1a. Solve the differential equations
y" + 5y' + 6y = 0, y(0) = 1 and y'(0) = 2
Note that each equation has right hand side zero. So, you don’t have to use the Laplace transform. You just use the characteristic equaiton.
Answers
y'' + 5y' + 6y = 0
has characteristic equation
r² + 5r + 6 = (r + 2) (r + 3) = 0
with roots at r = -2 and r = -3, hence the differential equation's characteristic solution is
[tex]y(t) = C_1 e^{-2t} + C_2 e^{-3t}[/tex]
Given that y(0) = 1 and y'(0) = 2, we have
[tex]y(t) = C_1 e^{-2t} + C_2 e^{-3t} \implies 1 = C_1 + C_2[/tex]
[tex]y'(t) = -2C_1 e^{-2t} - 3C_2 e^{-3t} \implies 2 = -2C_1 - 3C_2[/tex]
and solving the resulting system of equations yields C₁ = 5 and C₂ = -4.
So the particular solution to the ODE is
[tex]\boxed{y(t) = 5 e^{-2t} - 4 e^{-3t}}[/tex]
Related Questions
I need help please! I’ll give brainliest, thank you!
Answers
b) y intercept: -2 x intercept: -2 2
c) y= -2
d) x= -2 x= 2
e) None
i WILLLLLLL GIVE BRAINLIEST
Answers
Answer:
B
Step-by-step explanation:
All angles are the same, all sides are of same length.
What are the pros and cons of using disposable plastic and paper products for dine-in fast food restaurants over reusable plates, cups, and silverware? atleast 2 pros and 2 cons
Answers
Answer:
Disposable items decompose after some time thus making them eco-freindly(safe for the environment) they also don't make a giant mess that takes thousands of years to decompose and even if they do it doesn't take that long for them to decompose on the other hand they are more expensive to mass produce than reusable items and they also are more expensive to buy than non Disposable but reusable items.Non disposable but reusable Items when thrown away can take decades or even in some cases tens of thousands of years to decompose and can pose a threat to the environment they can be eaten by fish and other animals causing them in some cases to die they can cause a giant mess on the other hand they are cheap,and quick to make and you don't have to pay as much for dishes.Kohl's buys jeans from the manufacturer for $20 and then sells them in their store for $35.
What is the markup?
What is the % markup?
Answers
Answer:$15, 75%
$35-$20=$15
$15/$20*100=
Step-by-step explanation:
Point J is the midpoint of line segment KI. Find the length of JI.
Answers
Answer:
6
Step-by-step explanation:
The midpoint of a line segment divides it into two congruent parts:
KJ ≅ JI
JI = KJ = 6
The length of JI is 6 units.
Write a description of -5a + 3 > 1 inequality
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The sum of -5a and 3 is greater than 1
simplifying the expression 5/6÷3/6×3/5 gives
Answers
Answer:
Hope this helped you
Step-by-step explanation:
5/6 ÷ 3/6 = 5/6 × 6/3 = 5/3
5/3 × 3/5 = 1
5/6÷3/6x3/5
0.83÷0.50x0.60
0.83÷0.30
ANSWER: 2.767
I tried to make it as easy as possible!
pls mark brainliest!
Kara has 10 books on a shelf and decides to move 3 of them to an empty shelf.
In how many different ways can the empty shelf be filled?
Answers
Answer: 120
Step-by-step explanation: 10 [tex]10\int\limits^a_b {x} \, dx 3[/tex]
Abby earns a monthly salary of $3462 plus 2% commission. Last month, she sold
$5,250 worth of products. What was her gross pay?
Answers
Find 2% of what she sold by multiplying the amount she sold by 2%:
5250 x 2% = 5250 x 0.02 = $105
Now add that to her monthly salary:
3462 + 105 = $3,567
WILL GIVE BRAINLIEST AND MAX POINTS
Answers
Answer:
113.04
Step-by-step explanation:
The area of the square is 144 which means the length of each side of the square is 12. When the length on one side is 12 the radius of the circle will be half of the whole length. In this case, it means the radius is going to be 6. When we find the radius, we can use the formula r^2pie to find the area for the circle.
6 * 6 * 3.14
= 113.04
Answer:
Area = 113.04 in²
Step-by-step explanation:
Given:
Area of the square = 144 in²Area of a square
[tex]\sf A=s^2\quad \textsf{(where s is the side length)}[/tex]
Substitute the given area of the square into the formula and solve for s:
[tex]\begin{aligned}\sf A & = \sf s^2\\\implies \sf 144 & = \sf s^2\\\sf \sqrt{144} & = \sf \sqrt{s^2}\\\sf 12 & = \sf s\\\implies \sf s & = \sf 12\:\:inches\end{aligned}[/tex]
From inspection of the given diagram, the side length of the square is equal to the diameter of the circle. Therefore, the diameter is 12 inches.
Radius of a circle
[tex]\sf r = \dfrac{1}{2}\:d\quad \textsf{(where d is the diameter)}[/tex]
Substitute the found diameter into the formula and solve for r:
[tex]\begin{aligned}\sf r & = \sf \dfrac{1}{2}\:d\\\implies \sf r & = \sf \dfrac{1}{2}(12)\\\sf r & = \sf 6\:\:inches\end{aligned}[/tex]
Area of a circle
[tex]\sf A= \pi r^2 \quad \textsf{(where r is the radius)}[/tex]
Substitute the found radius into the formula and solve for A:
[tex]\begin{aligned}\sf A & = \sf \pi r^2\\\implies \sf A & = \sf 3.14 \cdot 6^2\\& = \sf 3.14 \cdot 36\\& = \sf 113.04\:\: in^2\end{aligned}[/tex]
Therefore, the approximate area of the paper circle is 113.04 in².
Ava, Zoe and Logan went to the market to buy some presents for a friend's birthday. The three of them
together spent $720. If Logan spent twice as much Zoe did and Zoe spent $40 less than Ava did, how
much did each of them spend?
Answers
a + z + l = 720
l = 2z = 2a - 80
4z + 40 = 720
4z = 680
z = 170
l = 340
a = 210
A right triangle has a hypotenuse with length 6 ft and a leg of length 3.4 ft.
What is the length of the other leg of the right triangle?
Enter the answer, rounded to the nearest hundredth.
Answers
Answer:
The answer is 4.94, rounded.
Step-by-step explanation:
The pythagorean theorem is : a^2+b^2=c^2
Inserting our numbers:
3.4^2+b^2=6^2
We can find 'B' by finding the other two numbers and subtracting 'A', from 'C'.
3.4*3.4= 11.56
6*6= 36
36-11.56= 24.44
Then, find the root of the difference
√24.44
4.94368283772...
Then round, and you have your answer!
4.94
help me out please omg bro
Answers
Answer:
$ 3.75
Step-by-step explanation:
divide 10.50 by 2.8 which gives us 3.75
Answer:
B $ 3.75
Step-by-step explanation:
hope it helps you
!!!!!!!!!!!!!!!!!!!!
Answers
hi can u guys help me thank u oh and i will give a brainly if correct :)
Answers
Answer:
226,080 cm³
Step-by-step explanation:
volume of cylinder : πr²h
Here given:
radius : 15 cmheight : 320 cmusing volume formula:
π(15)²(320)
72000π
72000(3.14) [ take π as 3.14 ]
226,080 cm³
Answer:
=> 226,080 cm³Step-by-step explanation:
Given:
Radius = 30/2 = 15cm
Height = 320cm
=> The volume of cylinder = πr²h
=> π×15×15×320
=> 3.14×225×320
=> 226,080cm³
which is like a radical to ^3 to the square root of 54 after simplifying
Answers
Answer:
The radical that is equal to ∛54 is 3∛2.
Step-by-step explanation:
Given
∛54
We need to find the radical that is similar to ∛54, we need to break down the radicand 54, into smaller numbers, therefore, take the LCM of the number,
54 = 2 x 3 x 3 x 3
As we are taking the cube root, therefore, we need numbers that are repeating thrice.
Thus, the radical can be written as,
[tex]\sqrt[3]{54} =\sqrt[3]{2x 3x 3x 3} \\\\\sqrt[3]{54} =3\sqrt[3]{2}[/tex]
Hence, the radical that is equal to ∛54 is 3∛2
Answer:
[tex]3\sqrt[3]{2}[/tex]
Step-by-step explanation:
Original expression:
[tex]\implies \sqrt[3]{54}[/tex]
Factorize 54 using prime factorization:
[tex]\implies \sqrt[3]{2 \cdot 3^3}[/tex]
Apply radical rule: [tex]\sqrt[n]{ab} =\sqrt[n]{a} \cdot \sqrt[n]{b}[/tex]
[tex]\implies \sqrt[3]{2} \cdot \sqrt[3]{3^3}[/tex]
Apply radical rule: [tex]\sqrt[n]{a^n} =a[/tex]
[tex]\implies \sqrt[3]{2} \cdot 3[/tex]
[tex]\implies 3\sqrt[3]{2}[/tex]
Susie is going to watch a programme which begins at 20:30 and lasts for one hour and forty five minutes what time will it finish?
Answers
Answer:
22:15
Step-by-step explanation:
1 hour = 60 mins
20:30 + 45 mins
= 21:15
Plus another hour
21:15+ 1 hour= 22:15
show the graph of f(x)=5^X
Answers
Answer:
i put it below
Step-by-step explanation:
but if you want to do it without a graphing calculator all you have to do is substitute random points then draw them on a graph
Can someone help me understand
Answers
Answer:
Its solving equations with variable on both sides
Step-by-step explanation:
Example: 8a = 3a+25
You have to make a variable on the both side
So.....
8a-3a = 3a+25-3a
And then solve it. So the last thing you will have is
5a = 25
If you want to the simplest form...divide 25 with 5
a = 25/5
a = 5
Hope this help you.
Find the area of the following shapes.
Area = __ mm^2
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Answer:
Formulae used:
Area of a rectangle = width × length
Area of a triangle = 1/2 × base × height
Area of blue shape:
Area of rectangle + area of triangle
= (9 × 15) + (1/2 × (15 - 9) × 15)
= 135 + (1/2 × 6 × 15)
= 135 + 45
= 180 mm²
Area of yellow shape:
area of rectangle AHPB + area of rectangle GFQP + area of rectangle EDCQ
= (4 × 12) + (6 × (12 - 9)) + (4 × 12)
= 48 + (6 × 3) + 48
= 48 + 18 + 48
= 114 m²
I need help finding MN in this geometry test and I can't figure it out on my own.
Answers
Answer:
I think it is 7.3. Cos35=6/MN.
Step-by-step explanation:
Cosine of 35 degrees= adjacent side /hypotenuse.
A number has three digits: 1, 4, and 1.
To the nearest hundred, the number rounds to 400. What is the number?
Answers
Answer:
411
Step-by-step explanation:
Because it has a 4 , 1 , and a 1
meaning the first number can't be 1 so it is automatically a 4.
and then the only 2 numbers left is 2 one's so you have to put them in their also automatically and 4 is asking 1 to round up can it.
411 can't round up,it would round down because 1 is 4 and below so it can't go up and goes down.
so 4 1 1 can't go up the number would have to be 450 to go to 500 but because it is 411 it goes down to 400 because it is rounded to 400.
Hope this helps have a awesome day:)
HiSET) On a road map, the distance between two cities is 5.1 inches. If 1.8 inches on the map represents 40 miles of actual distance, which of the following expressions gives the best estimate of the actual distance in miles between these cities?
a) 5/2 x 40 b) 5/2 ÷ 40 c) 6/40 x 2 d) 5/1 x 40 e) 5/40 x 2
Answers
Answer:
5.1*40/1.8
your closest answer is 1 (5/2*40)
Hope it helps!!!!!brainliest pls!!!!!!!!Answer:
5/2*40
Step-by-step explanation:
that's my answer, so i hope this helps
?/1
Evaluate g(-4) if
g(x)=x^2 −2x+5
Please answer with g(-4) =
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Answer:
g(-4) = 29
Step-by-step explanation:
g(-4) = (-4)^2 -2(-4)+5
= 16 + 8 +5
= 29
rewrite the expression 26×26⁸.
Answers
Answer:
26 x 26 x 26 x 26 x 26 x 26 x 26 x 26 x 26
Step-by-step explanation:
26 to the eighth power is like multiplying 26 times itself eight times. So since it started off as 26 times 26 eight times, you would times 26 by itself 9 times.
select the correct word form for 87,055
Answers
Answer: Eighty-seven thousand-fifty five
Step-by-step explanation:
Answer:
eighty seven thousand fifty five=87,055
Which is the best estimate for the volume of a coffee mug?
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Answer:
Step-by-step explanation:
The best estimate for the volume of a coffee mug would be the volume of a cylinder. The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]
The volume can be thought of as the area of a circle, being scaled by the height. The area of the circular base of the mug, multiplied by the height of the mug.
Help help math math math
Answers
Answer:
Yes
Step-by-step explanation:
hope it helps you...
Answer:
Yes!
Step-by-step explanation:
Paula weeded 40% of her garden in 8 minutes.How many minutes will it take her to weed all of her garden?
Answers
40% = 8 minutes
(100/40 = 2.5, 8 x 2.5 = 20)
100% = 20 minutes
Answer:
20 minutes
Step-by-step explanation:
Given:
40% of Paula's garden is weeded and it was done in 8 minutes.
Solution:
40% divided by 8 is 5% [ Division ]
100% divided by 5% = 20 minutes
1. A sum of money is divided between Laura and Joan in the ratio 2:3. Laura’s share is $8. Calculate Joan’s share?
Answers
Step-by-step explanation:
L : J
2:3
so Lara has 2 shares
2 shares = 8
what is one share
type in comments
and then I will explain the rest
The amount of the Joan's share will be $12.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
A sum of money is divided between Laura and Joan in the ratio 2:3.
Laura’s share is $8.
Let J be the amount of Joan's share and L be the amount of Laura's share.
Then the amount of Joan's share will be
L / J = 2 / 3
8 / J = 2 / 3
By the cross multiplication, then the equation will be
2J = 8 x 3
2J = 24
J = 24 / 2
J = $12
The amount of the Joan's share will be $12.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ5