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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2 is what percent of 40?
2 is 5% of 40
Hope it is useful
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
\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°
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
I need help plz and thank you
Answer:
10
30
18
Step-by-step explanation:
y = 3x + 6
y = (x + 4)2 – 10
What’s the solution set for this
The answer is,
y = -18, x = -8
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
−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
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
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
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
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
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
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.
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%
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:
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
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.
Simplify the following
√2+√3/3√2-2√3
Answer:
a
Step-by-step explanation:
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?
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.
y= 2/3 x +7
X= -4
please help me asap!
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
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
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
The length of a swimming pool would be about
А
3 feet
12 inches
12 yards
D
3 miles
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.