Given the ODE
(x - 1) y'' + y' = 0
we assume a solution of the form
[tex]y(x) = \displaystyle \sum_{n=0}^\infty c_n x^n[/tex]
with derivatives
[tex]y'(x) = \displaystyle \sum_{n=0}^\infty n c_n x^{n-1} = \sum_{n=0}^\infty (n+1) c_{n+1} x^n[/tex]
[tex]y''(x) = \displaystyle \sum_{n=0}^\infty (n+1) n c_{n+1} x^{n-1} = \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n[/tex]
Substituting these series into ODE gives
[tex]\displaystyle (x - 1) \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty (n+1)n c_{n+1} x^n - \sum_{n=0}^\infty (n+2)(n+1) c_{n+2} x^n + \sum_{n=0}^\infty (n+1) c_{n+1} x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty \bigg((n+1)n c_{n+1} - (n+2)(n+1) c_{n+2} + (n+1) c_{n+1}\bigg) x^n - 2c_2 + c_1 = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty \bigg((n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2}\bigg) x^n - 2c_2 + c_1 = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2}\bigg) x^n = 0[/tex]
Then the coefficients [tex]c_n[/tex] are given recursively by
[tex](n+1)^2 c_{n+1} - (n+2)(n+1) c_{n+2} = 0[/tex]
for all n ≥ 0, or equivalently,
[tex]c_{n+2} = \dfrac{n+1}{n+2} c_{n+1}[/tex]
which most closely resembles the second choice.
Adelle keeps track of the time her bus arrives at her stop. Since she has been keeping track, her bus has arrived on time 16 days and has been late on 4 days. Based on her data, what percentage of the time should Adele expect the bus to be late?
Answer:
25%
Step-by-step explanation:
4 days of 16 days is 25% or 1/4
Hope this helps! ;-)
Stephanie is helping a midwife weigh new-born babies. The scales are in pounds but the sheet she has to complete is in kilogrammes. The baby weighs 8.06 lbs. When she converts this on a calculator the display reads 3.65595152. What is this in kilogrammes to 3 decimal places?
The weight of baby in kg is, 3.659 kg.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The baby weighs 8.06 lbs.
Now, We know that;
⇒ 1 pound = 0.454 kg
Hence, The weight of baby in kg is,
⇒ 8.06 pounds = 8.06 × 0.454 kg
= 3.659 kg
Thus, The weight of baby in kg is, 3.659 kg.
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A shirt on sale for 25%off. Sandy paid 7.50 for the shirt. What was the shirts regular price
£10
Step-by-step explanation:
firstly what you have to do is
since the percentage is decreased
we will say 100 - 25% = 75%
then we say 7.50/75% = 10
So we know that the original price was
£10 pounds
As 10- 25%= 7.5
The shirt's regular price is 10.
Given,
A shirt on sale for 25%off.
Sandy paid 7.50 for the shirt.
We need to find the regular price.
The regular price is the same as the selling price.
We have,
Regular price = Paid price + offer discount%
offer discount = 25%
Paid price = 7.50
If after 25% off Sandy paid 7.50 which means Sandy paid only 75% of the price.
The regular price is always 100%
= Paid price + offer discount%
= 75% + 25%
So we have,
75% = 7.5
Multiplying 25/75 on both sides.
25/75 x 75% = 7.5 x 25/75
25% = 2.5
We see that the offer discount is 2.5.
We have,
Regular price = Paid price + offer discount%
= 7.50 + 2.5
= 10
Thus the shirt's regular price is 10.
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Alex believes the honor roll students at his school have an unfair
advantage in being
assigned to the science class they request. He asked 500 students at his school the
following questions: Are you on the honor roll?" and "Did you get the science class you
requested?" The results are shown in the table below:
Honor roll Not on honor roll Total
Received science class requested
64
315
379
Did not get science class requested 80
41
121
Total
144
356
500
Help Alex determine if all students at his school have an equal opportunity to get into
the science class they requested. Show your work, and explain your process for
determining the fairness of the class assignment process.
According to the information provided, it can be inferred that the conclusion reached by Alex is that there are no advantages to honor roll students.
How to calculate the percentage of students who received the requested classes?To calculate the percentages of students who received the requested classes, we must take into account the data in the table. Additionally, we must perform the following operations:
144 ÷ 100 = 1.44
64 ÷ 1.44 = 44.44%
According to the above, the percentage of students who are on the honor roll and receive their classes is 44.44%.
To calculate the percentage of students who are not on the honor roll and receive their classes, we do the following operation.
356 ÷ 100 = 3.56
315 ÷ 3.56 = 88.48%
According to the above, it can be inferred that the students who are on the honor roll do not have advantages over the others because the percentage of students who are not on the honor roll and receive their science classes is greater than the percentage of students who are on the honor roll and receive their classes.
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What is the image point of (1, -2) after a translation right 4 units and down 4 units?
Answer:
Hello!!!!
THE ANSWER: (5, -6)
Please read the explanation... it always helps... trust me...
Step-by-step explanation:
Okkeeeee lets beginnnn....
A translation is when you move a point of shape in a coordinate plane
so a translation of a point to the right means you are moving the point to the right of the coordinate plane meaning the positive side of the x-axis... so in this case you will need to add 4 to the x-coordinate....
simarily to the "down four units"
moving it down means subtraction.... meaning you need to subtract 4 from -2 which gets you -6...
I REALLY HOPE THIS HELPS!!! :)
a) Let A x B = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)} then, find A, B, n(A), n(B)
Step-by-step explanation:
A={1,2,3}
B={5,6}
n(a)=3
n(b)=2
47/6m+n- 7/2m-6/5n
Simplify
Answer:
[tex]\frac{13m}{3}-\frac{n}{5}[/tex]
Step-by-step explanation:
1) Simplify [tex]\frac{47}{6}m[/tex] to [tex]\frac{47m}{6}[/tex]
[tex]\frac{47m}{6}+n-\frac{7}{2}m-\frac{6}{5}n[/tex]
2) Simplify [tex]\frac{7}{2}m[/tex] to [tex]\frac{7m}{2}[/tex]
[tex]\frac{47m}{6}+n-\frac{7m}{2}-\frac{6}{5}n[/tex]
3) Simplify [tex]\frac{6}{5}n[/tex] to[tex]\frac{6n}{5}[/tex]
[tex]\frac{47m}{6}+n-\frac{7m}{2}-\frac{6n}{5}[/tex]
4) Collect like terms.
[tex](\frac{47m}{6}-\frac{7m}{2})+(n-\frac{6n}{5})[/tex]
5) Simplify.
[tex]\frac{13m}{3}-\frac{n}{5}[/tex]
Select the correct answer.
Given: , and
Prove:
Statements Reasons
vertical angles theorem
given
given
alternate interior angles theorem
??
definition of congruence
Which step is missing in the proof?
Based on the SAS congruence criterion, the statement that best describes Angie's statement is:
Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.
What is congruency?The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.
An included angle is found between two sides that are under consideration.
See image attached below that demonstrates two triangles that are congruent by the SAS Congruence Theorem.
Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.
The one pair of corresponding angles that are congruent MUST be "INCLUDED ANGLES".
Therefore, based on the SAS congruence criterion, the statement that best describes Angie's statement is:
Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.
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If f(x) = 3x - 1 and g(x) = x + 2 , find (f + g)(x)
Answer:
Answer:4x + 1
Step-by-step explanation:
(f + g)(x)=(3x - 1)+(x + 2)
=3x + x - 1 + 2
=4x + 1
Help. Please and thanks.
Answer:
D
Step-by-step explanation:
the other 3 options are all true.
the sum of all angles in a triangle is always 180°.
so, when T is 40°, that leaves 180-40 = 140° to the other 2 angles. in an isoceles triangle they must be equal to each other, so they are half of the remaining 140°, which is 70°.
and of course the 2 sides are equal (hence "isoceles").
Samuel worked 1/4 of a day on Tuesday and 3/8 of a day on Wednesday. Which
of these represents the fraction of a day he spent working on both days?
Rewrite 1/4 to have 8 as the denominator: 1/4 = 2/8
Now add the two days together:
2/8 + 3/8 = 5/8
Answer: 5/8
Answer correctly for branliest!
Two cars, A and B, are travelling along a straight road and in the same direction. Car B is 20 km
ahead of Car A. Car A is travelling at 60 km · while Car B at 50 km 1. They both start at 12:00
hours. At what time Car A will overtake Car B?
Answer:
2 o'clock
Step-by-step explanation:
Their 'closing speed' is 60 - 50 = 10 km/hr
they have 20 km between them
at closing speed this will take 20 km / 10 km/hr = 2 hours for the cars to meet....this would be at 14:00 or 2 oclock
Write 6 41 100 as a decimal number.
Answer:
From my calculation I think it is 6.4×10^5
It is in standard form
OR
641100÷100,000=6.411
I'm not sure yet,but you can confirm it
[tex]\huge\textbf{Hey there!}[/tex]
[tex]\huge\textbf{Assuming:}[/tex]
[tex]\mathsf{6\dfrac{41}{100}}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathsf{6\dfrac{41}{100}}[/tex]
[tex]\mathsf{= \dfrac{6 \times100 + 41}{100}}[/tex]
[tex]\mathsf{= \dfrac{600 + 41}{100}}[/tex]
[tex]\mathsf{= \dfrac{641}{100}}[/tex]
[tex]\mathsf{= 641\div100}[/tex]
[tex]\mathsf{= 6.41}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: \boxed{\mathsf{6.41}}}\huge\checkmark[/tex]
[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Can you match the teacher's comments to the definitions?
Answer:
Daniel =Were you thinking of perpendicular lines?
Oris= It seems like you've got the basic idea, but your definition could be more precise.
Kaoris= Yes well done...
Part 1: Complete the operations geometrically.
Use vector operations to draw the resultant vector.
⦁ Draw 2u + 4v.
Answer:
Step-by-step explanation:
The geometrically operations 2u + 4v is (2,12).
For immediately line graphs there is a linear relationship between the x and y values and so the line is instantly and should be drawn with a ruler. The gradient determines how steep the road is and the y-intercept tells us the vicinity wherein the immediate line intersects the y-axis.
Why is a graph a direct line?It continually goes up in steps of equal length, so it is a straight line. that is first-class as a way because it goes. It identifies the defining assets of a linear feature—that it has a constant rate of exchange—and relates that property to a geometric feature of the graph.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.
equation of a straight line is y=mx+cy represents vertical line y-axis.
x represents the horizontal line x-axis.
m is the slope of the line
slope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.Learn more about geometry here:-https://brainly.com/question/19241268
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HELP PLEASE 100 POINTS!!!
Given that triangle PHT is a right triangle and Line HY is an altitude, what is the missing justification in the proof that (PH)^2 + (HT)^2 = (PT)^2?
The missing reason is reflexive property.
Therefore, the correct option is D.
What is a triangle?A triangle is a type of polygon, which has three sides, and the two sides are joined end to end is called the vertex of the triangle.
Given that a triangle PHT is a right triangle and Line HY is an altitude.
According to the reflexive property, a side or an angle is congruent to itself.
If A is an angle of a triangle, then using reflexive property.
∠A ≅ ∠A
∠PHT ≅ ∠HYT (Both are right angles)
∠T ≅ ∠T (Reflexive property)
ΔPHT ~ ΔHYT (AA rule of similarity)
Other statements and reasons are already in the table.
Hence the correct option is D.
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What comes next in this pattern? 7/2, 6/3, 5/4, ... 4/9 4/7 4/5
Answer:4/3
4/3
Step-by-step explanation:
PLEASE I NEED HELP ASAP!!!!!!!!
Note: please add the answer next to the number its from so I can know which question was answered
Answer:
B, B
Step-by-step explanation:
< less than
> Greater Than
If it has a line under it it is equal too as well as greater or less.
The close dot means equal too and the open mean not equal to
Help please
50 points
Answer:
The answer would be B
Step-by-step explanation:
HELP ASAP PLEASE!!!!!!!
The circumference of a circular garden is 122.46 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer. feet
The radius of the circular garden whose circumference is 122.46 feet is: 19.5 feet.
What is the Circumference of a Circle?Circumference = 2πr, where r is the radius of the circle.
Given the following:
Circumference = 122.46 feetRadius (r) = ?π = 3.14122.46 = 2(3.14)(r)
122.46/2(3.14) = r
r = 19.5 feet.
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Write a slope-intercept equation for a line that passes through (-2,3) and (2,-5)
The slope of the given line is m
(Simplify your answer. Type an integer or a simplified fraction.)
Answer:
y - 3 = -2 * (x+2)
Step-by-step explanation:
4 divided by 5yards 1 foot
Which is not a reason an athlete uses technology to assess performance?
A. To monitor development.
B. To tailor to their training program.
C. To send to college recruiters.
D. To analyze technique.
The reason for which an athlete does not use technology to assess performance is To send to college recruiters.
What is technology?Technology is the culmination of collected knowledge and the application of skills, methods, and procedures utilized in manufacturing and scientific research. Technology is incorporated into the functioning of all machinery, with or without a thorough understanding of its function, for an organization's stated purpose.
The reason for which an athlete does not use technology to assess performance is To send to college recruiters.
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f(x) = x² + 2x − 3
Find f (2)
f(2) is equal to type your answer...
Answer:
f(2) = 5
Step-by-step explanation:
Given: f(x) = x² + 2x - 3
We are asked to find the value of the function when x = 2.
In the function, substitute 2 as the value of x and simplify:
f(2) = (2)² + 2(2) - 3
f(2) = 4 + 4 - 3
f(2) = 8 - 3
f(2) = 5
When x is equal to 2, the value of the function is 5.
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5. A rectangle whose length and width are 10 and 6, respectively, is shown below. The rectangle is continuously
rotated around a straight line to form an object whose volume is 150.
6
10
hich line could the rectangle be rotated around?
A. a long side
B. a short side
C. the vertical line of symmetry
D. the horizontal line of symmetry
TheThe line that the rectangle could be rotated around is: C. the vertical line of symmetry.
Vertical line of symmetryAnalysis
Volume=Base area×height
If the rectangle rotated around horizontal line of symmetry
V1=Ah=πr²h
=π×9×10
=90π
If the rectangle rotated around short line
V2=Ah=πr²h
=π×10²×6
=π×100×6
=600π
If the rectangle rotated around vertical line of symmetry
V3=Ah=πr²h
=π×5²×6
=π×25×6
=150π
Therefore the correct option is C.
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Select the expression that represents the following statement multiply 6 by 2, and then subtract 4. 2 - 4x6
6 x 2 - 4
6 + 6 + 4 - 2
6 × 4 - 2
You have found the ages (in years) of 5 gorillas. Those gorillas were randomly selected from the 29 gorillas at your local zoo: 8,4,14,16,8
Find the Average Age
Standard Devaluation
Answer:
the answer is 10
Step-by-step explanation:
(8+4+14+16+8)/5
3 years ago, the residents of Planet X found a black hole leading to another galaxy. Since then, they have been leaving Planet X at a rate of 120 residents per year.
The following equation describes this situation:
\quad -120\cdot 3 = -360−120⋅3=−360minus, 120, dot, 3, equals, minus, 360
What does -360−360minus, 360 tell us?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
A total of 360360360 residents left Planet XXX in the past three years.
(Choice B)
B
360360360 residents left Planet XXX each year.
(Choice C)
C
None of the above
Answer:
A total of 360 residents left Planet X in the past 3 years.
Step-by-step explanation:
120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.
Answers
A total of 360 residents left Planet X in the past 3 years.
Step-by-step explanation:
120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.A total of 360 residents left Planet X in the past 3 years.