The solution to the IVP is:
y(t) = 4e^(-t), y(0) = 2, y'(0) = 2.
To solve this IVP using Laplace transform, we first take the Laplace transform of both sides of the differential equation:
L{y' + 2y' + y} = L{0}
Using the linearity of the Laplace transform and the derivative property, we can simplify this to:
L{y'} + 2L{y} + L{y} = 0
Next, we use the Laplace transform of the derivative of y and simplify:
sY(s) - y(0) + 2sY(s) - y'(0) + Y(s) = 0
Substituting in the initial conditions y(0) = 2 and y'(0) = 2, we have:
sY(s) - 2 + 2sY(s) - 2 + Y(s) = 0
Simplifying this equation, we get:
(s + 1)Y(s) = 4
Dividing both sides by (s + 1), we get:
Y(s) = 4/(s + 1)
Now, we need to take the inverse Laplace transform to get the solution y(t):
y(t) = L^-1{4/(s + 1)}
Using the Laplace transform table, we know that L^-1{1/(s + a)} = e^(-at). Therefore,
y(t) = L^-1{4/(s + 1)} = 4e^(-t)
So the solution to the IVP is:
y(t) = 4e^(-t), y(0) = 2, y'(0) = 2.
Learn more about IVP here:
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\angle a∠aangle, a and \angle b∠bangle, b are complementary angles. \angle a∠aangle, a measures 59^\circ59
∘
59, degrees.
What is the measure of \angle b∠bangle, b?
Answer:
31°
Step-by-step explanation:
because angle a and angle b are complementary they equal 90 degrees in total
a+b=90
since angle a = 59°
59+b=90
so you use subtraction property of equality and subtract 59 from both side of the equal sign
59+b=90
-59 -59
b= 31°
ans of this question
4 (3c+4d)
Answer: 12c+16d
Step-by-step explanation: 4(3c+4d)
(4)(3c+4d)
(4)(3c)+(4)(4d)
12c+16d
Answer:
Întâi faci paranteza și după de ie faci cu 4
A nesting box for a falcon is put on top of a 96 ft pole. There are 3 ft in 1 yd.
Answer:
32 yards
Step-by-step explanation:
What is the percentage of sugar in the syrup made of 10kg of water and 5kg of sugar? Hi and have a good day :D
Answer:
33.33%
Step-by-step explanation:
the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%
Answer:
33.33%
Step-by-step explanation:
the syrup has a total of 15kg of ingredients, 5kg of it is sugar, so 15/5 which will end as 33.33%
help help help help help help ill give brainiest
Answer:
wowee,,, i hope these are right :,)
Step-by-step explanation:
5/3-x+1/3 : -3/2+2+1/2x
3/5-13/5 = 6.9+4.9
3x+0 = 3x
2x-3 = x-3+x
2x-6 = -6+2x
−4p+9=−5
Plzzzzzzz help
Answer:
p = 3.5 or p = 7/2
Step-by-step explanation:
-4p+9= -5
or, -4p = - 14
or, p = -14/-4
or, p = 7/2 = 3.5
Answer:
p = 3.5
Step-by-step explanation:
What you would do to get p is subtract 5 from both sides of the equation to leave the number and p, THEN divide both sides by the numerator of -4.
-4p + 9 = -5
- 9 -9
__________
-4p = -14
__ __
-4 -4
Thus, p = 3.5
6x+8> −16 please help
Answer:
x = 4
Step-by-step explanation:
I hope this helps sorry if its wrong
Jared made 12 3 fourhs cups of snack mix for a party his guests ate two thirds of the mix how much snack mix did his guests eat
Answer: Jared guests ate = 8 1/2 cups of the snack mix.
Step-by-step explanation:
Total snack mix made by Jared = 12 3/4 CUPS
Amount eaten by guests = 2/3 of Total snack mix
which means they ate = 2/ 3 x12 3/4
= 2/3 x 51/ 4
=17/2 = 8 1/2 cups of snack mix.
Jared guests ate 8 1/2 cups of the snack mix.
AKAJAXOSPAPXODAOAPA HELP
Answer:
He used 6 bananas at .50 which cost $3.00
12 oranges at .75 which cost $9.00 and
3 papayas at $1.25 which cost $3.75
Step-by-step explanation:
We can set up a system of equations using the information given.
b for banana, r for orange, p for papaya
b + r + p = 21. Also given r = 2b So substitute to simplify for calculating two unknowns:
b + 2b + p = 21 The number of items.
50b + 75(2b) +125p = 1575 The cost.
I multiplied everything by 100 to eliminate the decimals.
To solve by substituion, rewrite the first equation to get a value for p in terms of b
p = 21 - 3b
Substitute this value in the second equation and solve for b.
50b + 150b + 125(21–3b) = 1575
200b +2625 –375b = 1575 Subtract 2625 from both sides and combine the like terms:
–175b = 1575 –2625
–175b = –1050. Divide both sides by –175
b = 6
Substitute in the original equation to find the amount of each fruit:
b + r + p = 21
b = 6 bananas
r = 2b. 2(6) = 12 oranges. I used r so as not to mix up o with 0.
6 + 12 + p = 21
p = 21 –18
p = 3 papayas
PLEASE HELP WILL GIVE BRAINLY its down below
Answer:
A.) $383 500 000/year
B.) $826 750 000/year
Step-by-step explanation:
Just add the number of sales and divide to how many year of sales it was and you will get the answer.
Daniel used to collect baseball cards as a kid. He purchased a particular
card for $30 in 2006 and the value of the card increases by 2.5% per year.
How much is his card worth now (in 2021)? Use units and round
appropriately.
Answer:
[tex]y < 85 \div \div 9614 = 88[/tex]
Ты лоххх
Bethany uses the equation d = 4.25h to find the distance, d, she travels while walking for h number of hours. What is the constant of proportionality between d and h?
Answer:
4.25
Step-by-step explanation:
The distance Bethany travels is directly proportional to the number of hours she spends working
The formula for direct proportion is :
y = kx
Where k is a constant
in this question, the constant is given by 4.25
Petrol is poured into a barrel.
The graph shows the number of litres of petrol in the barrel.
Calculate how much petrol is being poured into the barrel each minute.
SOMEONE ANSWER THESE ASAP
MARKING BRAINLIEST
PLEASE HELPPPPP
Sorry this took a while; calculated a lot of things.
Step-by-step explanation:
A.
Combined:
2.67 times 23.76 = 63.4392
2.67 times - 21 and 5/6 = -58.295
63.4392 - 31.85 -58.295 = -26.7058
If you mean do both separate:
63.4392 - 31.85 = 31.5892
-58.295 - 31.85 = -90.145
B.
Combined:
11 and 3/4 times 23.76 = 279.18
11 and 3/4 times 21 and 5/6 = 256.541666667
279.18 + 256.541666667 + 56 and 3/8 = 592.096666667
If you mean do both separate:
279.18 + 56 and 3/8 = 335.555
256.541666667 + 56 and 3/8 = 312.916666667
Simplify the following
√2+√3/3√2-2√3
Answer:
a
Step-by-step explanation:
To get from home to his friend Clayton's house, Eric would have to walk 4 miles due north. To get from home to his friend Dale's house, Eric would have to walk 3 miles due east. What is the straight-line distance between Clayton's house and Dale's house?
PLEASE ANSWER!
Answer: 5 miles
Step-by-step explanation:
It's a triangle so if you use the pythagorean theorem your equations should look like this. Sqroot of 4^2+3^2 which equals 5. Hope this helps. :)
plzzzzzzzzzzzzz help
Answer:
[tex]5*\frac{1}{2}[/tex]
Step-by-step explanation:
We have a picture and are being asked to identify the multiplication problem that represents it.
So we have 5 triangles, all of which are color-coded in red, but only half of them are filled. When multiplying, the number that is before the * sign is the amount there is, while the number that is after the * is the amount going to multiply the amount of items there are. So looking at the picture, we can see 5 triangles, therefore :
5 *
2 * 1/5 is scratched out as an answer. As is starts with 2.
As for the second number, we acknowledge that all triangles are half in red, therefore the number is 1/2.
5 * 1/2
Scratching all other answers.
a number h is at most 15
Answer:
h inequality 15
hope it is helpful to you
2 is what percent of 40?
2 is 5% of 40
Hope it is useful
A small plane flying from Los Angeles to San Diego averaged 175 mph with a tailwind. On the return trip with headwind the average speed was only 125 mph. Write and solve a system to reflect this relationship. Find the speed of the headwind/ tailwind AND the speed of the plane on a calm day.
Answer: System of equations:
p + w = 175
p - w = 125
p is the plane's speed, w is the wind speed
The wind speed is 25 mph. The plane's speed on a calm day is 150 mph.
Step-by-step explanation:
Solve by elimination: Add the equations. w "cancels" solve for p:
p + w = 175
p - w = 125
2p = 300 divide both sides by 2
p = 150 the plane's speed
Substitute 150 for p and solve for w
150 + w = 175 Subtract 150 from both sides.
w = 25 the wind speed
if hector completed 120 questions last week and 144 this week, how much did he increase by?
Answer:
he increased by 24
Step-by-step explanation:
144-120
PLZ HELP ME I NEED HELP ASAP
Answer:
75 I hope this helped and brainliest please!
Step-by-step explanation:
The equation for surface area for a square pyramid is A=a squared + 2a times the square root of (a squared over 4) + height squared. Since everything is 5 yd, the answer is 75.
Write an expression for the perimeter of the triangle shown below:
Answer:
7.8x - 17
Step-by-step explanation:
1.8x - 7 + 1.8x - 7 + 3.4x - 3 now add like terms
(variables + variables and Coefficient + Coefficient) so the answer is
7.8x - 17
y = 3x + 6
y = (x + 4)2 – 10
What’s the solution set for this
The answer is,
y = -18, x = -8
I need help plz and thank you
Answer:
10
30
18
Step-by-step explanation:
y= 2/3 x +7
X= -4
please help me asap!
The length of a swimming pool would be about
А
3 feet
12 inches
12 yards
D
3 miles
A two digits number is 21 times the difference and 350% of the product of its digit. Find the quotient of the digit of number
Michael mowed lawns during the summer to earn extra money. He charged each customer $30 to cut the grass plus $9 for each hour of work. One customer paid Michael $93. How long did it take Michael to mow that customer's lawn?
In Exercises 13 and 14, find m_1, 22, and m23.
13.
14.
50°
3
1
3 115°
2 1
2
PLEASE HELP
Answer:
For Question 13 :∡ 1 = 130°; ∡ 2 = 50° ∡ 3 = 130°
For Question 14 :∡ 1 = 65°; ∡ 2 = 115° ∡ 3 = 65°
Step-by-step explanation:
Question 13:
There is multiple ways to solve those questions. However I will stick with the simple way.
1) We know that a straighteangle is = to 180°
2) Acording to the statment on step one we will say that ∡ 1 + the ∡ 50° = 180°
Resoectivelly
180° - 50° = ∡1
180° - 50° = 130°
∡ 1 = 130°
3) ∡ 2 + ∡ 1 = 180°
We already ∡ 1 from step 2, then
∡ 2 = 180° - 130°(∡1)
∡ 2 = 50°
4) ∡ 2 + ∡ 3 = 180°
∡ 3 = 180° - 50° (∡ 2)
∡ 3 = 130°
Question 14 1) We know that a straighteangle is = to 180°
2) Acording to the statment on step one we will say that
angle 1 + the angle 115° = 180°
Resopectivelly
180° - 115° = ∡ 1
180° - 50° = 65°
∡1 = 65°
3) ∡ 2 + ∡ 1 = 180°
We already∡ 1 from step 2, then
∡ 2 = 180° - 65°(∡1)
∡ 2 = 115°
4) ∡ 2 + ∡ 3 = 180°
∡ 3 = 180° - 115° (∡ 2)
Have fun