Find a power series for the function, centered at c. g(x) = 5x/x^2 + 3x - 4' c = 0 g(x) = sigma^infinity _n = 0 _________
Determine the interval of convergence. (Enter your answer using interval notation.)
________
Answers
The power series for the function
\(g(x) = 5x/(x^2 + 3x - 4)\)
centered at c = 0, we need to first factor the denominator of the function. We can factor
\(x^2 + 3x - 4 as (x + 4)(x - 1).\)
Therefore, g(x) can be written as:
\(g(x) = 5x/((x + 4)(x - 1))\)
Now, we can use partial fraction decomposition to express g(x) in terms of simpler fractions. We can write:
\(g(x) = 5/(x + 4) - 5/(x - 1)\)
Next, we can express each of the simpler fractions as a power series. For the first term, we have:
\(5/(x + 4) = 5/(4(1 + (x/4))) = (5/4)(1 - (x/4) + (x/4)^2 - (x/4)^3 + ...)\)
For the second term, we have:
\(-5/(x - 1) = -5/(-1(1 - (x/-1))) = (5)(1 + (x/-1) + (x/-1)^2 + (x/-1)^3 + ...)\)
Therefore, we can write:
\(g(x) = (5/4)(1 - (x/4) + (x/4)^2 - (x/4)^3 + ...) + (5)(1 + (x/-1) + (x/-1)^2 + (x/-1)^3 + ...)\)
Simplifying this expression and combining like terms, we can write:
\(g(x) = (5/4) + (15/16)x - (25/64)x^2 + (175/256)x^3 + ...\)
This is the power series for g(x) centered at c = 0.
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Related Questions
13 ft
8 ft
Jjjjjjjjjjjjj
Answers
Answer: if it is area 108ft2
Step-by-step explanation:
I'm sorry but I dont know what your question is.Find the measure of the smallest angle
Answers
Answer:
44°
Step-by-step explanation:
We Know
The sum of three angles in a triangle must add up to 180°.
Let's solve
3x + 15 + 4x - 12 + 79 = 180°
7x + 82 = 180°
7x = 98°
x = 14
Now we put 14 in for the x and find the other 2 missing angles.
3x + 15
3(14) + 15
42 + 15
57°
4x - 12
4(14) - 12
56 - 12
44°
So, the measure of the three angles are: 44°, 57°, and 79°. So, the measure of the smallest angle is 44°
62. [0/0.07 Points] DETAILS PREVIOUS ANSWERS MY NOTES PRACTICE ANOTHER For the given function find the average rate of change over each specified interval. f(x) = x² + x - 12 (a) [0, 4] x (b) [-2, 10] X HARMATHAP12 9.3.001.
Answers
The average rate of change of the function f(x) = x² + x - 12 over the interval [0, 4] is 8, and over the interval [-2, 10] is 36.
To find the average rate of change of a function over a given interval, we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.
(a) [0, 4]:
For the interval [0, 4], the endpoints are x = 0 and x = 4. We evaluate the function at these points:
f(0) = (0)² + (0) - 12 = -12
f(4) = (4)² + (4) - 12 = 16 + 4 - 12 = 8
The difference in the function values is 8 - (-12) = 20, and the difference in x-values is 4 - 0 = 4. Therefore, the average rate of change over this interval is 20/4 = 5.
(b) [-2, 10]:
For the interval [-2, 10], the endpoints are x = -2 and x = 10. We evaluate the function at these points:
f(-2) = (-2)² + (-2) - 12 = 4 - 2 - 12 = -10
f(10) = (10)² + (10) - 12 = 100 + 10 - 12 = 98
The difference in the function values is 98 - (-10) = 108, and the difference in x-values is 10 - (-2) = 12. Therefore, the average rate of change over this interval is 108/12 = 9.
In summary, the average rate of change of f(x) = x² + x - 12 over the interval [0, 4] is 5, and over the interval [-2, 10] is 9.
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A club has $5$ members from each of $3$ different schools, for a total of $15$ members. How many possible ways are there to arrange a presidency meeting under the following conditions: i. The club must choose one of the $3$ schools at which to host the meeting, and ii. The host school sends $2$ representatives to the meeting, and each of the other two schools sends $1$ representative.
Please answer this correctly, I will mark the person who gets it correct Brainliest.
Answers
Answer:
750
Step-by-step explanation:
Pick one of the schools as the host. There are C(5, 2) ways to select the two representatives from that school and C(5, 1) ways to pick a representative from each of the other schools. So once we have selected a host school, there are 10*5*5=250 ways to pick the representatives. However, any of the three schools can be the host, so we need to multiply 250 by 3 to get 750 ways.
The price of a jumper is increased by 17%and now is $319.41.
Find the original price.
The answers is in $.
Answers
Answer:
$54.3
Step-by-step explanation:
17% of 319.41
so u need only to multiply them
In order for quantity supplied to equal 6 units, the price per unit must be: a) $1. b) $2. c) $3. d) $4.
Answers
To determine the price per unit at which the quantity supplied equals 6 units, we need additional information such as the supply function or the relationship between price and quantity supplied. The price and quantity relationship in the supply function can vary depending on various factors such as production costs, market conditions, and technology.
Therefore, it is crucial to have more context or data to determine the specific price per unit required for the quantity supplied to be 6 units. In summary, without the supply function or more information, it is not possible to determine the exact price per unit at which the quantity supplied equals 6 units.
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Carlos needs to build a fence for his chickens. The area he wants to build a fence around is 40 feet long and 20 feet wide. How many feet of fence does he need to buy? (Hint: 40x2 + 30x2)
Answers
the answer is 140 calculate so umm yeah duh I mean 280 lets go baby!!!!
how many terms of series 64+16+4 have the sum 5461\64?
Answers
Answer:
5th term will approximate 5461/64
Step-by-step explanation:
5th term will approximate 5461/64
64+16+4+1+0.25 = 85.25 ≈ 5461/64 = 85.33
Need help on this activity!!
In this activity, you will rearrange and solve a rational equation and find and use the inverse of a rational equation.
As we’ve seen, for a circuit with two resistors arranged in parallel, we can calculate the total resistance in the circuit, , in ohms, with this equation.
Question 1
Part A
Question
Rewrite the equation to represent the resistance of resistor 2, , in terms of and .
Answers
Answer:
My best guess rn is the first option
Step-by-step explanation:
the last dude had it close but it was basically flipped as you can tell.
The answer is (C) \(R_2=\frac{R_TR_1}{(R_1-R_T)}\)
We need to make \(R_2\) the subject of the formula \(R_T=\frac{R_1R_2}{R_1+R_2}\)
First remove the denominator by multiplying both sides by the binomial \((R_1+R_2)\)
\(R_T\times (R_1+R_2)=\frac{R_1R_2}{R_1+R_2}\times(R_1+R_2)\\\\R_TR_1+R_TR_2=R_1R_2\)
Arrange all terms containing \(R_2\) on one side
\(R_1R_2-R_TR_2=R_TR_1\)
Factor out \(R_2\) from the LHS
\(R_2(R_1-R_T)=R_TR_1\)
Finally, divide both sides by the binomial \((R_1-R_T)\) to leave \(R_2\)
\(R_2(R_1-R_T)\times\frac{1}{(R_1-R_T)}=R_TR_1\times\frac{1}{(R_1-R_T)}\\\\R_2=\frac{R_TR_1}{(R_1-R_T)}\)
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Three game tickets and four ride tickets cost $39. Five ride tickets cost $15. All game tickets cost the same and all ride tickets cost the same. What is the ratio of the cost of a game ticket to the cost of a ride ticket?
Answers
Answer: 3:1
Step-by-step explanation:
Let the cost of a game ticket be g.
Let the cost of a ride ticket be r.
The information given can be formed into an equation which will be:
3g + 4r = 39
Since Five ride tickets cost $15, the cost of each ride ticket will be:
= $15/5
= $3.
Therefore, 3g + 4r = 39
We put the value of r = $3 into the equation
3g + 4(3) = 39
3g + 12 = 39
3g = 39 - 12
3g = 27
g = 27/3
g = 9
The cost of a game ticket is $9
The ratio of the cost of a game ticket to the cost of a ride ticket will be:
= 9/3
= 3/1
= 3:1
The ratio is 3:1
A clerical worker takes 4 times as long to finish a job as it does an executive secretary. Working together, it takes them 4 hr to finish the job. How long would it take
the clerical worker, working alone, to finish the job?
It would take the clerical worker
hr to finish the job working alone.
Answers
Let's denote the time taken by the executive secretary to finish the job as "x" hours.
According to the given information, the clerical worker takes 4 times as long as the executive secretary, so the time taken by the clerical worker is 4x hours.
When they work together, they finish the job in 4 hours. This can be represented by the equation:
1/x + 1/4x = 1/4
To solve for x, we can multiply both sides of the equation by the least common multiple (LCM) of the denominators, which is 4x:
4 + 1 = x
5 = x
So, the executive secretary takes 5 hours to finish the job. Since the clerical worker takes 4 times as long, the clerical worker would take 4 * 5 = 20 hours to finish the job working alone.
Therefore, it would take the clerical worker 20 hours to finish the job working alone.
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how do you find the area of a trapezoid that is on a rectangle
Answers
Answer:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
Hope that helps!
Find a basis for the vector space of polynomialsp(t)of degree at most two which satisfy the constraintp(2)=0. How to enter your basis: if your basis is1+2t+3t2,4+5t+6t2then enter[[1,2,3],[4,5,6]]
Answers
In the following question, among the conditions given, {q1, q2} is a basis for the vector space of polynomials p(t) of degree at most two that satisfy the constraint p(2) = 0. In this particular case, we must enter our basis as [[1,0,-4],[0,1,-2]], since q1(t) = t^2 - 4 and q2(t) = t - 2.
To find a basis for the vector space of polynomials p(t) of degree at most two which satisfy the constraint p(2)=0, we can take the following steps:
1. Rewrite the polynomials as linear combinations of the form a + bt + ct^2
2. Use the constraint p(2) = 0 to eliminate one of the coefficients a, b, or c
3. Normalize the polynomials so that they are unit vectors
For example, if your basis is 1 + 2t + 3t^2, 4 + 5t + 6t2 then you can enter it as [[1,2,3],[4,5,6]].
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Find the fourth degree polynomial function with zeros 8, -8, 8i, -8i. Write the function in factored form.
Answers
The fourth degree polynomial in factor form is p(x) = (x - 8) · (x + 8) · (x - i 8) · (x + i 8), whose standard form is p(x) = x⁴ - 4096.
How to derive the equation of polynomial in standard form
In this problem we must determine the equation of a polynomial such that it contains the roots 8, - 8, i 8 and - i 8. This can be done by using the definition of a polynomial in factor form:
p(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., m - 1, m}
Where:
a - Lead coefficientrₙ - n-th root of the polynomialm - Grade of the polynomial.And modify the expression by algebra properties until standard form is found. First, substitute the roots:
p(x) = (x - 8) · (x + 8) · (x - i 8) · (x + i 8)
Second, expand the expression by algebra properties:
p(x) = (x² - 64) · (x² - i² 64)
p(x) = (x² - 64) · (x² + 64)
p(x) = (x² - 64) · x² + (x² - 64) · 64
p(x) = x⁴ - 64 · x² + 64 · x² - 4096
p(x) = x⁴ - 4096
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HELP HELP HELP PLS I GIVE U EXTRA POINTS
Answers
Answer:
A= 45 degrees
Step-by-step explanation:
aight so basic info here: all triangles are equal to 180 degrees knowing this we gotta make equation
80+7x-4+8x-1=180
combine like terms
75+15x=180
15x= 105
x= 7
now plug it back in
7(7)-4
49-4
45
Graph the system of equations. y = 2x y = –x + 6 Two lines on a coordinate plane that intersect at the point 2 comma 4. One line has y intercept 0 and the other has y intercept 6. Two lines on a coordinate plane that intersect at the point negative 2 comma negative 4. One line has y intercept 0 and the other has y intercept negative 6. Two lines on a coordinate plane that intersect at the point 1 comma 2. One line has y intercept 0 and the other has y intercept 3. Two lines on a coordinate plane that intersect at the point 3 comma 3. One line has y intercept 0 and the other has y intercept 6.
Answers
The solution to the systems of equations graphically is (2, 4)
Solving the systems of equations graphicallyFrom the question, we have the following parameters that can be used in our computation:
y = 2x
y = -x + 6
Next, we plot the graph of the system of the equations
See attachment for the graph
From the graph, we have solution to the system to be the point of intersection of the lines
This points are located at (2, 4)
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What are vertical and adjacent angles? How do you find the measure of an unknown angle using these relationships? Give an example and show your work.
Answers
Vertical angles are two angles that are opposite each other and share a common vertex. Adjacent angles are two angles that share a common side and vertex.
To find the measure of an unknown angle using these relationships, you can use the vertical angle theorem which states that if two angles are vertical, then they have equal measure. For example, if angle A and angle B are vertical angles, then angle A = angle B.
Example:
Given: Angle A = 40°
Find the measure of angle B
Solution:
Since angle A and angle B are vertical angles, then angle A = angle B
Therefore, the measure of angle B = 40°
What is an angle?An angle is created when two straight lines or rays intersect at the same point. The point where all points converge is known as an angle's vertex. The Latin word angulus, which meaning "corner," is where the term "angle" comes from.
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Complete the sentence.
A ___ is an amount of decrease in price.
Answers
Answer:
Discount ?
Step-by-step explanation:
Dave said that these triangles are similar. Is it false or true?
Answers
Answer:
false
Step-by-step explanation:
the sum of the angles is 180, for the first triangle B is 180-(60+79)= 41°. and for the second F = 180-(60+42) = 72°. therefore they're not equal / similar.
the center of circle O is located at (25,20), and the radius of the circle is 10 units. Which of the following points lies on the circle?
A(-24,-17)
B(-17,-14)
C(19-28)
D(26-23)
Answers
We need to calculate the distance between each point and the center O. If the distance is equal to the radius, then the point is on the circle that is point D (26, -23) lies on the circle with center O(25, 20) and radius 10 units.
The equation of a circle with center (h,k) and radius r is (x - h)^2 + (y - k)^2 = r^2. We can use this equation to determine which point lies on the given circle.
Substituting the values of the center and radius in the equation, we get:
(x - 25)^2 + (y - 20)^2 = 100
For point D (26, -23), we have:
(26 - 25)^2 + (-23 - 20)^2 = 1 + 1681 = 1682
Substituting these values in the equation of the circle, we get:
(26 - 25)^2 + (-23 - 20)^2 = 100
1 + 1681 = 100
1682 ≠ 100
Therefore, point D does not lie on the given circle.
Similarly, we can check for points A, B, and C. However, we will find that none of these points lie on the given circle.
Therefore, the only point that lies on the given circle is point D (26, -23).
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if heart disease death rate were expressed as deaths per 10000 pepole instead of deaths per 100000 people how would the correlation between wine consumtption and heart disease death rate change
Answers
The correlation between wine consumption and heart disease death rate would not change.
Correlation refers to the statistical relationship between two variables, and it is measured on a scale from -1 to 1. A correlation of -1 indicates a perfect negative correlation (i.e., as one variable increases, the other decreases), a correlation of 0 indicates no correlation, and a correlation of 1 indicates a perfect positive correlation (i.e., as one variable increases, the other increases).
The units of measure used for the two variables do not affect the correlation between them. In other words, the correlation between wine consumption and heart disease death rate would be the same whether the death rate was expressed as deaths per 10000 people or deaths per 100000 people. The only thing that would change is the scale of the death rate variable, but this would not affect the correlation between the two variables.
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Select the correct answer. What is the general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)? A. x2 + y2 − 4x + 2y + 1 = 0 B. x2 + y2 + 4x − 2y + 1 = 0 C. x2 + y2 + 4x − 2y + 9 = 0 D. x2 − y2 + 2x + y + 1 = 0
Answers
Answer:
x^2 +4x + y^2 -2y +1 =0
Step-by-step explanation:
First we need to find the radius
Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2
A circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--2)^2 + (y-1)^2 = 2^2
(x+2)^2 + (y-1)^2 = 4
FOIL ing
x^2 +4x+4 + y^2 -2y +1 = 4
Combining like terms
x^2 +4x + y^2 -2y +5 -4 =0
x^2 +4x + y^2 -2y +1 =0
Answer and Step-by-step explanation:
Answer:
x^2 +4x + y^2 -2y +1 =0
Step-by-step explanation:
First we need to find the radius
Since the y coordinate is the same, the radius is the difference in the x coordinate -2 - (-4) = -2+4 = 2
A circle can be written in the form
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--2)^2 + (y-1)^2 = 2^2
(x+2)^2 + (y-1)^2 = 4
FOIL ing
x^2 +4x+4 + y^2 -2y +1 = 4
Combining like terms
x^2 +4x + y^2 -2y +5 -4 =0
x^2 +4x + y^2 -2y +1 =0
to calculate the price of a ______________ that pays ______________, we could begin with the general formula for the present value of a stream of cash flows.
Answers
To calculate the price of a bond that pays interest, we could begin with the general formula for the present value of a stream of cash flows.
Bonds are debt instruments that pay periodic interest and return the principal at maturity. The price of a bond is the present value of its expected cash flows, discounted back to the present at an appropriate interest rate. The general formula for the present value of a stream of cash flows is:PV = C1 / (1+r)^1 + C2 / (1+r)^2 + ... + CT / (1+r)^T Where :PV = the present value of the cash flows Ct = the cash flow at time t (in our case, the interest payment)T = the maturity date of the bondr = the required rate of return.
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how many paving stones each measuring 2.5 m by 2 m be required to pave a rectangular piece of ground 30 metres by 16.5 m?
Answers
Answer:
39 stones
Step-by-step explanation:
find area of each
paving stone: 2.5*2=5
ground: 30*6.5=195
195/5=39
what is the value of x 5x + 8
Answers
Answer:
2.3 is your answer sry if wrong
Step-by-step explanation:
Answer:
x=-3
Step-by-step explanation:
Write the equation of the line with a slope of -5/4 and a y-intercept of 2.
a) y=1/4x+2
b) y=2x-5/4
c) y=-1/4x+2
d) y=-5/4x+2
Answers
Answer:
D, y=-5/4x+2
Step-by-step explanation:
the slope always comes before "x", and the y-intercept comes last when written in slope intercept. So y=-5/4x+2 is correct.
Line FG passes through points (1, 1) and (3, 3). Line F′G′ is formed by dilating line FG by a factor of 4 about the origin. Which statement is true?Group of answer choicesLine F′G′ is the original line.Lines FG and F′G′ have different slopes.Lines FG and F′G′ are parallel to each other.Lines FG and F′G′ are perpendicular to each other.
Answers
SOLUTION
\(\begin{gathered} For\text{ line FG, we have points:} \\ F(1,1)\text{ and G\lparen3,3\rparen} \\ \end{gathered}\)\(\begin{gathered} For\text{ line F'G', we have points:} \\ F^{\prime}(4,4)\text{ and G'\lparen12,12\rparen} \end{gathered}\)That is the graph.
CONCLUSION
THE TWO LINES WILL HAVE THE SAME SLOPE.
Therefore, they could be considered as parallel since two parallel lines have the same slope.
Part A
STRUCTURE Find two consecutive even integers such that twice the lesser of the two integers is 4 less than two times
the greater integer.
a. Write and solve an equation to find the integers.
Answers
Answer:
0, 2 . . . . . (any pair of consecutive even integers)
Step-by-step explanation:
You want a pair of consecutive even integers such that twice the lesser is 4 less than two times the greater.
SetupLet x represent the lesser of the two even integers. Then the greater is (x+2) and the given relation is ...
2x = 2(x+2) -4
SolutionSimplifying gives ...
2x = 2x +4 -4
2x = 2x . . . . . . . true for any even integer x
Any pair of consecutive even integers will satisfy the relation.
one such pair is 0, 2
check: 2(2) -4 = 2(0)
The second angle of the triangle is 30 degrees larger than the first, while the third angle of the triangle is 3 times the second. How big is the first angle?
Answers
Answer:
45 degrees
Step-by-step explanation:
The first angle of the triangle is 45 degrees. This can be determined by the given information that the second angle is 30 degrees larger than the first and the third angle is 3 times the second. Since the second angle is 30 degrees larger than the first, the first angle must be 15 degrees, and the third angle must be 3x15=45 degrees.
What is the slope of this line?
(sorry for the quality.)
Answers
Answer:
slope = - 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (- 8,6) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line
m = \(\frac{-2-6}{0+8}\) = \(\frac{-8}{8}\) = - 1