Answer:
a) 20 days
b) 50 machines
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]
Saturn the ring system around saturn has a diameter of 170000miles. find the circumference of the ring system.
Answer:
534,070.75 miles
Step-by-step explanation:
The circumference formula is [tex]d\pi[/tex] or [tex]2r\pi[/tex].
But since we're given the diameter, 170,000, all we have to do is multiply it by [tex]\pi[/tex].
[tex]170000*\pi = 534070.75 (Rounded)[/tex]
Qiang is inviting 4 friends to a party each friend wants 4 cookies each box has 10 cookies how many boxes should qiang get
10. If pointer 1 is spun and then pointer 2 is spun, determine the probability of landing on a color other than red on both spins. The probability is (Type an integer or a simplified fraction.)
Answer:
Answer below
Step-by-step explanation:
1/8 is correct
in pic
_________________________________________
(Hope this helps can I pls have brainlist (crown)☺️)
i literally can't figure out the answer to this, help would be very much appreciated.
(PICTURE INCLUDED BELOW)
Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?
A. Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
B. Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis
C. Counterclockwise rotation about the origin by 270 degrees followed by reflection about the x-axis
D. Counterclockwise rotation about the origin by 270 degrees followed by reflection about the y-axis
Answer:
B
Step-by-step explanation:
The figure is in quadrant 1. When you do a 180 degree rotation it will out the image diagonally across into quadrant 3. Next reflect across the y-axis to get it in quadrant 4.
A 180 rotation will always end up diagonally across regardless if it is counterclockwise or clockwise.
Answer:
A. Counterclockwise rotation around the origin by 180 degrees followed by reflection around the x-axis.
Step-by-step explanation:
180° would be turning it counterclockwise 2 times. Thus putting it on the points of figure P'Q'R'S'.
Reflecting it across the x-axis would be putting it in the same position as P'Q'R'S'.
This being said, either way you did it, as long as you did it one of the two ways it would become a copy of PQRS. The answer is A.
Hope this helped you. Let me know if I got it correct!
- Abigail (:
Your school ID is a 5-digit number. The 9 is in the thousand place, the 0 is in the ones place, an 8 is in the thousands place, a 4 is in the tens place and a 2 is in the hundreds place. What is your school ID number?
Answer:
89240
Step-by-step explanation:
_ 9 _ _ _ is in the thousands
_ 9 _ _ 0 is in the ones
going to assume you meant 8 is in ten thousands
8 9 _ _ 0 is in ten thousands
8 9 _ 4 0 is in tens
8 9 2 4 0 is in hundreds
School number is 89240
Answer: 98,240
What we are doing here is changing from expanded form into standard form.
To do that, you add all the place values to get the total number. So, our place values are:
10,000 - Ten Thousands Place
1,000 - Thousands Place
100 - Hundreds Place
10 - Tens Place
Now, we will need to look at the problem.
It says, The 9 is in the ten thousand place, the 0 is in the ones place, an 8 is in the thousands place, a 4 is in the tens place and a 2 is in the hundreds place.
According to the question, the 9 will be in the Tens Thousands Place, so our first number will be, 90,000.
The 8 will be in the Thousands place, so our second number will be 8,000.
The 2 will be in the Hundreds place, so our third number will be 200.
The 4 will be in the Tens place, so our fourth number will be 40.
Since the one's place is 0, we don't need to worry about that number.
Putting the answer in an equation, it will be like this,
90,000 + 8,000 + 200 + 40Now we can add.
Adding these numbers up will equal to, 98,240.
Therefore, the answer is 98,240.
Tell whether the pairing is a function.
2.
Input
3
6
9
12
Output
1
2
N
1
Is it a function?
Answer:
I believe that it is function
Simplify as far as possible without using a calculator.
5(9/12−1/4)+0.5 pls answer correctly
Answer:
3
Step-by-step explanation:
5(9/12 -1/4) +0.5
= 5(9/12 -3/12) +1/2 . . . . . . express the fractions using a common denominator
= 5(6/12) +1/2 . . . . . . . add the fractions
= 5(1/2) +1/2 . . . . . . reduce the result
= (5 +1)(1/2) . . . . factor out 1/2 (easier than adding mixed numbers)
= 6/2 = 3
_____
A calculator can be a useful tool for evaluating numerical expressions.
If z=15, what would the expression z2 – 2z + 15 be equal to?
A 205
B 210
C 215
D
220
what is the value of the digit 4 in 0.342
Answer:
0.04 = four hundredths
Step-by-step explanation:
To find the value of a digit in a number, set all the other digits to zero.
The value of the 4 is ...
0.040
The 4 is in the hundredths place, so its value is four hundredths.
I need answers ASAP
Answer:
Simplifying
6r + r + -5r = 0
Combine like terms: 6r + r = 7r
7r + -5r = 0
Combine like terms: 7r + -5r = 2r
2r = 0
Solving
2r = 0
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Divide each side by '2'.
r = 0
Simplifying
r = 0
7r-5r < this is the answer
6r+r=7r
a ladder 7.5m long rests against a wall . the botton of ladder is 2.1m from the wall . calculate how far the ladder reaches up the wall.
PLEASE SOLVE THIS QUESTION!!
Answer:
h = √(7.5² - 2.1²) = 7.2 m
Step-by-step explanation:
Pythagorean theorem
I RELLY NEED HELP RIGHT NOW
Answer: 28
Step-by-step explanation:
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea level, as a function of time is
given by h(t) = – 4.9t2 + 235t + 269.
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
Find out the value for brainiest
Answer:
126 degrees
Step-by-step explanation:
first we should find the measurements of these angles
so (I know these are the names of lines but there's no name for these angles, that's why I'm addressing them with the name of each one's nearest line name)
C= 90 degree
B= 65 degree
A= 79 (coz 180- 101= 79)
therefore D= ?
the total interior angle of a quadrilateral is 360
so 360- (90+ 65+ 79)
360- 234 = 126 degrees
does the graph represent a function?
Answer:
No
Step-by-step explanation:
yes it is
for it to not be a function it would need to have a curve or somthing that make it go somehwere else
Is 40 is 50% of 80 true or false
With step by step evidence
Answer:
please mark brainliest
it is true
Step-by-step explanation:
if you multiplie 80 by 0.50 you will get 40,
ANSWER PLEASE!!! I WILL GIVE BRAINLIEST
NO BOTS OR WEBSITE LINKS
Answer:
San Francisco
Step-by-step explanation:
The cost per mile in San Francisco is 0.45 per mile, whereas it is 0.40 in New York
Help please!! I will mark brainilist and give a lot of points.
This is Pythagorean theorem.
Formula: a^2+b^2=c^2
When I say ^2 I mean to the power of 2.
The question is asking me to solve for a.
Then give me b and c which is b = 17 1/3 and c = 16.
How do I solve for a when b is greater than c? Won’t that give me a negative a? You can’t have a negative a right?
Unless I’m wrong.
Please help my solve this!!!!! :D
Answer:
a = 23.588
Step-by-step explanation:
a^2 = 17 1/3^2 + 16^2
a^2 = 300.4 + 256
a^2 = 556.4
a = 23.588 (I rounded to thousandths but you can round to whatever)
Hello there,
I just looked into the question and you are absolutely right whatever you inferred.I think the question might be wrong.The value of c should be greater than b.I guess it will like this:[tex]b = 16 \: \: \: c = 17 \frac{1}{3} [/tex]The values should be like this.I am solving the equation by this:[tex] {a}^{2} = {c}^{2} - {b}^{2} \\ = > {a}^{2} = {(17 \frac{1}{3}) }^{2} - {(16)}^{2} \\ = > {a}^{2} = {( \frac{52}{3} )}^{2} - {(16)}^{2} \\ = > {a}^{2} = ( \frac{52}{3} - 16)( \frac{52}{3} + 16) \\ = > {a}^{2} = ( \frac{52 - 48}{3} )( \frac{52 + 48}{3} ) \\ = > {a}^{2} = \frac{4}{3} \times \frac{100}{3} \\ = > {a}^{2} = \frac{400}{9} \\ = > a = \sqrt{ \frac{400}{9} } \\ = > a = \frac{20}{3} \\ = > a = 6 \frac{2}{3} [/tex]So, the value of a is [tex]a = 6 \frac{2}{3} [/tex]Hope you could get an idea from it.
Doubt clarification - use comment section.
If an item that originally cost $12 is increased to $16, what is the percentage of increase in the item?
Answer:
33.33%
Step-by-step explanation:
WILL GIVE BRAINLIEST
(5x-7)
(10x-32)
14
the perimeter of the pictured triangle is _____ in.
By converse of isosceles triangle theorem:
5x - 5 = 10x - 32
add 32 and -5x at both sides
27 = 5x (divide 5 both sides)
x = 5.4
5(5.4) - 5 = 27 - 5 = 22 inches
22 + 22 + 14 = 58 inches
Learning Task 2: Solve each proportion
1) 5/12 = 35/ n
2) n/ 52 = 180/ 120
3) 18/n = 21/28
4) n/4 = 24/6
5) 10/16 = n/56
1. [tex] \frac{5}{12} = \frac{35}{n} \\ 5n = 35 \times 12 \\ 5n = 420 \\ n = \frac{420}{5} \\ n = 84[/tex]
2. [tex] \frac{n}{52} = \frac{180}{120} \\ 120n = 180 \times 52 \\ 120n = 9360 \\ n = \frac{9360}{120} \\ n = 78[/tex]
Sierra is getting a loan to purchase a car, but she has a few options for loan terms. She is comparing the cost of each loan to determine which loan will cost the least in terms of interest paid. (Interest is the fee paid for the use of borrowed money, and it is expressed as a percentage of the amount borrowed multiplied by the amount of time the borrower takes to repay the loan.) All of the loan offers are for $10,000, and include an upfront fee of $200. They are all simple interest loans (as opposed to compound interest loans). Loan A is to be paid back over five years with an annual interest rate of 6 percent. Loan B is to be paid back over four years with an annual interest rate of 4 percent. Loan C is to be paid back over three years with an interest rate of 5 percent. How does Sierra figure out which loan will require the lowest interest payments?
Answer:
B
Step-by-step explanation:
Repost
A group of tourists are on a three-day hiking trip. They hike ⅛ of the trail on the first day. On the second day, they hike 4/7 of the remaining distance. On the third day, they hike 1/3 of the remaining distance, plus the final 8 km. How many kilometers long is the trail?
Answer:
You told me to resolve this question
solve pls brainliest
Answer:
4 cm
Step-by-step explanation:
Where 7 cm is located is parallel to the side of 11cm
11-7 is 4cm.
Hope that helps!
Solve for
x
6
(
x
−
6
)
=
5
(
x
+
1
)
Answer:
x = 41
Step-by-step explanation:
6(x−6)=5(x+1)
Step 1 - Expand the brackets:
6(x - 6) = 5(x + 1)
6x - 36 = 5x + 5
Step 2 - Add 36 to both sides of the equation:
6x - 36 + 36 = 5x + 5 + 36
6x = 5x + 41
Step 3 - Subtract 5x from both sides of the equation:
6x - 5x = 5x + 41 - 5x
x = 41
Hope this helps!
[tex]\large\underline{\sf{Solution-}}[/tex]
Given expression:
6(X - 6) = 5(X + 1)
⇛6X - 36 = 5X + 5
⇛6X - 5X = 5 + 36
⇛X = 41 Ans.
Read more:
Similar question
simplify 6/x-6+3x/x+5-1/(x-6)(x+5)....
https://brainly.com/question/9027174?referrer
hint: 180 *
1. Find the missing angle.
29
R
61
T
Answer:
∠ R = 90°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180° , that is
∠ R + ∠ S + ∠ T = 180° , substitute values
∠ R + 29° + 61° = 180°
∠ R + 90° = 180° ( subtract 90° from both sides )
∠ R = 90°
Find the slope of the line that contains the following pair of points:
(4,-5) and (-1, -3).
Step-by-step explanation:
slope is y2-y1/x2-x1
-3-4=-7
-1-4=-5
now that you have -7/-5, or negative seven fifths, simplify.
you get -0.4, or -2/5 as your slope
Hope this helps!!
Can someone help me please
Answer:
sorry i can answer that the asy
Answer:
Q1 - 10080
(sorry couldn't do q2 haha)
step by step;
