The particular solution of the differential equation is:
f(x) = -sin(x) + 3x + 3
To find the particular solution of the differential equation f''(x) = sin(x) that satisfies the initial conditions f'(0) = 2 and f(0) = 3, follow these steps:
1. Integrate f''(x) = sin(x) once with respect to x:
f'(x) = ∫sin(x) dx = -cos(x) + C₁
2. Use the initial condition f'(0) = 2 to find C₁:
2 = -cos(0) + C₁
C₁ = 3
So, f'(x) = -cos(x) + 3
3. Integrate f'(x) again with respect to x:
f(x) = ∫(-cos(x) + 3) dx = -sin(x) + 3x + C₂
4. Use the initial condition f(0) = 3 to find C₂:
3 = -sin(0) + 3(0) + C₂
C₂ = 3
So, the particular solution of the differential equation is:
f(x) = -sin(x) + 3x + 3
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Please help it is due today
i think answer is 8in2
please talk me my answer is correct or not
Answer:
8 inches squared
Step-by-step explanation:
4 3/4 of a cube + 4 1/4 of a cube + 4 whole cubes
4 + 4 = 8
How can I know 20 digits of Π… ??
And not know the 10 digits of your phone number?
The numbers 1 to 5 are placed in a hat. What is the probability that you will pick the number 1 pm
4, and without replacing the number in the hat, select the number 3? Write your answer as a
simplified fraction. *
What is the y-intercept?
Bryan has $15 to spend on taxi fare. The ride costs $5 plus $2.50 per mile. How many mile can Bryan go without spending all $15
Answer:
3 miles.
Step-by-step explanation:
He has to pay 5 just to ride, and 2.50 per mile.
2.50(x)+5=15
2.50(4)+5=15
10+5=15
So he can riide 3 miles without spending all his money.
CAN SOMEONE HELP ME PLEASE!!!
Answer:
i think this is right
Step-by-step explanation:
4
Shandra had $200 in her bank account on Monday. On Tuesday, she had a
debit of $50 and a credit of $25. How much money does Shandra have in
her bank account on Wednesday?
Answer:
175
Step-by-step explanation:
Please help ❤️❤️❤️❤️❤️❤️❤️
Answer:
-3/7
Step-by-step explanation:
find two lattice points
the ones I found are (-3, 3) and (4, 0)
use the slope formula
(0-3)/(4-(-3)) = -3/7
5
Evaluate the expression when x = 3 and y = 6
The product of 8 and a number x
Answer:
46
Step-by-step explanation:
First, we must write the mathematical form for "the product of 8 and a number x":
8
×
x
Then "6 more than this" would be:
(
8
×
x
)
+
6
So, to evaluate for
x
=
5
we substitute
5
for
x
and calculate:
(
8
×
5
)
+
6
→
40
+
6
→
46
All rational numbers are whole numbers? True or false
Target sells 3 apples $1.50 what is the cost of 20 apples
Answer:
$10
Step-by-step explanation:
1.50 divided by 3 = 0.50
0.50 x 20 = 10
- 6w = 354 w=__?
-45= -9m m__?
h/9 = 36 h=__?
18 = y/7
y=__?
f/-4 = - 13 f=__?
15 = n/-3 n=__?
Answer:
I don't really understand the question, there calculator websites you can use
Step-by-step explanation:
-20 2 -6 -18 4 -4 put them from least to greatest
The team won 18 of its 30 games. What was the team’s won-lost ratio?
Answer:
18:12 (accurate)
3:2 (simplified)
Step-by-step explanation:
The team won 18 games out of 30 total games. Find the amount of games lost by simply subtracting 18 with 30:
30 - 18 = 12
The ratio you are trying to find is won to lost, or won:lost. Plug in the corresponding numbers to the corresponding terms:
won:lost ⇒ 18:12
18:12 is the ratio.
If the teacher asks you to simplify, factor both sides. Divide 6 from both sides:
(18)/6 : (12)/6
3:2
3:2 is your simplified ratio.
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Erik used 28 centimeters of tape to wrap 7 presents. How much tape will Erik need in all if he has to wrap 12 presents? Solve using unit rates.
Answer:
Length of tape required to wrap 12 presents is 48 centimeters.
Step-by-step explanation:
Length of tape required to wrap 7 presents = 28 centimeters
Length of tape required to wrap 1 present = [tex]\frac{28}{7}=4[/tex] centimeters
Therefore,
Length of tape required to wrap 12 presents = 12 × Length of tape required to wrap 1 present
= 12 × 4
= 48 centimeters
help please I really need it
Answer:
If x is 6, y is 9
Step-by-step explanation:
In your equation, substitute 6 in for each x. This would be (6) + 3y = 4(6) + y.
This ends up being 6 + 3y = 24 + y.
After that, you can subtract y from both sides to get 6 + 2y = 24.
Then you can subtract 6 from both sides to get 2y = 18.
Finally, divide both sides by 2 to get y = 9.
josh has 1/4 gallon of orange juice he wants to share it equally between to friends and himself. how much orange juice will each person drink? a 1/12 b 1/8 c 1/3 d 3/4
Answer:
a
Step-by-step explanation:
1/4 divided by 3 = 1/(4*3) = 1/12
State whether the triangles are similiar if so write a similarly statement for brainliest
Answer:
Step-by-step explanation:
The triangles are not similar.
2x-2
Given f(x) = (2x-2) / 4 solve for f-1(3).
1) 1
2) 5
3) 7
4) 8
Answer:
Your Streak is on! Answer another question tomorrow and keep it going.
Step-by-step explanation:
Select all the expressions equivalent to:
20a + 10b
a
5(4a + 2b)
b
10(2a + b)
C С
2(10a + 5)
2(10a + 5b)
Od
Оe
5(4a - 2b)
Answer:
5(4a + 2b)
10(2a + b)
2(10a + 5b)
Step-by-step explanation:
we are trying to find equations equivalent to (20a + 10b), so distribute
5(4a + 2b) = 20a +10b YES
10(2a + b) = 20a +10b YES
2(10a +5) = 20a + 10 NO
2(10a + 5b) = 20a +10b YES
5(4a - 2b) = 20a - 10b NO
Adele rides her bike 28 miles in 3.5 hours. How far has Adele traveled on her bike if she rides for 8 hours?
Answer:
64 miles
Step-by-step explanation:
if you divide 28 by 3.5, this gives you the number of miles per hour, I got 8. Multiply that by 8 because that is the number of hours we are looking for and you get 64. That is the answer.
Type the expression that results from the following series of steps:
Start with
x
, add 3, then times by 6.
Answer:
6x+18
Step-by-step explanation:
(x+3) * 6= 6(x+3)=6x+18
Answer:
6(x+3) or 6x +18
Step-by-step explanation:
x
add 3
x+3
times by 6
6(x+3)
simplify
6x+18
Determine the equation that this graph represent
Find the simplest form
2 2
+
9.7
there's a random space in between the 2 and 2. not sure if it's meant to be 2.2 or 22 but i'll do both.
2.2 + 9.7 = 11.9
22 + 9.7 = 31.7
Which expression is equivalent to x^2 - 64?
Answer:
X= 8 and X=-8
Step-by-step explanation:
x^2-64
spilt into (x-8)(x+8)
set both equal to 0
0=x-8
x=8
0=x+8
x=-8
Bert is driving along a country road at a constant speed of 30 miles per hour. How long does it take for him to travel 50 miles?
The time of 1 hour 40 minutes Bert takes for him to travel 50 miles.
What is the distance?Distance is defined as the product of speed and time.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
Given that Bert is driving along a country road at a constant speed of 30 miles per hour
To determine the time it takes for him to travel 50 miles.
Let the time of x minutes it takes for him to travel 50 miles.
⇒ 30 miles/60 minutes = 50 miles/ x minutes
Cross multiplication apply in above equation,
⇒ 30x. x = 60x50
⇒ 3000 = 30x.
⇒ x = 100 minutes, or
⇒ 1 hour 40 minutes
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A jogger is running with an initial speed of 5 m/s. The jogger then sprints to the finish line, increasing their speed to 10 m/s over 5 seconds. What is the jogger's acceleration in m/s squared?
Answer:
Step-by-step explanation:
1 m/s square
Carris is making necklaces to sell at a local craft fair. She makes the necklaces by hand, so she uses a table to determine how many beads to make for the necklaces.
Answer: 48
Step-by-step explanation:
Each is 8x? So 8x1, 8x2 so on, then you get 48!
What is the range of the function shown on the graph above
0.009 in scientific notation
Answer:
9 x 10^-3
Step-by-step explanation: