diameter of the base of the cone, in meters?

Answers

Answer:

Diameter of the base of the cone = 8 meters

Step-by-step explanation:

State highway department uses a salt storage enclosure which is in the shape of a cone.

Height of the storage in conical shape = 9 meters

Volume of the storage = 48π m³

Let the radius of this conical storage = r meters

Formula to get the volume of a cone = [tex]\frac{1}{3}\pi r^{2}h[/tex]

Here 'r' is the radius of the base of the cone and 'h' is the height of the cone.

Therefore, Volume = [tex]\frac{1}{3}(\pi ) r^{2}(9)[/tex]

[tex]48\pi=3\pi r^{2}[/tex]

r² = [tex]\frac{48\pi }{3\pi }[/tex]

r = [tex]\sqrt{16}[/tex]

r = 4 meters

Since, diameter = 2r

                          = 2(4)

                          = 8 meters

Therefore, diameter of the base of the cone = 8 metres

Answer:

Explanation: it’s just right

Amir drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving. Graph the relationship between Amir's altitude relative to sea level (in meters) and time (in minutes).

Answers

Answer:

Graph these two points: (0, 360), (30, 0)

Step-by-step explanation:

Since Amir drove for 30 minutes at a rate of 12 meters, that means that he started at an elevation of 360 feet. The easiest way to graph this, is to place one dot at (0, 360), and at (30, 0).

The straight line joining the points (0, 360) and (30, 0) will be the graph.

What is the equation of a straight line? What do you mean by domain and range of a linear function?

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

(y - y₁) = m(x - x₁)                              {Point - slope form}

(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁)     {Two point - slope form}

x/a + y/b = 1                                       {intercept form}

x cos(β) + y sin(β) = L                         {Normal form}

For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have Amir who drove from Jerusalem down to the lowest place on Earth, the Dead Sea, descending at a rate of 12 meters per minute. He was at sea level after 30 minutes of driving.

We can write the equation of graph as -

y = - 12t + 360

At t = 0 -

y = 0 + 360

y = 360

and

at t = 30 minutes -

y = - 12 x 30 + 360

y = - 360 + 360

y = 0

The straight line joining the points (0, 360) and (30, 0) will be the graph.

Therefore, the straight line joining the points (0, 360) and (30, 0) will be the graph.

To solve more questions on straight lines, visit the link below-

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Whats 7 over 10m plus 9 plus 3 over 1 I need help

Answers

Answer:

12.7

Step-by-step explanation:

(7/10)+((9+3)/1)

(0.7)+(12)

12.7

12.7





Just took a test with this!!!

Please help me with this geometry question:((

Answers

Answer:

x = 13

RQ = 160°

Step-by-step explanation:

Inscribed angles are half the intercepted arc angle.

5x + 15 = ½ (RQ)

RQ = 10x + 30

Arc angles add up to 360°.

10x + 30 + 9x + 17 + 6x − 12 = 360

25x + 35 = 360

25x = 325

x = 13

Therefore, RQ = 160°.

X=13 that the answer to your question

What is -8.64 -0.024?
360
- 36
-360
36​

Answers

Answer:

(-8.64) / (-0.024) = 360

Step-by-step explanation:

You have to type like this in your question;

(-8.64) / (-0.024)

or [tex]\frac{-0.024}{-8.64}[/tex].

Bye!

Your answer will be 360

this is just a personal question if i have 47 assignments to do and i have to finish by the 20th of august how many do i need to do a day

Answers

Answer:

Hey there!

Today is August 7th, 2020.

Thus, August 20th is in 13 days.

If you have 47 assignments, you would have to do 3-4 a day to finish on time.

Hope this helps :) And good luck with your assignments.

Answer:

You have to do about 3 and a half assements a day.

Step-by-step explanation:

Just do 47 divides by 20 but since it is the 7th do 47 divides by 13

Have a nice day!

Which linear inequality is represented by the graph?
y


Answers

Answer:

the third one

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

What is the value of f(1)?

Answers

Answer:

A function normally tells you what y is if you know what x is.

Inverses. A function normally tells you what y is if you know what x is. The inverse of a function will tell you what x had to be to get that value of y. A function f -1 is the inverse of f if. for every x in the domain of f, f -1[f(x)] = x, and.

The two points on the coordinate plane represent Jane's house and her friend's house. Find the distance between the houses. Question 3 options: A) units B) units C) units D) units

Answers

Answer:

8.3

Step-by-step explanation:

To do this use the distance formula

[tex]d = \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

First find the coordinates Jane (-5, -2) Friend (3, -4)

Now solve for d (8.246)

Answer:

10 units or approx. 8.25 units

Step-by-step explanation:

Jane's house is at coordinate (-5,-2) and her friend's house is at coordinate (3,-4).

You can find the answer in 2 ways.

1) Hypotenuse (the diagonal side or side across from the right angle) - approx. 8.25 units

2) Down and Side (go down 2 units and go side 8 units) - 10 units

Hope that helps and maybe earns a brainliest!

Have great day ahead! :)

A building 50ft tall is on top of a hill A surveyor is at a point on the hill and observes that the angle of elevation to the top of the
building measures 48° and to the bottom of the building is 20°. How far is the surveyor from the bottom of the building?

Answers

Answer:

48-20

Step-by-step explanation:

The distance of the surveyor from the bottom of the building is  125.1 feet.

What is the angle of elevation?

You look straight parallel to the ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called the angle of elevation.

Assume the distance of the surveyor from the bottom of the building is represented by x.

First, we have to know that the Tan of 48° is equal to 1.11.

The equation to get the distance will then be;

tan(48) = 50/h

h = 45.05  feet

Now, tan(20) = 45.05  /x

x = 45.05  / 0.36

x = 125.1 feet

The distance of the surveyor from the bottom of the building is  125.1 feet.

Learn more about trigonometric;

brainly.com/question/21286835

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Sasha deposited $1,400 in an account that pays 1.5% simple interest. She created a graph of her
account balance equation (A = Prt + P) with a slope of 21.

true or false?

Answers

Answer:

The answer is False.

I would agree. It would be false


Calculate the surface area of a cube when the length of a side a = 15cm.
Surface area = 6a^2​

Answers

Answer:

[tex]\boxed{ \sf 1350 \ cm^2}[/tex]

Step-by-step explanation:

Surface area of a cube = 6a²

a = side length

The side length is given 15 cm.

[tex]6(15)^2[/tex]

[tex]6(225)[/tex]

[tex]1350[/tex]

The surface area of the cube is 1350 cm².

The surface area of the cube is 1350cm^2

hey im sry if im asking to many questions i really want help

Answers

Answer:

V= 6,000 cm^3

Step-by-step explanation:

(15*20*10) + (10*20*15)

3000 + 3000

6000 cm^3

Answer:

6000 cm³

Step-by-step explanation:

20 * 10 * 15 + (20 * 10 * 15) = 6000 cm³

What is the value of (-3 + 3) + (-2 + 3)?
0-5 - 61
D-5 + Bi
5 + 61
5-61

Answers

the answer is 1 hope this helps :)

Answer:

1

Step-by-step explanation:

(-3 + 3) + (-2 + 3) =

= 0 + 1

= 1

Jill paid $36 for calendars marked down $5 apiece from the original price, she could have gotten 5 fewer calendars. How many cards did she buy

Answers

Answer:

she bought 7 cards

Step-by-step explanation

7x5=35 and im sure there is tax

She bought 7 cards .. I say that bc if you divide 36 and 5 you’d get 7 and 5x7 is 35


The steepness or grade of a road is expressed as a percent. if a road rises 6feet for every 24 horizontal feet. What is the slope of the road? what percent grade is this ?

Answers

Answer:

  25%

Step-by-step explanation:

The ratio of rise to run is ...

  rise/run = 6 ft/24 ft = 1/4

Expressed as a percentage, this is ...

  1/4 × 100% = 25%

_____

Comment on this grade

Interstate highways are limited to a 7% grade. Most local jurisdictions limit the grade of a road to somewhere between 12% and 15%.

um the person above me answered it

To make a large poster of the bill of rights to hang on the classroom wall, a poster that is 22 inches by 46 inches is copied. In the classroom version is to be 3 1/2 times scale, what are the dimensions of the new document? PLEASE ANSWER QUICKLY WILL GIVE BRAINLIEST WHOEVER ANSWERS FIRST!! MUST BE CORRECT!!!!

Answers

Answer:

77 inches by 161 inches

Step-by-step explanation:

This is because you need to multiply 22 by 3.5(3 1/2) and the answer you get is 77 then you multiply 46 by 3 1/2 and the answer you get is 161.

So the dimensions of the new document is 77 inches by 161 inches.

Someone pls help . Thank you sm ! i forgot how to do this lol .

Answers

Answer:

x = - 20, h = 34

Step-by-step explanation:

i can't tell ypou what the class period is, but for -x = 20, multiply each side by -1, then you get x = -20

-32 = 2-h

+32 .  +32

0=34-h

+h .   +h

34=h

flip

h=34

X= -20 and H= 34 the first one you just carry the negative sign to the 20

If you transform x2 + y2 = 25 into 4x2 + 4y2 = 25, which option below describes the effect of this transformation on the radius? A. It multiplies the radius by 2. B.It multiplies the radius by 4. C.It divides the radius by 4. D.It divides the radius by 2.

Answers

Answer:

C. It divides the radius by 4.

Step-by-step explanation:

We have x2 + y2 = 25.

If all terms were multiplied by 4, we would have 4x2 + 4y2 = 100. But, the radius is 25 units. 100 / 25 = 4. So, the radius was divided by 4.

Hope this helps!

The correct answer is C

Sala earns 12 dollars each hour working part-time at a bookstore. She earns one additional dollar for each book that she sells. Let A be the amount (in dollars) that Salma earns in an hour if she sells B books. Write an equation relating A to B. Then graph your equation using the axes below.

Answers

Answer:

y=12a+b

Step-by-step explanation:

answer: y=12a+b :))))

5. Given that x=-2 is a zero of P(x)=2x3 + x² - 1 1x –10, factor
P(x) as a product of its linear factors. Then find the other zeros.

Answers

Step-by-step explanation:

x = -2 is a zero, so x + 2 is a factor of P(x).

Use grouping to factor.

P(x) = 2x³ + x² − 11x − 10

P(x) = 2x³ + 4x² − 3x² − 11x − 10

P(x) = 2x² (x + 2) − (3x² + 11x + 10)

P(x) = 2x² (x + 2) − (x + 2) (3x + 5)

P(x) = (x + 2) (2x² − (3x + 5))

P(x) = (x + 2) (2x² − 3x − 5)

P(x) = (x + 2) (x + 1) (2x − 5)

The other zeros are x = -1 and x = 5/2.

wat is (12+6-5*3)*(2*2+1-7+2)=

Answers

Answer:

[tex]\huge\boxed{0}[/tex]

Step-by-step explanation:

First we have to do the operation of multiplication

=> (12+6-15)*(4+1-7+2)

Now, Solving the terms inside the brackets

=> (18-15)*(5-7+2)

=> (3)*(-2+2)

=> (3)*(0)

=> 0

Answer:

[tex]\Huge \boxed{{0}}[/tex]

Step-by-step explanation:

[tex](12+6-5*3)*(2*2+1-7+2)[/tex]

Solve brackets.

[tex](12+6-15)*(4+1-7+2)[/tex]

[tex](3)*(0)[/tex]

Multiply both numbers.

[tex]3 \times 0 = 0[/tex]

If you're good at bearings please help meeeeee with full working out tyyyyyy

Answers

Letter B. Have a nice day
Bno. Is the correct answer

Please help me with this question. I need to submit today. Question number 4. Lhakpa is a name of the person.

Answers

Answer:

Known:

width: 1/3

length: 3/5

Ask:

the area of floor?

Solution:

We need to multiply the width and length first!

width × length

= 1/3 × 3/5

= 3/15

= 1/5

Next subtract the number of floor witch has full fraction 1/1, so

= 1/1 - 1/5

= 5/5 - 1/5

= 4/5

So, the area of the floor is 4/5

hope it helps ^°^

The Area of the Floor is 4/5

Write the equation for the following table:
X. Y.
0 3
1 7
2 11
3 15

Answers

Answer:

[tex] y = 4x + 3 [/tex]

Step-by-step explanation:

The equation of the table of values given can be written as [tex] y = 4x + 3 [/tex] .

When x = 0,

[tex] y = 4(0) + 3 [/tex]

[tex] y = 0 + 3 = 3[/tex] this corresponds with what we have in the table above.

Let's try another.

When x = 2,

[tex] y = 4(2) + 3 [/tex]

[tex] y = 8 + 3 [/tex]

[tex] y = 11 [/tex]

This also corresponds with what we have in the table.

Therefore, the equation of the table given is [tex] y = 4x + 3 [/tex] .

y=4x+12 thats the equation

Graph the line with the slope 1/3 that contains the point (-4, -3)

Answers

Answer:

So, 1 point is on (-4, -3)

Other point is on (-4, -7)

Step-by-step explanation:

Slope = y/x - y1/x1

=> -3 / -4 - ? = 1/3

=> -3 / -4  - 1/3 = ?

=> -3 -1 / -4 - 3

=> -4 / -7

So, -3 / -4 - (-4 / -7)

=> -3 +4 / -4 + 7

=> 1/3

So 1 point is on (-4 , -3)

Other point is on (-4, -7)

Answer:no

Step-by-step explanation:

No

f(x)2x/x+3,x≠-3 can somebody please explain.

Answers

Answer:

x cannot equal -3 because if -3 is plugged in for x, there will be a zero in the denominator and you cannot divide by 0

it cancels out. the equal sign have a slash through there
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