Please help me :) I will give BRAINLIEST !! Please help it’s so confusing for me!

The interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].

What is Power Series Representation for the Function ?

To find a power series representation for a function, we need to express the function as an infinite series of the form

                      [tex]$$f(x) = \sum_{n=0}^{\infty} a_n (x-x_0)^n$$[/tex]

where [tex]$x_0$[/tex] is the center of the series, and the [tex]$a_n$[/tex] are the coefficients of the series. To determine the interval of convergence for the series, we need to find the values of [tex]$x$[/tex] for which the series converges.

To find the power series representation for a given function, we can use the process of Taylor series expansion. This involves finding the derivative of the function at the point [tex]$x_0$[/tex], and using the derivative to find the coefficients of the series.

For example, suppose we want to find a power series representation for the function [tex]$f(x) = \frac{1}{1-x}$[/tex]  centered at [tex]$x_0 = 0$[/tex]. We can use the process of Taylor series expansion to find the power series representation as follows:

[tex]$$f(x) = \frac{1}{1-x} = \frac{1}{1-0} + \frac{0-1}{(1-0)^2}x + \frac{2 \cdot 0 - 1 \cdot 1}{(1-0)^3}x^2 + \dotsb$$[/tex]

Simplifying this expression, we get

[tex]$$f(x) = 1 + x + x^2 + x^3 + \dotsb$$[/tex]

This is the power series representation of [tex]$f(x)$[/tex] centered at [tex]$x_0 = 0$[/tex].

To determine the interval of convergence for this series, we can use the ratio test. If we let [tex]$a_n = 1$[/tex] for all [tex]$n$[/tex], then the series becomes

[tex]$$\sum_{n=0}^{\infty} a_n (x-x_0)^n = \sum_{n=0}^{\infty} x^n$$[/tex]

If we take the limit of the absolute value of the ratio of successive terms, we get,

[tex]$$\lim_{n \to \infty} \left| \frac{x^{n+1}}{x^n} \right| = \left| x \right|$$[/tex]

If [tex]$|x| < 1$[/tex], then the series converges. If [tex]$|x| > 1$[/tex], then the series diverges. If [tex]$|x| = 1$[/tex], then the test is inconclusive and we need to use another method to determine convergence.

Therefore, the interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].

To know more about Power Series Representation visit,

https://brainly.com/question/28158010

#SPJ4

Answer:

a. 750 pages

b. 45 pages

Step-by-step explanation:

If you're decreasing 45 of something each day from 750, it makes sense that the 'something' is pages; instead of decreasing, it's reading.

So

a. 750 pages

b. 45 pages

Tables and figures must all be labelled with numbered captions that clearly identify and describe them.

x = 61

Left hand triangle containing 1 angle of 74

Label the other angle opposite the marked side also as 74

Find the third angle. Call it y.

y + 74 + 74 = 180           Combine like terms

y + 148 = 180                 Subtract 148 from both sides.

y = 180 - 148

y = 32

Now work with the triangle on the right.

label the angle making up the right angle = z

32 + z = 90                             These two angles are complementary = 90

32 - 32 + z = 90 - 32              Subtract 32 from both sides

z = 58                                      Use 58 wherever you see z

x + x + z = 180                         Substitute

2x + 58 = 180                          Subtract 58 from both sides

2x = 122                                  Divide by 2

x = 61

To learn more about marking and figure refer to:

https://brainly.com/question/29037337

#SPJ1

a) If we select without taking the order into consideration there are  2380.

b) If we take the order into consideration, we have 57120 ways

We talk about the selection when we are talking about how a material can be chosen in the midst of many other materials that we have. In this case we are told that we want to choose 4 objects, without replacement, from 17 distinct objects.

If the order is not important then we need to do a combination and we have;

n!/r! (n - r)!

17!/4!(17 - 4)!

17 * 16 * 15 * 14 * 13!/4! * 13!

= 57120/24

= 2380

If we are looking at the order we have;

n!/(n-r)!

17!/(17 - 4)!

17 * 16 * 15 * 14 * 13!/13!

= 17 * 16 * 15 * 14

= 57120

Learn more about permutation:https://brainly.com/question/1216161

#SPJ1

Answer:

So, a+2a=180°

Simplify.

3a=180°

To isolate a , divide both sides of the equation by 3 .

3a3=180°3    a=60°

The measure of the second angle is,

2a=2×60°       =120°

So, the measures of the two supplementary angles are 60° and 120° .

Answer:

Somoeone can talk here boring

Answer:

this a quesy=tion?

Step-by-step explanation:

The domain and the range of the graphed function are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.

Thus the domain of this function is given as follows:

D: (-9, -1] U (0, 4].

As there is an interval between -1 and 0 for which the function is not defined, and open circle defines that the interval is open at x = -9 and at x = 0.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.

Then the range of the function is given as follows:

R: (-6, 8.6].

Open interval due to the open circle at y = -6, closed at the value between 8 and 10 which is of 8.6.

More can be learned about domain and range of functions at brainly.com/question/2264373

#SPJ1

The equation 3x - 6 = x + 6 - 5x has one solution, which is x = 12/7.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

3x - 6 = x + 6 - 5x

To determine the solutions, solve the equation,

3x - 6 = 6 - 4x

7x = 12

x = 12/ 7

The equation has one solution, which is 12/7.

To know more about Equation on:

https://brainly.com/question/187506

#SPJ1

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]

See attachment for the graph.

Step-by-step explanation:    

Given equation for t:

[tex]t=\dfrac{\ln (K)}{0.095}[/tex]

Substitute the given values of K into the equation for t and round the answers to one decimal place:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]

To sketch the graph of the given function (see attachment):

Answer:

True.

Step-by-step explanation:

Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.

The value of a + b must be between 5 and 11. If the value of a 3 or 4, and b will be 4 or 5.

An unknown in mathematics is a number that we are unsure of. In algebra, where they are also known as variables and denoted by symbols like x, y, and z, they are frequently utilised.

In science, a letter from the Roman or Greek alphabet stands in for an undetermined value. They are most frequently employed in physics, where equations are used to explain how different physical qualities relate to one another.

Given that

2 < a < 5, and 3 < b < 6

a is greater than 2 and lesser than 5 , so the value will be 4 or 3.

b is greater than 3 and lesser than 6, so the value will be 4 or 5.

a + b is

3 + 4 = 7 or 4 + 5 = 9

so the product of sum will be 7 or 9, it is between 5 and 11

Therefore,  a + b must be between 5 and 11.

To learn more about unknown value refer :

https://brainly.com/question/29245116

#SPJ1

Answer:

106*

Step-by-step explanation:

a triangle is 180*

to find angle BCA, you do 180 - (64+42)

that =74*

a straight line is also 180* so you do 180 - BCA

180-74=106

106

Answer:

y = (1/2)x + 2

Step-by-step explanation:

Go from point (-2,1) to (0, 2).

Start at point (-2, 1). First, go up 1 unit. That is a rise of 1.

Now go 2 units right. That is a run of 2.

slope = rise/run = 1/2 = m

The graph intersects the y-axis at 2, so the y-intercept = b= 2.

y = mx + b

y = (1/2)x + 2

To eliminate y from the first equation, we can multiply the entire equation by -2. This will give us:

-2x - 4y = -12

Now, if we add this equation to the second equation, the y terms will cancel out, leaving us with:

-2x - 4(2) + 5z = 26

-2x + 5z = 26

Now we have two equations in two variables, x and z. We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us:

x + 2(2) = -6

x = -10

Substituting this value of x into the second equation, we get:

-2(-10) + 5z = 26

20 + 5z = 26

5z = 6

z = 1.2

Finally, we can substitute the values of x and z back into the second equation to find the value of y:

-2(-10) - 6(1.2) + 5(1.2) = 26

20 - 7.2 + 6 = 26

12.8 = 26

This system of equations has no solution, since we have found values of x and z that make the second equation true, but substituting these values into the first equation results in a false statement. This means that there is no set of values for x, y, and z that will make all three equations true at the same time.

Answer:

no

Step-by-step explanation

y=x+9

4=1+9

1+9=10

10 is not equal to 4

y=10x+7

=40+7

47 does not equal 4

Quadratic function has minimum value which is -8.

correct option: 1

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

Here, the given function,

f(x) = x² - 2x - 7 .......... (i)

now, differentiate with respect to x

d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)

or, f'(x) = 2x - 2 ............. (ii)

Now, put f'(x) = 0

so, 0 = 2x - 2

or, 2x - 2 = 0

or, 2x = 2

or, x = 1

From equation (ii)

f'(x) = 2x - 2

now, differentiate with respect to x

f''(x) = 2 > 0

So, it implies that, the function has minimum value at x = 1

Now, putting x = 1 in equation (i), we get -

f(1) = (1)² - 2×(1) - 7

f(1) = - 8

Function has minimum value is: - 8.

Thus, correct option is : (1)

To know more about quadratic function refer to:

https://brainly.com/question/25841119

#SPJ4

Answer:

Look below

Step-by-step explanation:

Example for A

1/5 y= 3/5 x

1/5 y= 3/5 x +4

Example for B

0x=0y

0x=0y+3

Answer for C

add statement for the y not to be equal to 0

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula to create an equation for A in terms of n:

[tex]\implies A=2100\left(1+\dfrac{0.085}{n}\right)^{9n}[/tex]

Substitute each value of n into the equation:

[tex]\begin{aligned}n=1 \implies A&=2100\left(1+\dfrac{0.085}{1}\right)^{9 \times 1}\\&=2100\left(1.085\right)^{9}\\&=\$4376.10\end{aligned}[/tex]

[tex]\begin{aligned}n=2 \implies A&=2100\left(1+\dfrac{0.085}{2}\right)^{9 \times 2}\\&=2100\left(1.0425\right)^{18}\\&=\$4442.10\end{aligned}[/tex]

[tex]\begin{aligned}n=4 \implies A&=2100\left(1+\dfrac{0.085}{4}\right)^{9 \times 4}\\&=2100\left(1.02125\right)^{36}\\&=\$4476.86\end{aligned}[/tex]

[tex]\begin{aligned}n=12 \implies A&=2100\left(1+\dfrac{0.085}{12}\right)^{9 \times 12}\\&=2100\left(1.00708333...\right)^{108}\\&=\$4500.73\end{aligned}[/tex]

[tex]\begin{aligned}n=365 \implies A&=2100\left(1+\dfrac{0.085}{365}\right)^{9 \times 365}\\&=2100\left(1.00023287...\right)^{3285}\\&=\$4512.49\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

[tex]\implies A=2100e^{0.085 \times 9}[/tex]

[tex]\implies A=2100e^{0.765}[/tex]

[tex]\implies A=2100(2.14899437...)[/tex]

[tex]\implies A=\$4512.89[/tex]

Input the calculated values into the table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

A horizontal line indicates that the thing is travelling steadily. A line that slopes downhill indicates that an object is slowing down.

To learn more about horizontal line  refer to:

brainly.com/question/25081736

#SPJ1

Weekly paycheck of Catherine is $573.5 and her annual income is $29,904.01.

Unit rate is defined as the number of one quantity needed for a single other quantity.

In other words, if we know the unit rate, we can calculate any amount of one quantity corresponding to any amount of the other quantity by multiplying the unit rate with the number of other quantity.

Here unit rate of Catherine's pay = $15.50 per hour

Given that Catherine works 37 hours per week.

Weekly paycheck of Catherine = unit rate × number of hours per week

                                                    = 15.50 × 37

                                                    = $573.5

Annual Income of Catherine = Unit rate × number of hours per year

There are 52.143 weeks in a year.

Catherine works 37 hours per week.

Number of hours Catherine working in an year = 52.143 × 37 = 1929.291

Annual Income of Catherine = 15.50 × 1929.291

                                               = $29,904.01

Hence, calculation of student is wrong since the weekly paycheck is $573.5 and her annual income is $29,904.01.

To learn more about Unit Rate, click:

https://brainly.com/question/29781084

#SPJ1

Answer:

D

Step-by-step explanation:

5/3 x - 2/3 x = -4

3/3 x = -4

x = -4

Answer:

A = principal +interest

P = Principal Amount

r = rate

t = time

A = P(1 + rt)

5 000 = P[(1 + 0.05(821/364.25)]

5 000 = P(1 + 0.05(2.254)

5 000 = P(1 + 0.1127)

5 000 = 1.1127P

P = 4 493.5742

Therefore, you need to deposit an amount of $4 493.5742 to have $5 000 in 821 days.

Step-by-step explanation:

The graph of a quadratic function is called a parabola

The complete table is

x = -6, -3, 0, 3 6

y = -12  -3 0 -3 -12

From the question, we have the following equation that can be used in our computation:

y=-1/3 x²

From the table of values , we have the following x values

x = -6, -3, 0, 3 and 6

Substitute x = -6, -3, 0, 3 and 6 in y=-1/3 x²

So, we have the following representation

y = -1/3 (-6)² = -12

y = -1/3 (-3)² = -3

y = -1/3 (0)² = 0

y = -1/3 (3)² = -3

y = -1/3 (6)² = -12

So, the complete table of values is

x = -6, -3, 0, 3 6

y = -12  -3 0 -3 -12

Read more about quadratic function at

brainly.com/question/25841119

#SPJ1

The values of x that can't be equal for the expression are 0 and 5

From the question, we have the following parameters that can be used in our computation:

(5x-2)/(x^2-5x)

This means that we set the denominator to 0

So, we have

x^2 - 5x = 0

Factorize

(x - 5)x = 0

So, we have

x - 5 = 0 and x = 0

Solve for x

x = 5 and x = 0

Hence, the solution is x = 5 and x = 0

Read more about domain at

https://brainly.com/question/10197594

#SPJ1

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

18/120 = 0.15

0.15*100 = 15%

...

The solution is 15 %

The percentage of discount on the normal price of the jacket is given by the equation A = 15 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage of discount be represented as A

Now , the equation will be

The normal price of the jacket = $ 120

The discounted price of the jacket = $ 18

So ,

Discounted price of the jacket = A % of normal price of the jacket

Substituting the values in the equation , we get

18 = A % x 120

On simplifying the equation , we get

( A / 100 ) x 120 = 18

Divide by 120 on both sides of the equation , we get

A / 100 = 18/120

A / 100 = 0.15

Multiply by 100 on both sides of the equation , we get

A = 15 %

Therefore , the value of A is 15 %

Hence , the discounted percentage is 15 %

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

uuuuuuuuuuuuuuuurrrrrrrrrrrrrrrr mom

Given line:

Plot two points and connect.

One point is the y-intercept:

Another point with an even value of x as its slope is a fraction with denominator of 2:

Plot these two points and connect.

See below graph.

Answer:

3.5

Step-by-step explanation:

The ball reaches the ground when [tex]h(t)=0[/tex].

[tex]-16t^2+54t+7=0 \\ \\ 16t^2-54t-7=0 \\ \\ (8t+1)(2t-7)=0 \\ \\ t=-1/8, t=7/2 \\ \\ t>0 \implies t=3.5[/tex]