Find the function to which the given series converges within its interval of convergence. Use exact values. 1 3 x 9 x 2 2 ! 27 x 3 3 ! 81 x 4 4 ! 243 x 5 5 !

Answers

Answer 1

It looks like the series could be

[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]

Recall that

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].


Related Questions

2y=-x+9


3x - 6y=-15
pls helpppp

Answers

Answer:

Step-by-step explanation:

The given equations are:

1) 2y = -x + 9

⇒ x = 9-2y

2) 3x - 6y = -15

⇒3x = 6y - 15

x = 2y - 5

Equating the values of x, we get:

9 - 2y = 2y - 5

9 + 5 = 4y

14 = 4y

y = 3.5

Using this value of y in equation 1 we get:

x = 9 - 2(3.5) = 2

So, the solution set is (2, 3.5)

who was regarded as the father of geomotry

Answers

Answer:Euclid

Step-by-step explanation:

Euclid was an ancient Greek mathematician in Alexandria, Egypt. Due to his groundbreaking work in math, he is often referred to as the 'Father of Geometry'. Euclid's most well-known collection of works, called Elements, outlines some of the most fundamental principles of geometry.

Answer:

Euclid  

I hope this helps you!

0.75x + 0.8(x + 10) = 101
what is x

Answers

Step-by-step explanation:

0.75x + 0.8(x + 10) = 101

0.75x + 0.8x + 8 = 101

1.55x = 101 - 8

1.55x = 93

x = 93 ÷ 1.55

x = 60

help me pleaseeeeeeeeeeeeeee

Answers

Answer:

C

Step-by-step explanation:

Evaluating the options :

Option A

⇒ 5/2x + 7/2 = 3/4x + 14

⇒ 2.5x - 0.75x = 14 - 3.5

⇒ 1.75x = 10.5

⇒ x = 6

No ×

===========================================================

Option B

⇒ 5/4x - 9 = 3/2x - 12

⇒ 1.5x - 1.25x = -9 + 12

⇒ 0.25x = 3

⇒ x = 12

No ×

=========================================================

Option C

⇒ 5/4x - 2 = 3/2x - 4

⇒ 1.5x - 1.25x = -2 + 4

⇒ 0.25x = 2

⇒ x = 8

Yes √

C is the right answer.

There are 760 calculators,6 were defective what is the probability that a calculator chosen at random will be defective

Answers

Answer:

Unlikely

Step-by-step explanation:

well if you want the chance it’s unlikely. This is because you only have 6 defective calculators and the rest or majority are not defective.

calculate the area of this trapezium:
b = 15cm
h = 6cm
top part = 9cm
PLEASE I NEED THIS ASAP !!!

Answers

Answer:

72

Step-by-step explanation:

hopefully you dont need work since you need it asap :(

Answer:

Step-by-step explanation:

1/2 (a+b) x h

a+b = 9+15= 24 / 2 = 12

12 x 6 = 72cm2

The graph shows the probability distribution of a random variable.
What is the value of P(4≤X≤8)?

0.40
0.45
0.50
0.55

Answers

The answer is 0.50.

P(4<=X<=8)=P(x=4)+ P(x=5)+ P(x=6)+ P(x=7)+ P(x=8)= 0.05+ 0.15+0.15+0.15 +0 = 0.50

Notice that in 8 the line touches the x axis so it’s corresponding probability is 0.

The ratio of the number of squares to the number of triangles in simplest form is
added to make the ratlo of the number of squares to the number of triangles 1: 1 Is

Answers

The ratio of the number of squares to the number of triangles is 5 : 2

The number of triangles that should be added to make the ratio is 6

What are the ratios?

Ratio expresses the relationship between two or more numbers. It is the number of times that one value is contained in another number.

Ratio of the number of squares to the number of triangles = number of squares : number of triangles

10 : 4

5 : 2

The number of triangles that should be added to make the ratio 1 : 1 - 10 - 4 = 6

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please explain how to do this

Answers

I’m guessing you just have to multiply all the sides together and divide

PLEASE HELP ILL LIKE AND ITS WORTH 20 points !!

Answers

Answer:

EG=

[tex] \frac{28 }{ \sqrt{3} } [/tex]

EF=

[tex] \frac{56}{ \sqrt{3} } [/tex]

Step-by-step explanation:

You have to memories Trigonometric ratios of 60

I kinda need help with this

Answers

Applying the leg rule, the value of x in the given right triangle is: A. 6.

What is the Leg Rule?

The leg rule for solving a right triangle having an altitude is expressed as:

hypotenuse/leg = leg/part.

In the image given we have the following:

Hypotenuse = 4 + 5 = 9 units

Leg = x

Part = 4

Plug in the values into the leg rule formula:

9/x = x/4

(x)(x) = (9)(4)

x² = 36

x = √36

x = 6 units.

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HELPP PLEASE ASAP Use the Pythagorean theorem to find the missing length in the right triangle

Answers

Answer:

c = 10

Step-by-step explanation:

The pythagoras theorem :

a² + b² = c²

a = 6 and b = 8

6² + 8² = c²

36+64 = c²

100 = c²

c = √100

c= 10

Hope this helped and brainliest please

Sam Whittington was the fastest cyclist on record (in 2009) with a speed of 37.5 m/s. Calculate the time taken in hours to cycle 53.2 km.

Answers

Answer:

39.407 hour

Step-by-step explanation:

T = D/S

37.5 m/s in km/h

=375×18/10×5

=135 km/h

T = ABCDEFGHIOJKLMNOPQRSTUVWXYZ

What is the (LCD) 1/6and 1/3

Answers

Answer:

The LCD of 1/6 and 1/3 is 6.

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/6, 1/3

For the denominators (6, 3) the least common multiple (LCM) is 6.

LCM(6, 3)

Therefore, the least common denominator (LCD) is 6.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/6 = 1/6 × 1/1 = 1/6

1/3 = 1/3 × 2/2 = 2/6

Find (fog)(0).
f(x)
=
6x
g(x) = 3x + 6
(fog)(0)

Answers

Answer:

12

Step-by-step explanation:

The functions f(x) and g(x) are defined as f(x) = 6x and g(x) = 3x + 6

fog(x) = f(g(x))

= f(3x + 6)

= 6(4x +2)

6 x 4x = 24x

6 x 2 = 12

fog(x) = 24x + 12

(fog)(0) where x = 0

= 24(0) + 12

= 0 + 12

(fog)(0) = 12

Write the equation 2x - 4y = 14 in slope-intercept form, and then find the slope and y-intercept.

Answers

Answer:

y = 1/2x - 7/2

Slope: 1/2

Y-intercept: (0, -7/2)

Step-by-step explanation:

We know the slope-intercept form of an equation of a line is y = mx + c where slope is m and y-intercept is c.

So, -4y = (-2)x + 14 [divide both sides by -4]

-4/-4 = -2/-4 + 14/-4

y = 1/2 -7/2

Hence the slope =  1/2 and y-intercept = -7/2.

(2x+1)(x^2+8x-3)
help standard form​

Answers

Answer:

[tex]2x^3+17x^2+2x-3[/tex]

Step-by-step explanation:

[tex]\left(2x+1\right)\left(x^2+8x-3\right)\\=2xx^2+2x\cdot \:8x+2x\left(-3\right)+1\cdot \:x^2+1\cdot \:8x+1\cdot \left(-3\right)\\=2x^3+17x^2+2x-3[/tex]

In this equation, the variables were isolated to simplify the problem, following the order of operations. Negative-three either became an exponent or positive integer, 3, subtracted by a byproduct of the previous equation.

Fawzia has an action figure collection of 500 action figures. She keeps 58% of the action figures on her wall. How many action figures does she keep on her wall?

Answers

Answer:

290

Step-by-step explanation:

Formula :

Number of action figures on wall = Total number of figures × % of figures on wall

=============================================================

Given :

⇒ Total number of action figures = 500

⇒ % of action figures on wall = 58%

=============================================================

Solving :

Action figures on wall = 500 × 58%

⇒ Action figures on wall = 500 × 58/100 (all % are ratios of 100%)

⇒ Action figures on wall = 5 × 58

⇒ Action figures on wall = 290

Total action figures

58% of 5000.58(500)2.9(100)290action figures

Done!

find the angle of this sector.
on the image ​

Answers

Answer:

[tex]\alpha =107.4^{o}[/tex]

Step-by-step explanation:

[tex]15=\frac{\pi (8)\alpha }{180}[/tex]

[tex]\alpha =\frac{(15)(180)}{8\pi } =\frac{2700}{25.13}=107.4[/tex]

Hope this helps

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ s=15\\ r=8 \end{cases}\implies 15=\cfrac{\theta \pi (8)}{180}\implies 15=\cfrac{2\pi \theta }{45} \\\\\\ 675=2\pi \theta \implies \cfrac{657}{2\pi }=\theta \implies 104.56^o\approx \theta =a[/tex]

can someone help me asap !!

Answers

Answer:

The answer is negative. Answer choice B

Step-by-step explanation:

Here is the question:

-3^40(5.6/2.1)

According to order of operations, we must do -3^40 first.

Its important to note that -3^40 is different than (-3)^40. In the problem you specified, the ^40 only applies to the 3, not -3. So, first we do 3^40 which is a huge number. And then, we need to add a negative symbol to that huge number. So now we have a massive negative number multiplied by 5.6/2.1, which is obviously positive. Obviously, a negative number multiplied by a positive number is still negative. Therfore, the answer is negative.

I hope my answer helped you :)

If you are happy with my answer please vote Brainliest. Thanks!

10 identical spheres of radius 7cm are to be painted. What is the total area of surface to be painted​

Answers

Answer:

Surface area =  4 π r2 square units

Step-by-step explanation:

What does X= please help

Answers

Answer:

27

Step-by-step explanation:

The first angle you get with 180-61 = 119

The second angle you get by the rules of the circle which is 68/2 = 32

And finally X= 180 - 119 - 32 = 27

Find the equation of the lien shown.

Answers

Answer:

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

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (6, 3) ← 2 points on the line

m = [tex]\frac{3-0}{6-0}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

y = [tex]\frac{1}{2}[/tex] x ← equation of line

What is Oiler's Number and what equations can you do with it?

Answers

The first few digits are: 2.7182818284590452353602874713527 (and more ...) It is often called Euler's number after Leonhard Euler (pronounced "Oiler"). e is an irrational number (it cannot be written as a simple fraction).

HELP FOR BRAINLIEST & 100
please

Answers

Answer:

Hi,

Step-by-step explanation:

1) PC=PD since PC*PA=PD*PB

2)25 since PO²=PA²+r² PO=14.5, PB=14.5+10.5=25

3)

6²=3*x==> x=12


A stainless steel patio heater is a square pyramid. The length of one side of the base is 23.4 in. The
slant height of the pyramid is 93.2 in. What is the height of the pyramid?
The height of the pyramid is aboutin.
(Round to one decimal place as needed.)

Answers

The height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.

What is a square pyramid?

In geometry, it is defined as the shape having a square base with equal sides length and all the vertex of the square's joints at the top, which is perpendicular to the center of the square.

We have a square pyramid.

Length of the pyramid = 23.4 in

The slant height of the pyramid = 93.2 in

From the figure:

Base length CB  = DC = 23.4 in

In a right-angled triangle, BCD

Applying Pythagoras theorem:

DC² + CB² = DB²

23.4² + 23.4² = DB²

DB = 33.092 in

OB = (1/2)DB

OB = (1/2)33.092 = 16.546 in

In the right-angle triangle AOB, again applying Pythagoras theorem:

AO² + OB² = AB²

h² + 16.546² = 93.2²

AO = h (height of the square pyramid)

AB = slant height = 93.2 in

After calculating, we get:

h = 91.719 ≈ 91.72 in

Thus, the height of the square-based pyramid is 91.72 in if the length of one side of the base is 23.4 in.

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2. Find the area and the perimeter of these figures.

Answers

Answer:

A = 16.78 km squared

P = 14.28 km

Step-by-step explanation:

Area of triangle: (5*4)/2 = 10

Area of Semi-circle: (πr2)/2 = 6.28

Area of figure: 10 + 6.28 = 16.78

Perimeter: 5 + 3 + (2πr)/2 = 8 + (2π) = 8 + 6.28 = 14.28

Hope this helps!

Answer:

i don't know the perimeter but I do know the area hope this helps if it doesn't I am sorry

Ok for area for a triangle is 1/2 ×base×height and for a semi circle it is pi (π)or 3.14 or 22/7×rsquare with is radius x radius

Step-by-step explanation:

lets start with the triangle so it is 1/2×3/1×5/1×4/1 =30/1 =30sqkm

now for the semi circle it is 22/7×2/1×2/1=88/7=12.5÷2=6.2 why is 4/1 turned into 2/1 it is because you are finding area and 4 is the diameter but we need radius so the radius is half of the diameter

so 30+6.2=36.2kmsq

What is the conditional probability that you will randomly select a green box if there are 6,000 boxes. Of those boxes 2,000 are green.

Select one:

a.
1/6


b.
1/5


c.
2/6


d.
1/3

Answers

The conditional probability that you will randomly select a green box is 1 / 3.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability of selecting a green box = number of green boxes / total number of boxes

2000 / 6000 = 1/3

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The femur is the upper leg bone, and the tibia is one of the lower leg bones. the average length of the fumer is 50.5 cm,and the average length of the tibia is 43.03 cm. estimate the total length of the leg if the bones were placed end to end

Answers

50.5 cm + 43.03 cm = 93.53

For the function f(x) = 3x + 7, find the following:
a) f(2)=
c) f(x) = 8
b) f(-3) =
d) f(x) = 10

Answers

Answer:

a) 13

b) 1/3

c) -2

d) 1

Step-by-step explanation:

This is quite simple if you look at it from a different perspective. Imagine that when it says "f(2)" That you are plugging the number 2 in for every x on the right side of the equation:

For example:

f(x) = 3x + 7

f(2) = 3(2) + 7

f(2) = 6 + 7

f(2) = 13

________

f(-3) = 3x + 7

f(-3) = 3(-3) + 7

f(-3) = -9 + 7

f(-3) = 7 - 9 (This is just for those that hate negative values. You can rearrange the values as long as their sign is the same when you do move them. Ex: -14 + 6 - 4 + 9 == 9 + 6 - 14 - 4. I hope that makes sense.

f(-3) = -2

The other way is quite simple as well, if you look at it from a different perspective. Imagine that when it says "f(x) = 8" that you are changing the f(x) to the number 8:

For example:

f(x) = 8

f(x) = 3x + 7

8 = 3x + 7

8 - 7 = 3x

1 = 3x

x = 1/3

f(x)= 10

f(x) = 3x + 7

10 = 3x + 7

10 - 7 = 3x

3 = 3x

3/3 = x

1 = x

I hope this helps!

Answer:

a) 13
b) 1/3
c) -2
d) 1

Step-by-Step Explanation:

=> f(x) = 3x + 7

a) f(2)

Substitute the Value of ‘x’ :-

= 3x + 7
= 3(2) + 7
= 6 + 7
=> 13

Hence, f(2) = 13

b) f(x) = 8

Equate the Function to 8 :-

3x + 7 = 8
3x = 8 - 7
3x = 1
=> x = 1/3

Hence, x = 1/3

c) f(-3)

Substitute the Value of ‘x’ :-

= 3x + 7
= 3(-3) + 7
= -9 + 7
=> -2

Hence, f(-3) = -2

d) f(x) = 10

Equate the Function to 10 :-

3x + 7 = 10
3x = 10 - 7
3x = 3
=> x = 3/3 = 1

Hence, x = 1
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