You need to re copy and paste it, I can’t see the full possible answers/question.
Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)
(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 3
You're looking for a solution of the form
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]
Differentiating twice yields
[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]
[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]
Substitute these series into the DE:
[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]
[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]
Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:
[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]
which indicates that the coefficients in the series solution are governed by the recurrence,
[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]
Use the recurrence to get the first few coefficients:
[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]
You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,
-7 = -7/0!
-7/2 = -7/2!
-7/6 = -7/3!
and so on, with only the coefficient in the n = 1 position being the odd one out. So we have
[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]
which looks a lot like the power series expansion for -7eˣ.
Fortunately, we can rewrite the linear term as
3x = 10x - 7x = 10x - 7/1! x
and in doing so, we can condense this solution to
[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]
Just to confirm this solution is valid: we have
y = 10x - 7eˣ ==> y (0) = 0 - 7 = -7
y' = 10 - 7eˣ ==> y' (0) = 10 - 7 = 3
y'' = -7eˣ
and substituting into the DE gives
-7eˣ (x - 1) - x (10 - 7eˣ ) + (10x - 7eˣ ) = 0
as required.
which one of these points lies on the line described by the equation below y - 5 = 6 ( x - 7 )
Answer:
the answer would be (7,5)
John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?
in the given circle the radius is 9 cm what is its diameter?
Answer:
18
Step-by-step explanation:
The diameter is equal to twice the length of the radius
So if the radius is 9 then the diameter is 9 * 2 = 18
In which direction does the parabola x=2y2+1 open?
A up
B down
C Right
D left
Answer and Step-by-step explanation:
First, we need to set this equation equal to y, which means we need to get y by itself, and all other terms equal to y.
x = [tex]2y^2 + 1[/tex]
Subtract 1, then divide by 2 on both sides.
[tex]x - 1 = 2y^2\\\\\frac{x-1}{2} = y^2[/tex]
Now, take the square root of both sides.
[tex]y=\sqrt{\frac{x-1}{2}}[/tex]
We see that the value with the x (1) is positive, and that we have a square root function, which means the parabola would open to the right.
(If the x value was negative, the square root function's parabola would open to the left)
So, C (Right) is the correct answer.
#teamtrees #PAW (Plant And Water)
I hope this helps!
Oh Brian~
I need help again
Answer:
18c^3d^9
Step-by-step explanation:
2c^3 d^2 * 9d^7
We know that we add the exponents when the base is the same
2*9 c^3 d^(2+7)
18c^3d^9
Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3
Answer: r = 50 miles/h
Step-by-step explanation:
Let r be the rate of average speed.
Then
r = D/t
r = 150/3
r = 50 miles/h
please click thanks and mark brainliest if you like :)
If two numbers differ by 9 the same of their squares is 653. What are the numbers?
Answer:
Two numbers differ by 9 and the sum of their square is 653. What are the numbers?
Well,that's a mathematical question from algebra and it's quite difficult to answer such questions by writing through the circumstances offered by apps like quora.
However,I have tried to answer your question in an understandable way.Hope you may not find it difficult to analyze.
Let the numbers be x and (9+x)
Therefore,according to given,
x^2 + (9+x)^2 =653
=>x^2 + (9)^2 + x^2 + 2×(9)×(x)=653 (Applying the formula of (a+b)^2)
=>x^2 + 81 + x^2 + 18x =653
=>2x^2 + 18x + (81-653)=0
=>2x^2 + 18x - 572=0
=>2x^2 + (44x - 26x) - 572=0
=>2x^2 + 44x - 26x - 572=0
=>2x(x + 22) - 26(x + 22)=0
=>(x + 22)(2x - 26)=0
But since the number can't be negative
Therefore, x=13
Hence,the required numbers are 13 and 22.
Step-by-step explanation:
in first hope you like it
help, please!
find x
This shape consists of two primary special triangles, 30-60-90 and 45-45-90.
the side with the 60° will be half of the hypotenuse because 30° is across from it.
the side with the 30° will be 5.5√3 because 60° is across from it, and any sides that has 60° across from it is associated with a √3.
x is 5.5√6 because any sides that is "below" the 45° angles are associated with a √2 times the side that's above the 45°
Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Martha arrive first and Armando last?
c. Find the probability that Martha will arrive first and Armando last.
Show your work
Answer:
a) 120
b) 6
c) 1/20
Step-by-step explanation:
a) 5! = 120
b) (5 - 2)! = 6
c) 6/120 = 1/20
find the range of values of a for which 11- 2a>1 is ____
Answer:
a<5
Step-by-step explanation:
11-2a>1
-2a>1-11
-2a>-10
a<5
PLEASE HELP 40 POINTS
Express each logarithm in terms of ln 3 and ln 5.
ln 81 / 125
The solution is 4ln3 - 3ln5, which is correct option(C).
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmatic operation are called arithmatic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation : Divides left hand operand by right hand operand
For example 4/2 = 2
According to the problem, we will use some of the basic logarithmic properties,
Given expression,
⇒ ln81/125
⇒ ln81 - ln125 [used property : logₐ(x/y) = logₐx - logₐy]
⇒ ln3⁴ - ln5³ [ 81 =3⁴ and 125 = 5³ ]
⇒ 4ln3 - 3ln5 [used property : logₐ(xⁿ) = nlogₐx]
Hence, the solution is 4ln3 - 3ln5
Learn more logarithmic properties here:
brainly.com/question/24211708
#SPJ2
Scientists have increased their ability to make observations beyond their own senses through the invention of specialized equipment such as Xray telescopes.
Which best explains how such technology has affected society?
Technology has replaced humans' need for independent observation and thought.
Technology has replaced humans' need for independent observation and thought.
Technology has replaced the need for the experimentation in the scientific process.
Technology has replaced the need for the experimentation in the scientific process.
Human knowledge of the universe is limited by ineffective technology.
Human knowledge of the universe is limited by ineffective technology.
Human knowledge of the universe beyond Earth has increased.
Answer:
D
Step-by-step explanation:
A is rather a strange choice. The tools are used as extensions of our senses. That's all that technology has done. We still need to observe things for ourselves if we are to learn. I actually really do not know what this statement means. My answer reflects what I think is true. Our need to observe and think is not hindered.
B is never going to be true. We still have to test things out, even with the best tools that we have.
C: The exact opposite is true. Our knowledge of the universe has expanded beyond our belief with the better tools of technology that we have.
D: This is the opposite of C and is the answer.
(SAT PREP) Find the value of x in each of the following excersises
Answer:
The answer is 155.
Step-by-step explanation:
We can find the remaining parts of the triangle angles.
a man spends RS 608 a month. If he earns Rs 640, what percentage of his invome does he save??.
Please explanation
Answer:
5%
Step-by-step explanation:
given,
Earns= Rs 640
spends= Rs 608
saves= (Rs 640 - Rs 608)
=Rs 32
therefore, 32/640x100
answer = 5%
Answer From Gauth Math
Answer:
5%
Step-by-step explanation:
save=640-608=32
(32/640)*100%
5%
1 poir
Question 1. Jessica has $1,625.00 to purchase a five-year Certificate of
Deposit (CD). In the chart, there are CD rates frombankrate.com. What
would the account ending balance be at Synchrony Bank if it is
compounded quarterly? *
Use the Compound Interest Formula to calculate the ending balance. A = P(1 + 5)nt
Nationwide
Bank
Nationwide
2.01%
No
Synchrony Bank
all synchrony
1.95%
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Answer:
$1790.99
Step-by-step explanation:
Given:
$1625 is invested at an annual rate of 1.95% compounded quarterly for 5 years
Find:
the ending balance
Solution:
The compound interest formula applies.
FV = P(1 +r/n)^(nt) . . . Principal P at rate r for t years, compounded n per year
FV = $1625(1 +0.0195/4)^(4·5) = $1625(1.004875^20) ≈ $1790.99
The account ending balance would be $1790.99.
what Is the si unit of temperature
Answer:
the Si unit of temprature in Kelvin (K)
Step-by-step explanation:
Answer:
The answer is Kelvin (k).
Step-by-step explanation:
The kelvin (K) is defined by taking the fixed numerical value of the Boltzmann constant k to be [tex]1.380649*10^{-23}[/tex] when expressed in the unit of joule per kelvin. The temperature 0 K is commonly referred to as "absolute zero." On the widely used Celsius temperature scale, water freezes at 0 °C and boils at about 100 °C. One Celsius degree is an interval of 1 K, and zero degrees Celsius is 273.15 K. An interval of one Celsius degree corresponds to an interval of 1.8 Fahrenheit degrees on the Fahrenheit temperature scale.
The kelvin is also the fundamental unit of the Kelvin scale, an absolute temperature scale named for the British physicist William Thomson (known as Lord Kelvin). An absolute temperature scale has as its zero point absolute zero (−273.15° on the Celsius temperature scale and −459.67° on the Fahrenheit temperature scale), the theoretical temperature at which the molecules of a substance have the lowest energy; hence, all values on such a scale are nonnegative.
If side A is 10 inches long, and side B is 24 inches, find the length of the unknown side.
Step-by-step explanation:
Right Triangles and the Pythagorean Theorem. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.
e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hours. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean
Answer:
Step-by-step explanation:
[tex]p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\dfrac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \dfrac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}[/tex]
i need help with this question asapppppp
9514 1404 393
Answer:
$11,680.58
Step-by-step explanation:
Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.
__
The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.
The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...
0.205×21,465 = 4400.325 ≈ 4400.33
The the total tax due on $70,000 is ...
$7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000
_____
Additional comments
The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.
__
Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.
≤ 48535 -- income × 0.15
≤ 97069 -- income × 0.205 -2669.425
≤ 150,473 -- income × 0.26 -8008.22
≤ 214,368 -- income × 0.29 -12,522.41
> 214,368 -- income × 0.33 -21,097.13
In this case, the second row of this simpler table would give the tax on $70,000 as ...
tax = 70,000 × 0.205 -2669.425
tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Chapter 11 part 2:
What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.
The three main log rules you'll encounter are
log(A*B) = log(A) + log(B)log(A/B) = log(A) - log(B)log(A^B) = B*log(A)The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.
Here are examples of each rule being used (in the exact order they were given earlier).
log(2*3) = log(2) + log(3)log(5/8) = log(5) - log(8)log(7^4) = 4*log(7)----------------
Here's a slightly more complicated example where the log rules are used.
log(x^2y/z)
log(x^2y) - log(z)
log(x^2) + log(y) - log(z)
2*log(x) + log(y) - log(z)
Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.
The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities
a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?
Solution :
a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.
P (correct in the 4th attempt)
= [tex]$(1-0.75)^3 \times 0.75$[/tex]
= 0.01171875
b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.
P( X = 3) for X = B in (n = 10, p = 0.75)
= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]
= 0.0031
c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :
There are = 6 success, p = 0.75.
Therefore, this is a case of a negative binomial distribution.
[tex]$E(X)=\frac{k}{p}$[/tex]
[tex]$=\frac{6}{0.75}$[/tex]
= 8
So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]
[tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]
= 1.6330
The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.
Answer:
0.9332
Step-by-step explanation:
We are given that
Mean diameter, [tex]\mu=73[/tex]
Variance, [tex]\sigma^2=4[/tex]
We have to find the probability that the diameter of a selected bearing is less than 76.
Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]
[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]
[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]
Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]
[tex]P(x<76)=P(Z<1.5)[/tex]
[tex]P(x<76)=0.9332[/tex]
Hence, the probability that the diameter of a selected bearing is less than 76=0.9332
Help me please and thank you
Answer:
Option C is correct
Step-by-step explanation:
[tex]log( {10}^{3} )[/tex]
Use logarithm rules to move 3 out of the exponent.[tex]3 \: log \: (10)[/tex]
Logarithm base 10 of 10 is 1.[tex]3×1[/tex]
Multiply 3 by 1.[tex]3[/tex]
Hope it is helpful....I need help with ged
Answer:
General Educational Development (GED) tests
What do subject do you need help?
Step-by-step explanation:
The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.
I’m new to this app and I need help with those two questions please help!!
y=x²-10x-7
a>0 so we will be looking for minimum
x=-b/2a=10/2=5
y=25-50-7=-32
Answer: (5;32)
y=-4x²-8x+1
а<0 so we will be looking for maximum
х=-b/2a=8/-8=-1
у=4+8+1=13
Maximum point (-1;13)
Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d
Answer:
10/21 of the distance
Step-by-step explanation:
2/7 distance
------------------
3/8 tank
The rest of the tank is 8/8 - 3/8 = 5/8
2/7 distance x
------------------ = ----------------------
3/8 tank 5/8 tank
Using cross products
2/7 * 5/8 = 3/8x
10/56 = 3/8x
Multiply each side by 8/3
10/56 * 8/3 = 3/8x * 8/3
10/3 * 8/56=x
10/3 * 1/7 =x
10/21 =x
10/21 of the distance
Find the coordinates of the vertices of the figure after the given transformation: T<0,7>
A. X′(1,−1),L′(0,2),W′(2,1)
B. X′(−4,2),L′(−5,5),W′(−3,4)
C. X′(3,2),L′(2,5),W′(4,4)
D. X′(0,−3),L′(−1,0),W′(1,−1)
Answer: B
Step-by-step explanation:
Why did historians choose to study this topic?
the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)
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Answer:
all real numbers
Step-by-step explanation:
The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.
The domain of g(x) = f(-x) is all real numbers.
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
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Answer:
b. y = f(x -3)
Step-by-step explanation:
The translation right h and up k units is ...
y -k = f(x -h)
Here, the red graph is translated right 3 and up 0, so the translated function is ...
y = f(x -3)
_____
Additional comment
You can check this if you like by listing a couple of corresponding points:
y = f(x)
1 = f(-3) . . . . left-most point on black graph.
The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...
1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)
