Answer:
[tex]y(x) = 0[/tex]
Step-by-step explanation:
Let P(1) = 0, the differential equation becomes:
y" + 3y' + 2y = 0
Also let y' = my and y'' = m²y
Substitute
m²y+3my+2y = 0
(m²+3m+2)y = 0
The auxiliary equation is expressed as:
m²+3m+2 = 0
Factorize
m²+2m+m+2 = 0
m(m+2)+1(m+2) = 0
(m+1)(m+2) = 0
m+1 = 0 and m+2 = 0
m₁ = -1 and m₂ = -2
Since the value of m is real and distinct, the solution to the differential equation will be expressed as:
[tex]y = C_1e^{m_1x}+C_2e^{m_2x}\\[/tex]
[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\[/tex]
Given the initial condition y(0) = 0
[tex]y(0) = C_1e^{-0}+C_2e^{-2(0)}\\0 = C_1+C_2\\C_1+C_2 = 0 ................. 1[/tex]
If y'(0) = 0
[tex]y'(x) = -C_1e^{-x}-2C_2e^{-2x}\\y'(0) = -C_1e^{-0}-2C_2e^{-2(0)}\\0 = -C_1-2C_2\\C_1-2C_2 = 0...................... 2[/tex]
Solve eqn 1 and 2 simultaneously
From 1:
C₁ = -C₂ .......... 3
Substitute equation 3 into 2:
-C₂-2C₂ = 0
-3C₂ = 0
C₂ = 0
Substitute the constant into the differential equation.
[tex]y(x) = C_1e^{-x}+C_2e^{-2x}\\\\y(x) = 0[/tex]
At the marget 8 apples cost 4 dollars how much does 9 apples cost
Answer:
8 /4 = 2
answer: each apple cost 2$
Answer:
$4.50.
Step-by-step explanation: Since the market is selling 8 apples for $4, we can determine that one apple is 50 cents. Knowing that information, we can apply that same rule to 9 apples, resulting in a total of $4.50. Hope this answered your question.
Roy bought running shoes for $44.98. If the sales tax is 7%, how much did he pay in total?
Answer:
$48.13
Step-by-step explanation:
before $44.98
sale tax 7.00% or 3.15
after-tax price $48.13
Uh help i don`t get this (ez question) :D
Answer:
Dividend divided by Divisor = Quotient
5 divided by 8 = 0.625
Step-by-step explanation:
What is the equation of the following graph
Answer:
Undefined
Step-by-step explanation:
Budget Rental Car charges an initial fee of $20 plus an additional $30 per day to rent a car. Enterprise Rental Car charges an initial fee of $36 plus $28 per day. For what number of days is the total cost charged by the companies the same?
I need an answer ASAP!! :)
Answer:
8 days
Step-by-step explanation:
A 3-yard roll of butcher paper costs $8.55. What is the price per foot?
Answer:
$2.85
Step-by-step explanation:
8.55/3
Answer:
$2.85 per foot
Step-by-step explanation:
all u gotta do is 8.55/3
you earn $25 for washing 5 cars how much do you earn for washing 4 cars
being a rectangle is a necessary condition for being a square
Answer:
false
Step-by-step explanation:
all rectangles are squares not all squares are rectangles
Find the value of f(-5).
y=f(x)
Answer:
???
Step-by-step explanation:
???
Help and brainliest? :(
please i need help asap. if u can help that’d be great
Answer:
The answer is B. (2x-3)
Why is "3 meals a day" a unit rate? it compares 1 meal to 1 day. lt compares 1 meal to 3 days. It compares 3 meals to 1 day. It compares 3 meals to 3 days.
Answer:
Compares 3 meals to 1 day
Step-by-step explanation:
The world has made it a basis that most people eat 3 meals a day.
One meal for Breakfast:
This Time Ranges from 6 to 11 am
One meal for Lunch:
This Time Ranges from 11 to 3 pm
One meal for Dinner:
This Time Ranges from 3-10 pm
Hope I could help! If you need anymore assistance, feel free to ask me!
what is 86,503 written in expanded form
Answer:
80,000+6,000+500+3
Step-by-step explanation:
Decode it
Answer:
eighty- six thousand five-hundred and three
Step-by-step explanation:
what is the graph of the equation Y= 66x - 1200
Answer:the answer is b :)
Step-by-step explanation:
The perimeter of a kite can be found using the formula P = 2S + 2L. Which equation expresses S in terms of P and L?
Answer:
Step-by-step explanation:
P = 2S + 2L
2S + 2L = P
2S = P - 2L
S = [tex]\frac{P-2L}{2}[/tex]
Answer:
0.5P - L
Step-by-step explanation:
P = 2S + 2L
P - 2L = 2S +2L - 2L
P - 2L = 2S
0.5P - L = S
Explain how to write an equation from a graph in slope intercept form .
Step-by-step explanation:
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form (0, b). The y- coordinate is the value of b in the equation.
pls give brainest i only have 2
The slope intercept form is given by y = mx + c
What is the Slope Intercept Form of a Line?The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.
Given here: Slope intercept form
We know that, the equation of a line in point slope form, where (x1, y1) is the point and slope m is:
(y – y₁) = m(x – x₁)
Here, (x, y₁) = (0, c)
Substituting these values, we get;
y – c = m(x – 0)
y – c = mx
y = mx + c
Therefore, the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c
Hence, The slope intercept form is given by y = mx + c
Learn more about slope intercept form here:
https://brainly.com/question/29146348
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what is 200 times 1238
Step-by-step explanation:
the answer is 247,600
hope this helps
Answer: the answer is 247,600
Step-by-step explanation:
The attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot over a weekend. The ratios for the three days were equivalent.
Friday there was 4
Saturday there was ???
4(-8x + 5) – (-33x – 26) =
Answer:
1x + 46 or x + 46
Step-by-step explanation:
4(-8x + 5) – (-33x – 26)
-32x + 20 + 33x + 26
1x + 46
or x + 46
Evaluate: -8/9 + 4/9 - 2/9
A. -14/9
B. -2/3
C. 10/9
D. -1/3
Answer:
-2/3
Step-by-step explanation:
Add the first two then subtract
The answer to the equation is B, [tex]-\frac{2}{3}[/tex]
First, you must add the the fractions. You add the numerator because all three fractions have like denominators.
[tex]-\frac{8}{9} +\frac{4}{9} -\frac{2}{9}=\frac{6}{9}[/tex]
Then, you must simplify [tex]-\frac{6}{9}[/tex]
[tex]-\frac{6}{9} =-\frac{2}{3}[/tex]
The answer to the equation is [tex]-\frac{2}{3}[/tex]
expand and simplify (x +2)(x+ 1)
Answer:
x²+3x+3
Step-by-step explanation:
(x+2)(x+1)
x²+x+2x+3
=x²+3x+3
Answer:
x² + 3x + 2
Step-by-step explanation:
Given
(x + 2)(x + 1)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 1) + 2(x + 1) ← distribute both parenthesis
= x² + x + 2x + 2 ← collect like terms
= x² + 3x + 2
Figure B is a scaled copy of Figure A.
Answer:
1/3
Step-by-step explanation:
On left side its 6:2 so 6/2 is 3
the scale factor is 1/3 because figure is a reduction
hope it helps ;)
Answer:
1/3
Step-by-step explanation:
The side that's highest is 9 units, the the image its 3. 3/9= 1/3
Use the distributive property to simplify the expression, then combine like terms -12 - 5p +2(6p+p)
Answer:
-12 + 9p
Step-by-step explanation:
Original Equation:
-12 - 5p + 2(6p + p)
Distributive property.
2 x 6p = 12p
2 x p = 2p
Equation:
-12 - 5p + 12p + 2p
Subtract 5p from 12p
-12 + 7p + 2p
Add.
-12 + 9p
Hope this helped :)
Please consider Brainliest :)
A trucking company wants to evaluate whether a decrease in the weight of their trucks helps to increase gas mileage. The company randomly selects 100 of their truck drivers, driving trucks that are identical in every way other than weight, to monitor gas mileage over a 1-year period. Results showed an association between truck weight and gas mileage. Which is a possible confounding variable for the provided scenario?
Answer:
D- the aggressiveness of the driver's driving style
Step-by-step explanation:
Jessica prepared 36 kilograms of dough after working 6 hours. How much dough did Jessica prepare if she worked for 8 hours? Assume the relationship is directly proportional.
Answer:
48
Step-by-step explanation:
because 36 divided by 6 is 6 and that is how much dough she produces in an hour so if you added two more 6s to 6 to make it 8 meaning you are adding 12 because that is how much dough she makes in an hour
Michael has $1,058.60 in his checking account. He is going to spend $499.66 on a new television, and he will spend the rest on speakers that cost $42.00 each. Which of the following inequalities would determine the maximum number of speakers, x, Michael can buy without spending more money than he has in his account?
help
Answer:
he can buy 13 speakers.
Step-by-step explanation:
first you do 1,058.60- 499.66. Then you take the answer and and divided it by 42.00 and got 13.
find the perimeter of the polygon if
What are the numbers so I can do the problem.
Kathrine uses 7/10 of a gallon of red paint to paint 3/5 of her wall. How many gallons of red paint will she use to paint her whole wall?
A.21/50
B.7/15
C.1 1/6
D.1 3/10
Answer:
It is 1 3/10
Step-by-step explanation:
I NEED HELP NOWWWWW AHHHHHHHHH IM SO DUMB AND THANK YOU FOR HELPING ME
Answer:
9
Step-by-step explanation:
someone help me on my homework before i lose my sanity pls its my most recent question im done <3
DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA DA
Answer:
da de da da da de do re mi fa so la mi AAAAAAAAAAA
Step-by-step explanation:
I can speak the language of the gods xD