Write the following function as a power series and give the interval of convergence f(x)= 3x^² / 5-23√x
Answers
The function f(x) = 3x^2 / (5 - 23√x) can be expressed as a power series by using the geometric series expansion. The resulting power series will have an interval of convergence that depends on the domain of the function.
To express f(x) as a power series, we can rewrite the denominator as (5 - 23x^(1/2)). Using the geometric series expansion formula, we can write:
1 / (5 - 23x^(1/2)) = 1/5 * (1/(1 - (-23/5)x^(1/2)))
Expanding the right-hand side using the geometric series formula, we have:
1 / (5 - 23x^(1/2)) = 1/5 * (1 + (-23/5)x^(1/2) + (-23/5)^2 x + ...)
Now, multiplying this series by 3x^2, we get:
f(x) = 3x^2 / (5 - 23√x) = (3/5)x^2 + (3/5)(-23/5)x^(5/2) + (3/5)(-23/5)^2 x^(9/2) + ...
The interval of convergence of this power series depends on the domain of the original function. It will converge for values of x within a certain range that needs to be determined based on the convergence criteria.
Learn more about geometric series expansion here: brainly.com/question/16774911
#SPJ11
Related Questions
help in class ioejwrfahfu9vparwhgv
Answers
3/1 tama poyong unna nag answer
Miguel rode his bike to work which was 15 miles from home. However he was too tired to ride back so he got a ride in a car from a co-worker. He spent a total of 2 hours traveling. The average speed of traveling by car was 3 times faster than on his bike. What was Miguel’s average speed on his bike and in the car?
Answers
Answer:
2hrs(3x faster) :
6hrs = 15 miles
2.5 miles per hour - bike2hrs = 15 miles
7.5 miles/hr = carStep-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Solve t/12=4.
The solution is t=
Answers
You just need to find out how many times 12 goes into a number, 4 times.
Which is 48 because 12x4 is 48 and you can check your answer by dividing 48/12=4
Answer:
T = 48
Step-by-step explanation:
multiply both sides by 12 to isolate t
t/12(12) = 4(12)
t = 48
EXAMPLE 3
If m26 = 142°, find each measure. Give your reasoning.
a. mZ1 =
b. m 2 =
6
N
c. m23 =
32
d. mZ4 =
4
8
e. m25 =
f. m27 =
g. m 8 =
Answers
Answer:
Answer in the attached image.
A birdwatcher on a cliff saw an eagle 8 meters below him. Earlier, he had spotted the eagle 9 meters below him. What is the difference from earlier to now? ___ meter(s)
Answers
Answer:
1 meter
Step-by-step explanation:
Previous spot of the eagle = 9 meters below him
Present spot of the eagle = 8 meters below him
What is the difference from earlier to now?
Diffetence in the spotting = Earlier position - present position
= 9 meters - 8 meters
= 1 meter
Corinna has $80. She wants to buy a $256 plane ticket. She will save up her earnings from working at the museum where she earns $16 per hour. Which inequality shows the number of hours, n, Corinna must work so that she has a total of at least $256?
Answers
Answer:
80+16h≥256
Step-by-step explanation:
the 80 represents the $80 that Corinna already has
the 16h represents the amount of money made at the museum, with h being the number of hours worked
the inequality symbol is a greater than or equal sign because Corinna must have at least $256 to get the plane ticket, which means you either have to have the exact amount amount or more than the exact amount needed
Can someone help me with this math homework please!
Answers
Answer:
14
Step-by-step explanation:
7h-5(3h-8)=-72
or, 7h-15h+40=-72
or, 40+72=15h-7h
or, 112=8h
or, h=112/8
therefore,h=14
Answer:
Step-by-step explanation:
PLEASE HELP!! How can you find the annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100? What does knowing the APR allow you to do?
Answers
APR is obtained by dividing the finance charge for the loan by the total amount borrowed, given by this formula APR = ((F / P) x 12) x 100
What is the annual percentage rate?The formula for APR (annual percentage rate) is given as;
APR = ((F / P) x 12) x 100
Where;
F is the finance charge for the loanP is the total amount borrowed12 represents the number of months in a yearThe annual percentage rate (APR) of a loan if you know the number of monthly payments and the finance charge per $100, is calculated as follows;
Multiply the finance charge per $100 by 12 to get the finance charge per year.Divide the result by the total amount of the loan.Learn more about APR here: https://brainly.com/question/3861581
#SPJ4
A movie theater in town posted these prices for tickets and snacks.
A 2-column table with 7 rows. Column 1 is labeled Item with entries adult ticket, child ticket, drink, popcorn, veggie cup, soft pretzel, apple slices. Column 2 is labeled cost (dollars) with entries 9, 6, 1.35, 3.50, 1.74, 2.65, 3.85.
Sally and Anne went to the movies. They each purchased a drink. They also bought one popcorn and one veggie cup to share. Which expression can be used to find how much money each woman spent?
One-half (9 + 1.35 + 3.50 + 1.74)
9 + 1.35 + one-half (3.50 + 1.74)
18 + 2.70 + one-half (3.50 + 1.74)
9+1.35+2(3.50+1.7)
Answers
Answer:
9 + 1.35 + one-half (3.50 + 1.74)
Step-by-step explanation:
Sally pay
9 - adult ticket
1.35 - drink
1/2 ( 3.50 popcorn + 1.74 veggie cup)
= 9 + 1.35 + 1/2(3.50 +1.74)
consider the following binomial experiment: 290 people have been exposed to the flu. if the probability that a person contracting the flu on exposure is 0.37, find the variance of these 290 people contracting the flu. a) 182.7000 b) 39.7010 c) 0.2331 d) 67.5990 e) 493.7838 f) none of the above.
Answers
The variance of the 290 people contacting the flu, given the probability of contacting the flu, is d) 67.5990
How to find the variance ?When given the probability in a binomial experiment, and the number of people in the experiment, you can find the variance by the formula:
= Number of subjects in experiment x Probability of contacting the flu x ( 1 - probability of contacting the flu)
Number of subjects in experiment = 290 people
Probability of contacting the flu = 0.37
The variance of the people contacting the flu is:
= 290 x 0.37 x ( 1 - 0.37)
= 290 x 0.37 x 0.63
= 67.5990
Find out more on binomial experiments at https://brainly.com/question/14307841
#SPJ1
Find the values of x and y
Answers
Answer:
x = 36, y = 84
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for x
x = 180 - (96 + 48) = 180 - 144 = 36
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
y is an exterior angle of the triangle, thus
y = 48 + 36 = 84
Imagine that an uncharged pith ball is brought into the electrostatic field of a charged rod. The side of the pith ball closest to the negatively charged end of the rod will Question 12 options: A) be given a negative charge produced by the movement of electrons from the other end of the ball. B) be given a positive charge produced by the movement of electrons to the other end of the ball. C) not experience any induced charge and remain neutral. D) be given a negative charge produced by the movement of electrons from the rod.
Answers
The side of the pith ball closest to the negatively charged end of the rod will be given a positive charge produced by the movement of electrons to the other end of the ball. Therefore, option B) is the correct answer.
When an uncharged pith ball is brought into the electrostatic field of a charged rod, the charged rod induces a separation of charges in the pith ball. This phenomenon is known as electrostatic induction. The negatively charged end of the rod repels electrons in the pith ball, causing them to move to the opposite end of the ball.
As a result, the side of the pith ball closest to the negatively charged end of the rod will experience a shortage of electrons and will become positively charged. Conversely, the side of the pith ball farthest from the negatively charged end of the rod will have an excess of electrons and will acquire a negative charge.
The side of the pith ball closest to the negatively charged end of the rod will be given a positive charge produced by the movement of electrons to the other end of the ball.
Learn more about electrostatic here:
https://brainly.com/question/14889552
#SPJ11
81x^6-(y+1)^2 what are the U and V
Answers
The simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is 729x^6 - V^2.
In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.
To simplify the expression using the given values, we substitute \(U = 3x^3\)and V = y + 1 into the original expression:
\(81x^6 - (y + 1)^2\)
Replacing U and V:
\(81(3x^3)^2 - (V)^2\)
Simplifying:
\(81 \times 9x^6 - V^2\)
\(729x^6 - V^2\)
Therefore, the simplified form of the expression \(81x^6 - (y + 1)^2\) in terms of U and V is\(729x^6 - V^2.\)
In this way, we can represent the original expression in a simplified form using the assigned values for U and V.
For similar question on expression.
https://brainly.com/question/723406
#SPJ8
Consider the expression: \(81x^6 - (y + 1)^2\)
If\(U = 3x^3\) and V = y + 1, what is the simplified form of the expression in terms of U and V?
In this question, we are given specific values for U and V and asked to express the given expression in terms of those values.
What is the Square root of 21353641 by division method?
Answers
Answer:
that's how you it first divide by 4 then by 6 then by 2 then 1
The square root of 21353641 by the division method is approximately 4621.
What is the Square rootTo find the square root of 21353641:
Group the number into pairs from right to left: 21, 35, 36, and 41.Find the largest digit 'x' such that 'x' multiplied by twice the divisor gives a product less than or equal to 2135. In this case, 'x' is 4.Set the divisor as twice the current quotient plus 'x.' In this case, the divisor is 84.Repeat the process by bringing down the next pair of digits and finding the new quotient. The process continues until all pairs are exhausted.The final quotient obtained through the division method is approximately 4821.Learn more about Square root from
https://brainly.com/question/428672
#SPJ2
Need some help with that
Answers
The work done in each of the cases is:
B) W = 8,400 N*m
C) W = 17,500 N*m
How to find the work done?The work can be defined by the product between the force and the distance translated.
W = Force*Distance
So, if there is a force of 120N and the vehicle moves 70 meters, the work done is:
W = 120N*70m = 8,400 N*m
C) Similar case to the above one, here the force is F = 3.5 KN = 3,500N
And the distance is d = 15m
Then in this case the work done is:
W = 3,500N*15m = 17,500 N*m
Learn more about work at:
https://brainly.com/question/25573309
#SPJ1
Find the zeros of the following quadratic function
Answers
The zeros of the quadratic function \(f(x) = 2x^2 - 5x + 2 are x = 1/2 and x = 2.\)
What is quadratic function?A quadratic function is a mathematical function of the form:
\(f(x) = ax^2 + bx + c\)
where a, b, and c are constants, and x is the variable. The highest power of the variable x in a quadratic function is 2, which means it is a second-degree polynomial.
In a quadratic function, the graph is a parabola, which can open up or down depending on the sign of the leading coefficient a. If a > 0, the parabola opens up, and if a < 0, the parabola opens down. The vertex of the parabola represents the minimum or maximum value of the function, depending on the direction of the parabola.
To find the zeros of the quadratic function:
\(f(x) = 2x^2 - 5x + 2\)
We need to solve the equation:
\(2x^2 - 5x + 2 = 0\)
We can factor this quadratic equation as follows:
\(2x^2 - 4x - x + 2 = 02x(x - 2) - 1(x - 2) = 0(2x - 1)(x - 2) = 0\)
So the zeros of the quadratic function are:
x = 1/2 or x = 2.
Therefore, the zeros of the quadratic function is:\(f(x) = 2x^2 - 5x + 2 are x = 1/2 and x = 2.\)
To know more about quadratic function, visit
brainly.com/question/27958964
#SPJ1
If two angles of a triangle are congruent to two angles of another triangle then the remaining pairs of angles are blank
Answers
Answer:
Congruent
Step-by-step explanation:
\(express \: \: \sqrt{48} + \sqrt{108} \: \: in \: \: \: form \: \: of \: \: k \sqrt{6} \\ where \: \: k \: \: is \: \: a \: \: \: surd.\)
pls help me!!
Answers
Answer:
\(10 \sqrt{3} \)
Step-by-step explanation:
\( \sqrt{48} + \sqrt{108} \: \: in \: \: \: form \: \: of \: \: k \sqrt{6} \\ \sqrt{48} + \sqrt{108} = \sqrt{(4 \times 4 \times 3)} + \sqrt{(9 \times 3 \times 4)} = \\ 4 \sqrt{3} + 6 \sqrt{3} = 10 \sqrt{3} \)
Calculate the value of 2x and 3x
Answers
Answer:
2x= 88
3x = 132
Step-by-step explanation:
The sum of the angles that form a circle is 360
2x+3x+140 = 360
5x+140 = 360
5x+140-140 = 360-140
5x= 220
Divide by 5
5x/5 = 220/5
x=44
2x= 2*44=88
3x = 3*44=132
The area of a segment of a circle is the area of the corresponding sector of the circle _____ the area of the corresponding triangle.
Answers
Answer:
The area of a segment of a circle is the area of the corresponding sector of the circle minus the area of the corresponding triangle.
Step-by-step explanation:
We know area of segment of a circle is the area of the corresponding sector of the circle minus the area of the corresponding triangle.
A school counselor surveyed 90 randomly selected students about the languages they speak. Of the students surveyed, 15 speak more than one language fluently. Based on these results, how many of the 1,800 students at the school can be expected to speak more than one language fluently? A.288 B.300 C.113 D.389
Answers
Answer:
b
Step-by-step explanation:
Because the population is too large and it would be impractical to survey the whole population, a sample of the population is chosen to take part in the survey. This sample is taken as been representative of the whole population
Based on the sample, the fraction of students that speak more than one language fluently = 15/90= 0.166667
Population that would speak more than one language fluently = 0.166667 x 1800 = 300
The average prison sentence for a person convicted of second-degree murder is 15 years. If the sentences are normally distributed with a standard deviation of 2.4 years, find the following probabilities. Round the final answers to four decimal places and intermediate z -value calculations to two decimal places. Part 1 out of 2 A prison sentence is greater than 18 years. P(X > 18)
Answers
The probability of a prison sentence greater than 18 years for a person convicted of second-degree murder is 0.1056 or about 10.56%.
We must normalize the variable using the following method in order to determine the likelihood that a person convicted of second-degree murder will serve a jail term longer than 18 years:
\(z = (x - μ) / σ\)
where: mean of the distribution (15 years), delta: standard deviation, and x: value of interest (18 years in this example) (2.4 years).
When we enter the values, we will get that:
z = (18 - 15) / 2.4 = 1.25
Then, we can use a calculator or table of the standard normal distribution to determine the probability associated with this z-score. The likelihood of a sentence longer than 18 years is represented by the region to the right of the value z = 1.25. We determine that the region to the right of 1.25 is roughly 0.1056 using a common normal distribution table.
Hence, the likelihood that a person convicted of second-degree murder will serve a sentence in jail longer than 18 years is 0.1056 or roughly 10.56%.
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ1
what dose absolute value mean
Answers
Answer:
the magnitude of a real number without regard to its sign.
Step-by-step explanation:
Answer:
the magnitude of a real number without regard to its sign
Step-by-step explanation: or something like that
Find the length of the segment with endpoints of (3,2) and (-3,-6).
(Will Mark Brainlyest!)
Answers
Answer:
i think its (x2,y2)=(19,3)
Step-by-step explanation:
sorry if its wrong
oscar is thinking of a number he says my number is between 200 and 220 it is divisible by 6 the sum of all the digits is 3 how to sole such a question
Answers
The answer is: Oscar's number is 210.
What is Sum?
In mathematics, the sum is the result of adding two or more numbers or quantities together. It is a basic arithmetic operation and is often denoted by the symbol "+".
To solve this question, we need to find a number that satisfies the following conditions:
The number is between 200 and 220.
The number is divisible by 6.
The sum of all the digits is 3.
Let's start by finding all the multiples of 6 that are between 200 and 220:
204 = 2 + 0 + 4 = 6
210 = 2 + 1 + 0 = 3
216 = 2 + 1 + 6 = 9
Out of these numbers, only 210 has a sum of digits that is equal to 3. Therefore, the number that Oscar is thinking of is 210.
To check that 210 is between 200 and 220, we can see that it is indeed between the two numbers:
200 < 210 < 220
And to check that 210 is divisible by 6, we can see that:
210 ÷ 6 = 35
Therefore, the answer is: Oscar's number is 210.
Learn more about Sum
https://brainly.com/question/24205483
#SPJ1
If the scale on a map is inches /miles = 1 /10, find the following actual distances.
a. 2 inches b. 1/2 inches c. 3.5 inches
Answers
Answer:a-20miles
b-5miles
C-35 miles
Step-by-step explanation:
):
How does the graph of g(x) = (x − 8)3 + 3 compare to the parent function f(x) = x3?
a. g(x) is shifted 8 units to the left and 3 units up.
b. g(x) is shifted 3 units to the right and 8 units down.
c. g(x) is shifted 8 units to the right and 3 units up.
d. g(x) is shifted 3 units to the right and 8 units up.
Answers
Answer:
The right answer is C.
Step-by-step explanation:
The parent function is:
\(f(x)=x^3\)
If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.
\(f(x)=(x-8)^3\)
graph shifted toward right by \(8\) units right
\(f(x)=(x-8)^3+3\)
graph shifted toward right by \(3\) units up
Thus the new function is:
\(g(x)=(x-8)^3+3\)
From your meal, what would you say were good and healthy food choices?
A. slice of pizza
B. serving of chips
C. baby carrots
D. small orange
E. glass of whole milk
Answers
Answer:
c d e
Step-by-step explanation:
Answer:
I would say C and D is a good and healthy food.
Step-by-step explanation:
Pizza and chips are junk-foods(not healthy)
Whole milk can get you an heart disease, so not healthy.
Baby carrots is fat-free and has a lot of Vitamin A, which is good and healthy.
Small oranges have lots of Vitamin C, which is good and healthy for you.
The option left is baby carrots and small orange, so those two are the best choices.
3. An artist is selling children's crafts. Necklace cost $2.25 each, and bracelets cost $1.50 per each. Select all the combinations of necklaces and bracelets that the artist could sell for exactly $12.00.
Answers
The artist could sell 4 necklaces and 2 bracelets or just 8 bracelets for exactly $12.
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
Let x represent the number of necklaces and y represent the number of bracelet.
Necklace cost $2.25 each, and bracelets cost $1.50 per each. The artist could sell exactly $12.00. Hence:
2.25x + 1.5y = 12
From the graph, the points (4,2) and (0, 8) satisfy this equation
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
volume of a cone = r²h,
where r is the radius and h is the height.
A frustum is formed by removing a small cone from a similar, larger cone, as
shown below.
a) Calculate the radius of the original large cone.
b) Calculate the volume of the frustum to the nearest integer.
50 m height
10 m height of frustum
6m radius of frustum
Answers
Answer:
7.5 m 457.5\(\pi\) \(m^{2}\)
Step-by-step explanation:
First, visualize the original cone and the smaller cone as overlapping similar triangles. The scale factor of the original cone to the smaller cone is 50:40, so if the smaller cone has a radius of 6 m, then the radius of the original cone would be 7.5 m.
The volume of the frustum is the volume of the original cone minus the volume of the smaller cone. The formula for the volume of a cone is V = \(\frac{1}{3} \pi r^{2}h\).
Original Cone = \(\frac{1}{3} \pi r^{2}h\) = \(\frac{1}{3} \pi *7.5^{2}*50\) = 937.5\(\pi\)
Smaller Cone = \(\frac{1}{3} \pi r^{2}h\) = \(\frac{1}{3} \pi *6^{2}*40\) = 480\(\pi\)
Frustum = 937.5\(\pi\) - 480\(\pi\) = 457.5\(\pi\)