Answer:
[tex]n + (13 - 6) = 124[/tex]
[tex]n+13-6=124[/tex]
[tex]n+7=124[/tex]
[tex]n+7-7=124-7[/tex]
[tex]n=117[/tex]
I NEED ANSWER NOW PLSSSSS
Differential Equation
1. The given equation is probably supposed to read
y'' - 2y' - 3y = 64x exp(-x)
First consider the homogeneous equation,
y'' - 2y' - 3y = 0
which has characteristic equation
r² - 2r - 3 = (r - 3) (r + 1) = 0
with roots r = 3 and r = -1. Then the characteristic solution is
[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]
and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.
Now we use variation of parameters, which gives a particular solution of the form
[tex]y_p = u_1y_1 + u_2y_2[/tex]
where
[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]
[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]
and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is
[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]
Then we find
[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]
[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]
so it follows that the particular solution is
[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]
and so the general solution is
[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]
2. I'll again assume there's typo in the equation, and that it should read
y''' - 6y'' + 11y' - 6y = 2x exp(-x)
Again, we consider the homogeneous equation,
y''' - 6y'' + 11y' - 6y = 0
and observe that the characteristic polynomial,
r³ - 6r² + 11r - 6
has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields
r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)
and from this we see the characteristic solution is
[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]
For the particular solution, I'll use undetermined coefficients. We look for a solution of the form
[tex]y_p = (ax+b)e^{-x}[/tex]
whose first three derivatives are
[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]
[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]
[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]
Substituting these into the equation gives
[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]
[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]
[tex]-24ax+26a-24b = 2x[/tex]
It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is
[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]
and the general solution is
[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]
Prepare an accounting equation for the following business transaction
1. Purchased supplies on account, 4,000
2. Purchased furniture and fixtures for cash, 3,000
3. Paid account in no. 1.
4. Paid advance advertisement for promoting the business 1,000
5. Paid the note 2,000
Answer:
you draw a T. form and then you can start to in debit and credit
(3/4x-1) - (1/3x+4) what is the difference
Answer:
[tex]\huge\boxed{\dfrac{5}{12}x-5}[/tex]
Step-by-step explanation:
[tex]\left(\dfrac{3}{4}x-1\right)-\left(\dfrac{1}{3}x+4\right)=\dfrac{3}{4}x-1-\dfrac{1}{3}x-4=\left(\dfrac{3}{4}x-\dfrac{1}{3}x\right)+(-1-4)\\\\=\left(\dfrac{3\cdot3}{4\cdot3}x-\dfrac{1\cdot4}{3\cdot4}x\right)+(-5)=\left(\dfrac{9}{12}x-\dfrac{4}{12}x\right)-5=\dfrac{9-4}{12}x-5\\\\=\dfrac{5}{12}x-5[/tex]
In the final exams, 40% of the students failed chemistry, 25% failed physics, and 19% failed both chemistry and physics. What is the probability that a randomly selected student failed physics given that he passed chemistry?
I have answered the question in the image below, but I would like to know if it is correct. If it is not, please include an explanation of why, as well as the step by step to get the correct answer
Answer:
10%
Step-by-step explanation:
If 40% failed chemistry then 60% passed chemistry.
If 19% failed both chemistry and physics, and 25% failed physics, then 6% passed chemistry and failed physics.
If we let p' represent failing physics and c represent passing chemistry, then ...
P(p'|c) = P(p'c)/P(c)
P(p'|c) = 6%/60% = 0.10 = 10%
If the randomly chosen student passed chemistry, the probability is 10% that he failed physics.
__
Your answer is correct.
To solve this problem, we can use conditional probability.
Let's assume that there were 100 students in the final exam.
According to the problem, 40% of the students failed chemistry, which means that 60% of the students passed chemistry.
We can see that 25% of the students failed physics, and 19% of the students failed both chemistry and physics.To find the probability that a randomly selected student failed physics given that he passed chemistry, we need to use Bayes' theorem:
[tex]\sf P(Failed\: Physics | Passed\: Chemistry) = \dfrac{P(Failed\: Physics\: and\: Passed\: Chemistry)}{ P(Passed\: Chemistry)}[/tex]
We already know that P(Failed Physics and Passed Chemistry) = 6 students (from the Venn diagram), and P(Passed Chemistry) = 60 students (since 60% of the students passed chemistry).
Therefore,
[tex]\sf P(Failed\: Physics | Passed\: Chemistry) = \dfrac{6}{60} = 0.1\: or\: 10\%[/tex]
So the probability that a randomly selected student failed physics given that he passed chemistry is 10%.
Last year, Christine opened an investment account with $5600. At the end of the year, the amount in the account had decreased by 26.5%. How much is this
decrease in dollars? How much money was in her account at the end of last year?
Decrease in amount:
$
Year-end amount:
Answer:
Decrease amount: $1484 Year-end amount: $4116
Step-by-step explanation:
26.5% of 5600 is 1484. We then subtract 1484 from 5600 because that is how the percentage of decrease, which gives us 4116 dollars. This means her year-end account is 4116 dollars, and the decrease amount is 1484 dollars. Hope this helps!
It’s for pre college
Answer:
Not a function
Step-by-step explanation:
The cost of 1 m ribbon is ₹ 75. Find the cost of 7/5 metres of ribbon
Given that
The cost of 1 m ribbon = Rs.75
The cost of 7/5 m ribbon
→ (7/5)×75
→ (7×75)/5
→7×15
→₹ 105
The cost of 7/5 m ribbon is ₹105.
A bus company uses a grid to locate bus stops. The bus station is at (3, 4). The point (7, 6) represents the first bus stop. The location of each stop after that is determined using the same relationships as those between the coordinates of the bus station and the first bus stop. A coordinate plane is titled Which point represents the fourth bus stop? A. (11, 8) B. (13, 12) C. (15, 10) D. (19, 12)
Answer:
D. (19,12)
Step-by-step explanation:
For each bus stop, the X coordinate increases 4, and the Y coordinate increases 2.
Name x y Point
bus station: 3 4 (3,4)
1st bus stop: 7 6 (7,6)
2nd bus stop: 11 8 (11,8)
3rd bus stop: 15 10 (15,10)
4th bus top: 19 12 (19,12)
Answer:
Step-by-step explanation:
19,12
1. (5 points) Suppose over the past 6 years, you have earn annual raises.
6
Three times your raise was 4%, twice you received only a 2% raise and one
you received a 10% raise. If your current salary is $85,000, what was your
salary before all of those raises?
9514 1404 393
Answer:
$66,027.66
Step-by-step explanation:
The multiplier for the salary with each raise is (1 + raise). That means the original salary is multiplied by ...
(1.04^3)×(1.02^2)×(1.10) = 1.28733935616 = k
Your original salary (O) satisfies ...
O×k = $85,000
O = $85,000/k ≈ $66,027.66 . . . original salary
Ophira’s insurance company has notified her that her premiums will increase due to a poor insurance score and a recent claim she filed. The recent claim has increased her premiums by 41%, and her poor insurance score will cost her an additional $25 per month. Ophira currently pays $815 per year for insurance. How much will she pay next year?
$1149.15
$1672.15
$1449.00
$1449.15
Answer:
$1449.15
Step-by-step explanation:
currently paying 815
to pay next year: 41% increase + 25 extra per month
⇒ 141%·815 + 12·25
= 1149.15 + 300
= 1449.15
a chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second Brian contains 15% vinegar. The chef wants to make 390 mL of a dressing that is 8% vinegar. How much of each brand should she use?
Answer:
273 mL of 5%117 mL of 15%Step-by-step explanation:
Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...
0.15q + 0.05(390 -q) = 0.08(390)
0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify
q = 117 . . . . . . . . . . . . . . . . . . multiply by 10
390-q = 273
The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).
__
Additional comment
You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.
amy is building a house. the basement floor is at -15 feet, The roof of the house is above the ground 25 feet. Write an inequality to compare the heights.
Answer:
25/15
Step-by-step explanation:
Can someone please explain this to me please?
Will give brainly if you actually answer the question
Answer:
Step-by-step explanation:
24)
3x - 10 > 2
3x - 10 + 10 > 2 + 10
3x > 12
3x/3 > 12/3
x > 4
5x - 15 < -5
5x - 15 + 15 < -5 + 15
5x < 10
5x/5 < 10/5
x < 2
B) x > 4 or x < 2
25) 1.5/60 = 12/x
x = 12(60) / 1.5
x = 480
B) 480 miles
This distance from Old Faithful to Mammoth Hot Springs is actually about 52 miles by road, so there must have been MASSIVE number of road closures to get this result...or else their scale is incorrect. 1.5 inch to 6.0 miles would be a much more accurate scale making the distance 48 miles.
solve pls brainliest
Answer:
1/3
Step-by-step explanation:
Determine the more basic function that has been shifted, reflected, stretched, or compressed.
[tex]v(x) = -2\sqrt{x-1} + 3\\\\f(x) =[/tex]
Answer:
Shifted, reflected, and stretched
Step-by-step explanation:
Horizontal Shift: Right 1 Unit
Vertical Shift: Up 3 Units
Reflection about the x-axis: Reflected
Vertical Stretch: Stretched
In the expression -3×+4y-2 what are the variables
Answer:
x and y are the variables
Fighting for my life rn
Answer:
I think the other side on top is 129 degrees
Step-by-step explanation:
Im not 100 percent sure sorry if im wrong!!!
An 18 foot long ramp is placed at a loading dock that is 5 feet above ground. How far is the bottom of the ramp from the dock?
Answer:
sqrt299
Step-by-step explanation:
Because the loading dock and the ground are perpendicular we know that they are at a 90° angle. Therefore we can use the equation :
a=5
b= ?
c=18
(Then we can move all of the numbers together but what you do to one side you must do to the other)
Therefore,
(Now to make b a single variable we must square root both sides)
Therefore,
Now with all of these as numbers, we can plug this into a calculator *For all of those who have teachers who need EVERY Step see below I continue
Where and
(approximately)
Distributive property to simplify 6(8) + 6(-2)
Answer:
36
Step-by-step explanation:
You would multiply 6x8+6x(-2), and that would equal 48+(-12) which is basically 48-12 = 36.
Which of the following best describes a ratio?
Often time we want to relate one amount or quantity with another, from the given options the one that best describes a ratio is option
A. A comparison of two numbers
A ratio indicates how many times one number contains another. E.g, if there are five balls and nine lemons in a bowl of fruit, then the ratio of balls to lemons is five to nine. Similarly, the ratio of lemons to oranges is 5∶8
Learn more on ratios:
https://brainly.com/question/2328454
How many pints are equivalent to 2 1/4 gallons.
Answer:
21.6171
Step-by-step explanation:
Have a great day!
f(x) = 9x ^ 2 - 3 then what is f(3) ? Work must be shown for this problem or no credit will be earned.
Answer:
f ( 3 ) = 81
Step-by-step explanation:
→ Substitute in x = 3
9 × 3² - 3
→ Simplify
9 × 9 - 3
→ Simplify again
78
Write the ratio as a ratio of whole numbers using fractional notation.
39 days to 15 days
[tex] \frac{39 \: \: days}{15 \: \: days} \\ = \frac{39}{15} \\ dividing \: \: \: both \: \: \: numerator \: \: \: and \: denominator \: \: \: by \: \: \: 3 \\ = \frac{13}{5} \\ = 13 : 5[/tex]
Answer:13:5
Hope it helps.
Do comment if you have any query.
A recipe for 24 cookies requires112 cups of sugar. If Ben wants to make 36 cookies, how much sugar does he need?
Answer:
168 cups of sugar
Step-by-step explanation:
36 cookies require you to use what the recipes calls for plus one half.
112 divided by two is 56
112 + 56 = 168 cups
I hope that this helps!
For this case we have the following data:
24 cookies require 1 1/2 cups of sugar. To know the amount of sugar that is required to make 36 cookies, we make a rule of three:
24 -----------> 1 1/2
36 -----------> x
Where x represents the amount of sugar required to make 36 cookies.
Thus, cups of sugar are required to make 36 cookies.
How long is a distance of 8 km if measured on a map with a scale of 1:50,000?
Answer: 400,00 km
Step-by-step explanation: 1:50,000 = 8:x
8 * 50,000 = 400,000
So, 8km on the map is 400,000 km in real life.
Would appreciate brainly <3
At Sidney's Hats, 84% of the 50 hats are baseball caps. How many baseball caps are there?
Answer:
thats what i said
Step-by-step explanation:
Solve each inequality. Graph and check the solution.
e
1.
<3
2
0 1 2 3 4 5 6 7 8 9 10 11
Answer:
xxxx
Step-by-step explanation:
True or false? The point (−5, 0) lies on the y-axis.
\well the answrnist that brcause if u think it guys up
Wawra has a collection of 9 books. He compared his collection with shemal and found that shemal has 3 books fewer than he does. Write an equation showing this, using b as the number of books shemal has.
Answer:
9-3=b
Step-by-step explanation:
9-3=b
Answer:
B=6
Step-by-step explanation:
Let "b" be the number of books Shemel has.
Let "a" be the number of books Wawra has.
Eqution:
A-3=B ("3" is given in question)
9-3=B (Substituting with variables given)
B=9-3
B=6
Hence, Shemel has "6" books.
Hope it helps !