Find the first five non-zero terms of power series representation centered at x = 0 for the function below. f (x) = ln (7 - x) What is the radius of convergence?

Answers

Answer 1

The first five non-zero terms of the power series representation centered at x = 0 for the function f(x) = ln(7 - x) are:

ln\((7) - (x/7) - (x^2/49) - (x^3/343) - (x^4/2401)\)

The radius of convergence of the power series representation is 7.

To find the power series representation of f(x) = ln(7 - x), we can use the Taylor series expansion of ln(1 + x) centered at x = 0.

The Taylor series expansion of ln(1 + x) is given by:

ln(\(1 + x) = x - (x^2/2) + (x^3/3) - (x^4/4) + ...\)

In this case, we have f(x) = ln(7 - x), so we substitute (7 - x) for x in the Taylor series expansion:

f(x) = ln\((7 - x) = (7 - x) - ((7 - x)^2/2) + ((7 - x)^3/3) - ((7 - x)^4/4) + ...\)

Simplifying the terms and expanding further, we get:

f(x) = ln(7) \(- x - (x^2/2*7) - (x^3/3*7^2) - (x^4/4*7^3)\) + ...

The first term ln(7) is a constant and represents the coefficient of the x^0 term in the power series representation. The subsequent terms are the non-zero terms of the power series.

The radius of convergence of this power series is 7. It means that the power series converges for values of x within a distance of 7 units from the center x = 0. The series may converge or diverge for values of x outside this interval.

Therefore, the first five non-zero terms of the power series representation are ln(7) - (x/7) - (x^2/49) - (x^3/343) - (x^4/2401), and the radius of convergence is 7.

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Related Questions

pls help if you can asap!!!!

pls help if you can asap!!!!

Answers

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

Y=4x-1 fill in table

Answers

Answer:

please provide table

there is no table in question

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.
1. N ⊃ O
2. N ⊃ P / N ⊃ (O • P)

Answers

The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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what is the latitude and longitude of los angeles california

Answers

Answer:

34.0522° N, 118.2437° W

Step-by-step explanation:

What is 734 divided by 2

Answers

Answer:

The answer to your question is 367

Step-by-step explanation:

I hope this helps answer your question

:D

Answer:367

Step-by-step explanation:

because I know what it is!

I hope this helped

The table below shows the typical hours worked by employees at a company. A salaried employee makes $50,000 per year. Hourly employees get paid $20 per hour, but get $30 per hour for each hour over 40 hours.
Sun.
Mon.
Tues.
Wed.
Thurs.
Fri.
Sat.
0
8
8
9
9.5
7.5
4

Answers

b) Hourly pay. Hourly employees make more per week than salaried employees

What is the rate of change?
X
у
0
4
1.
4.
2.
4.

What is the rate of change?X041.4.2.4.

Answers

Answer:

The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values  

The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period. Subtract one and multiply the resulting number by 100 to give it a percentage representation.

Step-by-step explanation:

I know it`s not the answer but I hope it helps a little Δ    Δ

                                                                                   ⊂∵°ω°⊃

Guys I wouldn't be asking if I had absolutely no clue on how to solve this but I am so please please help me!!!!

Guys I wouldn't be asking if I had absolutely no clue on how to solve this but I am so please please

Answers

Its simple, so these are two "y=mx+b" form lines that are limited by the signs on the right. Your first line f(x)=-x-4 has to be between -3 and 1 on the x-axis.

You would plot a point at (0,-4) like normal, then go down one, right one as the slope is -1. you would make the dot at 1 though unfilled as x does not equal to 1. It is less than 1.  º Should look like the dot I just inserted.

The second line would be plotted, at (0,-6). You would then make a horizontal line between 1 and 5. º-------• (Should look like this)

       

IMPORTANT:

FILLED DOT - EQUAL TO

UNFILLED DOT - Not equal to

Guys I wouldn't be asking if I had absolutely no clue on how to solve this but I am so please please
Guys I wouldn't be asking if I had absolutely no clue on how to solve this but I am so please please

Alejandra is packing a bag for a flight. The airline has a baggage weight limit, and Alejandra has already packed her bag with some essentials. All she has left is her outfits and shoes, which must weigh less than 30 pounds total.

If Alejandra estimates that one outfit welghs two pounds and one pair of shoes weighs three pounds, which graph represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit?​

Answers

there are no pictures of a graph BUT i can give you the intercepts.

x=2

y=12

OR

x=4

y=8

OR (sorry i cant see the graph options its one of the three)

x=8

y=3

its a solid line

x are the shoes

y are the outfits

The region below the line 2x + 3y = 30 is considered and the graph is drawn.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Alejandra is preparing her suitcase for takeoff. Alejandra has already stuffed her luggage with the necessities because the airline has a weight restriction on checked bags. She only has her clothes and shoes remaining, which together must weigh no more than 30 pounds.

If Alejandra determines that one pair of shoes weighs three pounds and one dress weighs two pounds.

Let 'x' be the number of outfits and 'y' be the number of shoes. Then the inequality is formulated as,

2x + 3y < 30

The region below the line 2x + 3y = 30 is considered and the graph is drawn.

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Alejandra is packing a bag for a flight. The airline has a baggage weight limit, and Alejandra has already

4x-8y=16what is the domain?

Answers

Answer:

The answer is 4x

Step-by-step explanation: This is because all of the domains are usually in the dominant variable which in most cases is x

The endpoints of the directed line segment AB are A(−7, 4) and B(8, 9). Find the coordinates of point P along AB¯¯¯¯¯¯¯¯ so that the ratio of AP to PB is 2 to 3.

Answers

Answer:

The coordinates of point P along the segment AB is (-1, 6).

Step-by-step explanation:

It is known that ratio of AP to PB is:

\(\frac{AP}{PB} = \frac{2}{3}\)

Or vectorially speaking:

\(\overrightarrow{AP} = \frac{2}{3}\overrightarrow{PB}\)

The vector that represents the segment AB is:

\(\overrightarrow{AB} = \vec B -\vec A\)

If \(\vec A = (-7,4)\) and \(\vec B = (8,9)\), then:

\(\overrightarrow{AB} = (8,9)-(-7,4)\)

\(\overrightarrow {AB} = (8+7,9-4)\)

\(\overrightarrow{AB} = (15,5)\)

But \(\overrightarrow{AB} = \overrightarrow{AP} + \overrightarrow{PB}\), then:

\(\overrightarrow{AB} = \frac{2}{3}\overrightarrow{PB} +\overrightarrow{PB}\)

\(\overrightarrow{AB} = \frac{5}{3}\overrightarrow{PB}\)

\(\overrightarrow{PB} = \frac{3}{5}\overrightarrow{AB}\)

\(\overrightarrow{PB} = \frac{3}{5}(15,5)\)

\(\overrightarrow{PB} = \left(9, 3\right)\)

The location of \(\vec P\) is derived of this formula:

\(\overrightarrow{PB} = \vec B - \vec P\)

\(\vec P = \vec B - \overrightarrow{PB}\)

If \(\vec B = (8,9)\) and \(\overrightarrow{PB} = \left(9, 3\right)\), then:

\(\vec P = (8,9) - (9,3)\)

\(\vec P = (8-9,9-3)\)

\(\vec P = (-1, 6)\)

The coordinates of point P along the segment AB is (-1, 6).

jenny reads a book with 92 pages. jenny's book has 13 more pages than the book macy reads. which equation could you solve to find how many pages, m, macy's book has?

Answers

Since Jenny has a book with 92 pages and Macy has a book that has 13 less pages than Jenny’s, you can do 92 - 13 = M. M = 79

what is the domain of the graph in set Notation?

what is the domain of the graph in set Notation?

Answers

\(\begin{gathered} the\text{ domain goes from -6 to 4.} \\ In\text{ set theory notation, this is written as} \\ x\in\lbrack\text{-6,}4\rbrack \end{gathered}\)

the hypotenuse of a right triangle is 29, and the legs are consecutive numbers, what is the sum of the legs

Answers

The sides are 20 and 21 in   right triangle.

What defines a right triangle?

The term "right triangle" refers to a triangle with an interior angle of 90 degrees.

                 The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side of the right triangle that is opposite the right angle and is also its longest side, and the height and base are the two arms of the right angle.

29² = x²  + (x+1)²

x²+ x² +2x +1 = 841

2x² +2x -840 =0

x² + x -420 =0

(x+21)(x-20)=0

x=20

the sides are 20 and 21

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how do you write 5.81 as a fraction?

Answers

Answer:

5 81/100

Step-by-step explanation:

Answer:

5.81 in fraction form is 581/100.

Step-by-step explanation:

Step 1:

Address input parameters & values.

Input parameters & values: The decimal number = 5.81

Step 2:

Write it as a fraction

5.81/1

Step 3:

Multiply 100 to both numerator & denominator

(5.81 x 100)/(1 x 100) = 581/100

It can be written as 581% = 581/100 or 581/100

Step 4:

To simplify 581/100 to its lowest terms, find LCM (Least Common Multiple) for 581 & 100.

1 is the LCM for 581 & 100

Step 5:

As LCM is 1, the fraction can't be factorized further

581/100 is a simplest fraction for the decimal point number 5.81

Elaine Thompson and Tori Bowie are practicing running the curve at track practice. Elaine is running around the curve of a track in lane 1 (radius =17.3 m ) at a tangential (i.e. linear) velocity of 4.2 m/s. Tori is running around the curve in lane 8 (radius =34.6 m ) with a tangential velocity of 4.6 m/s. a. Which runner has the greater angular velocity, Elaine or Tori? b. Which runner is experiencing greater centripetal (a.k.a. radial) acceleration, Elaine or Tori? c. During their cool down run, Elaine ran at a constant angular velocity of 0.6rad/ s in lane 1 and Tori ran at a constant angular velocity of 0.5rad/s in lane 8. Which runner is experiencing greater centripetal (a.k.a. radial) acceleration, Elaine or Tori?

Answers

a) Elaine has a greater angular velocity than Tori, Elaine has the greater angular velocity.

b) Tori has a greater centripetal acceleration than Elaine, Tori is experiencing greater centripetal acceleration.

c) Both Elaine and Tori would experience the same centripetal acceleration during their cool-down run, regardless of their angular velocities

a. Angular velocity is defined as the rate of change of angular displacement. It is given by the formula:

ω = v / r

where ω is the angular velocity, v is the tangential velocity, and r is the radius of the curve.

For Elaine: ω = 4.2 m/s / 17.3 m = 0.242 rad/s

For Tori: ω = 4.6 m/s / 34.6 m = 0.133 rad/s

Since Elaine has a greater angular velocity than Tori, Elaine has the greater angular velocity.

b. Centripetal acceleration is the acceleration directed towards the center of the circular path. It is given by the formula:

a = ω^2 * r

where a is the centripetal acceleration, ω is the angular velocity, and r is the radius of the curve.

For Elaine: a = (0.242 rad/s)^2 * 17.3 m = 0.099 m/s^2

For Tori: a = (0.133 rad/s)^2 * 34.6 m = 0.622 m/s^2

Since Tori has a greater centripetal acceleration than Elaine, Tori is experiencing greater centripetal acceleration.

c. The centripetal acceleration remains the same regardless of the angular velocity. It only depends on the radius of the curve. Therefore, both Elaine and Tori would experience the same centripetal acceleration during their cool-down run, regardless of their angular velocities.

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Beckett asked his classmates, "How many days do you floss your teeth


typical week?" The table shows Beckett's data.


Days of Flossing per Week


7


7


7


4


3


1


0


6


6


7


2.


6


5


3


N


4


How many observations did he record?


A. 20


B. 12


O c. 4


O D. 16

Answers

Answer: B

Step-by-step explanation: I did the quiz :p

Hope this helps

The correct answer is B. 12. There are 12 numbers in the table, which represents the number of observations Beckett recorded.

The table shows the number of days each of Beckett's classmates floss their teeth in a typical week. The number of observations recorded is simply the number of classmates, or the number of entries in the table. In this case, there are 12 entries, so the answer is 12.

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Help me, please
Which statement is true about the following pair of rectangles?

Help me, pleaseWhich statement is true about the following pair of rectangles?

Answers

Answer:

C

Step-by-step explanation:

\( \frac{27}{33} = \frac{9}{11} \)



Easy? Please help me

Sarah earns $


8.50

8.50 per hour babysitting. She needs to make at least $

187

187 to buy a new bike.


Write an inequality to represent the number of hours Sarah needs to work to afford the bike.



187

h



8.50

187h≥8.50


187

h



8.50

187h≤8.50


8.50

h



187

8.50h≥187


8.50

h



187

8.50h≤187

Answers

Answer:

The answer is A

Step-by-step explanation:

Hope it helps!

what is \root(8)(6) in exponential form

Answers

The exponential form of the given expression ⁸√6 is

\(6^{1/8}\)

How to write the expression in exponential

To express ⁸√6 in exponential form, we need to determine the exponent that raises a base to obtain the given value.

In this case  the base is 6 and the exponent is 8.

hence we  can be written as 6 raised to the power of \(6^{1/8}\)

So, the exponential form of ⁸√6 is \(6^{1/8}\)

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25% of 48 is what value?

Answers

Answer:

12

Step-by-step explanation:

Because 25% is 1/4 of something, and 1/4 of 48 is 12.

Question 4(Multiple Choice Worth 1 points)
(02.04 LC)
Write the equation of a line that goes through point (4, 0) and has an undefined slope.
Ox=4
Ox=0
Oy=4
Oy=0

Answers

Answer:

Ox=4 is the answer for the question

Two Pounds of grapes cost six dollars complete the table showing the price of different amounts of grapes at this rate.

Answers

Answer:

do lsibras a  6 dolares cadanax  u

Step-by-step explanation:

Answer:

Here is a chart to help you answer your problem hope it help :)

Step-by-step explanation:

Two Pounds of grapes cost six dollars complete the table showing the price of different amounts of grapes

Solve for x
650
35°
7x + 10

Solve for x650357x + 10

Answers

Answer:

x = 10

Step-by-step explanation:

By interior angle sum property of a triangle:

65° + 35° + (7x + 10)° = 180°

100° + (7x + 10)° = 180°

(7x + 10)° = 180° - 100°

(7x + 10)° = 80°

7x + 10 = 80

7x = 80 - 10

7x = 70

x = 70/7

x = 10

X= 10. ...................

6 3⁄4 meters to centimeters

Answers

Step-by-step explanation:

To convert 6 3/4 meters to centimeters, we need to multiply the value by 100.

First, convert the mixed number to an improper fraction:

6 3/4 = (6 * 4 + 3)/4 = 27/4

Now, multiply the fraction by 100:

(27/4) * 100 = 675/2 = 337.5

Therefore, 6 3/4 meters is equal to 337.5 centimeters.

Use

A

=

P

(

1

+

r

n

)

n

t

where:

A

= the amortized amount (total loan/investment amount over the life of the loan/investment)

P

= the initial amount of the loan/investment

r

= the annual rate of interest

n

= the number of times interest is compounded each year

t

= the time in years


Find how long it takes

$

1

,

900.00

to double if it is invested at

10

% compounded annually.


It will take

years. (Round answer to 3 decimal places.)

Answers

Using the formula A = P(1+r/n)nt, we can solve for t to find how long it takes for an investment to double.  It will take approximately 6.721 years for an investment of $1,900.00 to double if it is invested at 10% compounded annually.

Let P = 1900 (the initial investment), r = 0.1 (the annual interest rate), n = 1 (since it is compounded annually), and A = 2P = 3800 (since we want to find how long it takes for the investment to double).
Plugging these values into the formula, we get: 3800 = 1900(1 + 0.1/1)^(1*t)
Simplifying the right side, we have:  3800 = 1900(1.1)^t
Dividing both sides by 1900, we get:
2 = 1.1^t
Taking the natural logarithm of both sides, we have:
ln(2) = t*ln(1.1)
Solving for t, we have:
t = ln(2) / ln(1.1)
Using a calculator, we get:
t ≈ 6.721 years

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i thought of an integer.if i multiply it by itself you will get 9.What is my number

Answers

the number is 3 because 3 multiplied by itself (3) is equal to 9.

Answer:

Your number is 3

Step-by-step explanation:

3*3 is 9 and there are no other numbers multiplied by itself to get 9

Based on her recipe, Elena knows that 5 servings of granola have 1,750 calories.
Write an equation to represent the relationship between the number of calories and the number of servings of granola.

Answers

Answer:

1,750 ÷5= 350

Step-by-step explanation:

there are 350 calories in each serving 1,750 is the total

1750 divided by 5 is 350 there is 350 calories in one serving of granola

Choose the correct answer below. A. The proportion of numbers in the population is equal to the mean of the sample proportions. B. The proportion of numbers in the population is equal to the mean of the sample proportions of numbers. C. The proportion of numbers in the population is not equal to the mean of the sample proportions. D. The proportion of numbers in the population is equal to the mean of the sample proportions of numbers.

Answers

Answer:

A. The proportion of numbers in the population is equal to the mean of the sample proportions

Step-by-step explanation:

The relationship between the  mean \(\mu _{\overline p}\), and standard deviation, \(\sigma _{\overline p}\), of the sample proportion and the population proportion, p, are given as follows;

\(\mu _{\overline p}\) = p

\(\sigma _{\overline p} = \sqrt{\dfrac{p \cdot (1 - p)}{n} } \times \sqrt{\dfrac{N - n}{N - 1} }\)

Where;

N = The size of the population

n = The sample size

Therefore, the proportion of numbers in the population is equal to the mean of the sample proportions

match the correct term with its definition chord [ choose ] tangent [ choose ] secant [ choose ] diameter [ choose ]

Answers

Chord [a straight line segment that joins two points on the circumference of a circle]

Tangent [a straight line that touches a circle or sphere at a single point]

Secant [a straight line that intersects a circle at two points]

Diameter [a straight line passing through the center of a circle and connecting two points on the circumference]

In geometry, there are several terms related to circles, such as chord, tangent, secant, and diameter. Here are their definitions:

Chord: A chord is a line segment connecting any two points on the circumference of a circle. It is the longest segment that can be drawn inside a circle.

Tangent: A tangent is a line that touches the circumference of a circle at only one point, called the point of tangency. It is perpendicular to the radius at the point of tangency.

Secant: A secant is a line that intersects a circle at two points. It can be a line that passes through the center of the circle, in which case it is the diameter of the circle.

Diameter: The diameter is the longest chord of a circle, and it passes through the center of the circle. It is twice the length of the radius.

Understanding these terms is important in solving problems related to circles and their properties. For example, in finding the length of an arc or the area of a sector, we need to know the chord or diameter of the circle, and the angle or central angle subtended by the arc or sector. In constructing tangents to circles, we need to know the point of tangency and the radius or diameter of the circle.

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show that solutions to x 0 = sin(tx) are even A farm has 21 goats. All of the goats sleep in three separate rooms. One more goat sleeps in Room 2 than sleeps in Room 1 and one more goat sleeps in Room 3 than sleeps in Room 2 . How many goats sleep in each Room? Imagine that you gets an email one morning . It appears to be from your bank . The email warns that someone broke ( 1) .......... your account . It says that you need to (2 )....... in to check some things . You click the link in the email . It takes you to a site that looks very much like your bank's . You enter your username and (3 ).............You submit the form . You've just been phished ! Phishing is a type of attack that happens over the Internet . Users receive an email or text message that seems like it came from a (4)............. source. These users are being (5 )............ They are interacting with dangerous hackers . The attackers copy trusted companies . 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Jennifer received a sizable inheritance from her grandmother. she wants to give a portion of the money to a charity. she has a couple of charities in mind but wants to be sure that the charities are well-organized and that most of the money will be used for the goals of the charity instead of operating costs. how can jennifer finds out more about the charities in which she is interested? apply green's theorem to evaluate the integral. c (3yxdx 2xdy), c: the boundary of 0 (xvi)What are the different departments of State bank? Help Please:(! Will mark brainliest!According to the article, what effect did the British invasion have on mainstream popular music? A. It cut sales of American records to young audiences. B. It encouraged corporate takeovers of smaller markets. C. It brought African sounds to mainstream audiences. D. It put London at the center of the music industry. More than 120,000 American Japanese were forced from their homes and incarcerated in ten relocation centers and several prisons during World War II. Within months of the attack on Pearl Harbor, President Franklin Delano Roosevelt sent them to these concentration camps by executive order. Most of the evacuees and prisoners, more than 70 percent of them, were American citizens, born in the United States. Their first-generation immigrant parents, however, were forever aliens, prevented from gaining naturalized citizenship by the Immigration Act of 1924. Most of them, citizens and aliens alike, were fiercely patriotic. Guarded by soldiers in machine-gun towers, none of them were charged with any crime against the United States. In fact, there was not a single American of Japanese descent, alien or citizen, charged with espionage or sabotage during the war. These men, women and children were locked up for the duration of the war because they looked like the enemy, the troops of Imperial Japan, a place most of them had never seen....The dangers of history repeating itself seem greater given that this story is often forgotten, or treated as a footnote in the larger, mostly heroic description of World War II found in American history textbooks. Even at the time, the American Japanese concentration camps were underreported or misrepresented. Although there were periodic national stories about the roundup and incarceration of the American Japanese, much of that coverage treated the evacuation as something like a vacation trip to the country. The camps were generally portrayed as resorts, pioneer communities was the euphemism of the day. Americans, their sons shipping off to Europe and the Pacific, had a lot on their minds in those days--and California was still far away from most of America. Based on this document, what is one way the US Government restricted the civil liberties of Japanese Americans during World War II? Why would a historian find this to be a biased source of information? You were just hired by a company that wants to produce apps that help people become healthier by exercising, eating well, and reducing stress. On which customer motivations would you recommend the company focus? Describe the app you would design, the customer motivation it meets, and why your app is the right design for your potential customers. Your initial post should be a 5-7 sentence paragraph. ead the sentence a student wrote.As he listened to the haunting notes of the song the author realized he had found the inspiration for his next suspense novel.The teacher reviewing this sentence would point out that since this is acomplex sentence, there should be a comma after song.compound sentence, there should be a comma after realized.complex sentence, there should be a comma after inspiration.compound sentence, there should be a comma after found. in a patient with type 1 diabetes mellitus admitted for hyperglycemia, fats are being broken down for energy. which alternative fuel does the breakdown of fats produce? Refer to the short-run data in the accompanying graph. The profit-maximizing output for this firm is Three factories build the same widget An equation of an ellipse is given. x/36 + y/64 = 1 (a) Find the vertices, foci, and eccentricity of the ellipse.(b) Determine the length of the major axis. Determine the length of the minor axis. What is the value of the logarithm log 750?