Answer:
The equation of the line is y = -2/3x - 29/3
Step-by-step explanation:
The slope of these points (-7,-5) and (-1,-9) is m = -2/3
Once you plug that into the y = mx + b equation, you can see that the y-intercept is -29/3.
Put all of that into the y = mx + b equation and you'll get --> y = -2/3x - 29/3
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.
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?
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
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
(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%
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 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’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
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)
9514 1404 393
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.
someone help me pls i need to pass summer school
Answer:
A
Step-by-step explanation:
The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain
14 → 4
12 →5
10 →6
8 →7
find the derivative of y=(x³-5)⁴(x⁴+3)⁵
Answer:
[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]
Step-by-step explanation:
Explain why the equation x=x+1 is a contradiction
Answer:
It results in no solution.
Step-by-step explanation:
If you subtract x on both sides, this will leave you with 0 ≠ 3. The result is no solution. This is why it is contradictory.
Algebra II Part 1
Choose the expression or equation that correctly represents this information
Rose works eight hours a day for five days a week. How many hours will she work in sa
weeks?
hours = 40 = 6
hours = 40.6
hours = 6 = 40
Answer:
240 i.e 40*6
Step-by-step explanation:
if rose works 8hrs per day then she works 40 hrs per week (5 days) therefore 40 hrs per 6 weeks =40*6=240
Answer:
40
Step-by-step explanation:
I need help answering this ASAP
Answer:
A the input x=3 goes to two different output values
Step-by-step explanation:
This is not a function
x = 3 goes to two different y values
x = 3 goes to t = 10 and y = 5
Complete the equation describing how x
and y are related.
Х у
y = [? ]x +
07
1 9
2 11
3 13
4 15
5 17
Enter the answer that
belongs in [?]
Answer:
Hello,
Answer 2
Step-by-step explanation:
7=2*0+7
9=2*1+7
11=2*2+7
13=2*3+7
15=2*4+7
17=2*5+7
y=2*x+7
An other way:
[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]
The complete equation is [tex]y = 2x+7[/tex].
What is equation?An equation is a condition on a variable such that two expressions in the variable should have equal value.
What is substitution?Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.
According to the question.
We have a table which shows the relation between x and y.
Let the missing term be a and b.
The the given equation becomes
[tex]y = ax + b[/tex]
For finding the value of a and b.
Substitute x = 0 and y = 7 in equation y = ax + b.
[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]
Again, substitute x = 1 and y = 9 in the equation y = ax+ b
[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]
substitute the value of a and b in the equation y = ax + b.
[tex]\implies y = 2x+ 7[/tex]
Therefore, the complete equation is [tex]y = 2x+7[/tex].
Find out more information about equation and substitution here:
https://brainly.com/question/2581775
#SPJ2
596 is divisible by 2?
a.yes
b.no
Answer:
It's yes
Step-by-step explanation:
Answer:
yep
Step-by-step explanation:
number is even, so it can be evenly divided by 2. :)
What is the equation of the line that passes through (4,3) and (2, -1)?
y = 4x -13
y = 6x+4
y = 2x-5
y = 1/2 x -2
Answer:
y=2x-5
Step-by-step explanation:
By using two-points form:
y-y1/y2-y1=x-x1/x2-x1
p(x1,y1)=(4,3)
p(x2,y2)=(2,-1)
Subtitute points in formula:
y-3/-1-3=x-4/2-4
y-3/-4=x-4/-2
y-3/-2=x-4/-1
1(y-3)=2(x-4)
y-3=2x-8
y=2x-8+3
y=2x-5
Note:if you need to ask any question please let me know.
After running 3/4 of a mile tess has only run 1/3 how long is the race in miles but I want to know how you did it
One angle of a triangle is equal to the sum of the remaining angles. If the ratio of measures of the ren
is 2:1, find the measures of the three angles of the triangle.
9514 1404 393
Answer:
90°, 60°, 30°
Step-by-step explanation:
The remaining angles have a ratio of 2:1, so total 3 "ratio units". The first angle is equal to that sum: 3 ratio units, so all of the angles together total 3+2+1 = 6 ratio units. The total of angles is 180°, so each ratio unit is 180°/6 = 30°.
The first angle is 3 ratio units, or 90°.
The second angle is 2 ratio units, or 60°.
The third angle is half that, or 30°.
The three angles are 90°, 60°, 30°.
Solving Equations by Dividing 2) 9x= -135 Solve for x. 0 -144 O 126 O 15 0 -15
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]
[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]
[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]
[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]
[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]
[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]
[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
help asap!!
Find the length of AB
A. 2.89
B. 33.13
C. 378.63
D. 377.19
Answer:
C
Step-by-step explanation:
[tex] \sin( 5 ^{o} ) = \frac{33}{ab} \\ ab = 378.63[/tex]
factorise completely 4x^(2 )(x + 1) - 6x (x+1)
Answer:
[tex] {4x}^{2} (x + 1) - 6x(x + 1) \\ = (x + 1)(4 {x}^{2} - 6 x ) \\ = (x + 1)(2x)(2x - 3)[/tex]
explanation:
first choose the common factor by observation, it is (x + 1):
factorise it out:
= (x + 1)(4x² - 6x)
by observation in (4x² - 6x), common factor is 2x.
Factorise 2x out:
= (x + 1)[2x(2x - 3)]
Answer:
(4x2-6x) (x+1)
now common factor is (x+1) ,so,(4x2-6x) (x+1)
Smart phone: Among 239 cell phone owners aged 18-24 surveyed, 103 said their phone was an Android phone. Part: 0 / 30 of 3 Parts Complete Part 1 of 3 (a) Find a point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone. Round the answer to at least three decimal places. The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is .
Answer:
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
Step-by-step explanation:
The point estimate is the sample proportion.
Sample proportion:
103 out of 249, so:
[tex]p = \frac{103}{249} = 0.4137[/tex]
The point estimate for the proportion of cell phone owners aged 18-24 who have an Android phone is 0.4137.
