The particular solution to the differential equation with the initial condition y(0) = 1 is:
[tex]y = 1 + cos(t) + 1 - e^{(cos(t))[/tex]
To solve the given differential equation:
dy/dt + sin(t) = 1
We can rewrite it in the standard form of a first-order linear homogeneous differential equation:
dy/dt = 1 - sin(t)
The integrating factor for this equation is [tex]e^{(\int(-sin(t))dt)} = e^{(-cos(t)).[/tex]
Now, multiply both sides of the equation by the integrating factor:
[tex]e^{(-cos(t)) \times dy/dt} = (1 - sin(t)) \times e^{(-cos(t))[/tex]
The left-hand side can be rewritten using the chain rule:
[tex]d/dt [e^{(-cos(t))} \times y] = (1 - sin(t)) \times e^{(-cos(t))[/tex]
Integrate both sides with respect to t:
[tex]\int d/dt [e^{(-cos(t))} \times y] dt = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]
[tex]e^{(-cos(t))} \times y = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]
To evaluate the integral on the right-hand side, let u = -cos(t), du = sin(t) dt:
[tex]e^{(-cos(t))} \times y = \int (1 - sin(t)) \times e^{(-cos(t)) dt[/tex]
[tex]= \int (1 - sin(t)) \times e^u du[/tex]
[tex]= \int (e^u - sin(t) \times e^u) du[/tex]
[tex]= e^u - \int sin(t) \times e^u du[/tex]
Now, integrate the second term by parts:
[tex]\int sin(t) \times e^u du = -e^u \times cos(t) + \int e^u \times cos(t) dt[/tex]
Substituting the expression back into the equation:
[tex]e^{(-cos(t))} \times y = e^u - (-e^u \times cos(t) + \int e^u \times cos(t) dt)[/tex]
Simplifying:
[tex]e^{(-cos(t))} \times y = e^{(-cos(t))} + e^{(-cos(t))} \times cos(t) - \int e^{(-cos(t))} \times cos(t) dt[/tex]
To solve the remaining integral, let v = -cos(t), dv = sin(t) dt:
[tex]\int e^{(-cos(t))} \times cos(t) dt = \int e^v \times (-dv)[/tex]
[tex]= -\int e^v dv[/tex]
[tex]= -e^v + C[/tex]
[tex]= -e^{(-cos(t))} + C[/tex]
Substituting back into the equation:
[tex]e^{(-cos(t))} \times y = e^{(-cos(t))} + e^{(-cos(t))} \times cos(t) - (-e^{(-cos(t))} + C)[/tex]
Divide both sides by [tex]e^{(-cos(t))[/tex]:
[tex]y = 1 + cos(t) + 1 + C \times e^{(cos(t))[/tex]
Using the initial condition y(0) = 1, we can substitute the values into the equation:
[tex]1 = 1 + cos(0) + 1 + C \times e^{(cos(0))[/tex]
[tex]1 = 1 + 1 + C \times e^1[/tex]
[tex]C \times e = -1[/tex]
Therefore, the particular solution to the differential equation with the initial condition y(0) = 1 is:
[tex]y = 1 + cos(t) + 1 - e^{(cos(t))[/tex]
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Complete question =
Solve the following differential equation for values of t between 0 and 4, with the initial condition of y= 1 when t = 0,
dy/dt + sin(t) = 1
A 30, Y-connected alternator is rated at 1,600KVA, 13.5KV. The armature effective AC resistance per phase is 1.50. The percentage regulation for a load of 1,280kW at unity power factor is 3.5%. Determine: (a) synchronous reactance of the alternator (b) %VR at full-load 0.8pf leading (c) What is the effect on %VR value if taken at half-load lagging pf? Justify and explain briefly your answer on one(1) sentence.
(a) The synchronous reactance of the alternator is 0.001953125 Ω.
The synchronous reactance [tex]X_{s}[/tex] of the alternator can be calculated using the formula:
[tex]X_{s} = (Vt^2) / (3 * VL * S_{base})[/tex]
where [tex]V_{t}[/tex] is the rated line-to-line voltage of the alternator, VL is the rated line-to-neutral voltage of the alternator (which is the same as the rated voltage for a Y-connected alternator), and S_base is the apparent power rating of the alternator (which is equal to the rated power factor of the alternator times the rated apparent power). Substituting the given values, we get:
[tex]X_{s} = (13.5^2) / (3 * 13.5 * 1600) = 0.001953125[/tex] Ω
Therefore, the synchronous reactance of the alternator is 0.001953125 Ω.
(b) The percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.
The percentage voltage regulation (%VR) at full-load 0.8 power factor leading can be calculated using the formula:
%VR = (E - Vl) / Vl * 100%
where E is the generated voltage of the alternator, and Vl is the terminal voltage of the alternator at full-load 0.8 power factor leading. We can assume that the armature resistance and inductance are negligible compared to Xs for this calculation. Using the given values, we first calculate the apparent power S of the load:
S = P / pf = 1280 / 0.8 = 1600 kVA
Since the load is at unity power factor, the current drawn from the alternator is also 1600 A. Therefore, the voltage drop across Xs is:
Vx = Xs * I = 0.001953125 * 1600 = 3.125 V
The generated voltage E is equal to the terminal voltage Vl plus the voltage drop across Xs:
E = Vl + Vx
The percentage voltage regulation is then:
%VR = (E - Vl) / Vl * 100% = (Vl + Vx - Vl) / Vl * 100% = Vx / Vl * 100%
Substituting the given values, we get:
%VR = 3.125 / 13.5 * 100% = 23.15%
Therefore, the percentage voltage regulation at full-load 0.8 power factor leading is 23.15%.
(c) If the %VR value is taken at half-load lagging power factor, it will be higher than the %VR value at full-load 0.8 power factor leading. This is because the load impedance at half-load lagging power factor has a lower magnitude than the load impedance at full-load 0.8 power factor leading, which means that the voltage drop across [tex]X_{s}[/tex] will be a larger fraction of the terminal voltage, resulting in a larger %VR value.
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a whole number that is a factor of two or more numbers is called a
Answer: Common factor
common factor. a whole number that is a factor of two or more nonzero whole numbers
Step-by-step explanation:
[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]
[tex] \: \: \: \red{ \boxed{ \boxed{ \huge{ \tt{ \: common \: factor \: }}}}}[/tex]
a whole number that is a factor of two or more numbers is called a common factor.Write the equation of the circle ?
Center (-1,0)
Radius:4
Answer:
(x+1)^2 + y ^2 = 16
Step-by-step explanation:
center: (-1,0)
radius=4
(x-h)^2 + (y-k)^2 = r^2
(h,k) = center
plug in the center
(x+1)^2 + (y+0) ^2 = r^2
r^2 = (4)^2
r^2=16
(x+1)^2 + y^2 = 16
Complete the two-way frequency table below, which shows the relationship between adults' gender and whether these adults buy a truck or a car for their first new vehicle. From a sample of 94 adults, the following data are collected:
Truck Car Total
Female 9 36
Male 18 31
Total 94
What is the probability (rounded to the nearest whole percent) that an adult will buy a car, given that he is a male? Are the events being male and buying a car independent? (1 point)
63%; they are dependent
46%; they are dependent
63%; they are independent
33%; they are independent
I will come back to this question when it has been further clarified.
(Honestly I just really need to delete this answer since I misread the question but it doesn't give me an option to delete it).
Factor the expression completely. 12X+18
Answer:
6(2x+3)
Step-by-step explanation:
There's really no way to explain this. Take the number that all of the numbers in the equation can be divisible by and then single it out and then yeah.
Hope this helped! :)
Which expression is equivalent to -6(-2\3 +2x)
-4-12x
-4+2x
4-12x
4+12x
Answer:
4 - 12x
Step-by-step explanation:
Use the distributive property.
-6(-2/3 +2x) =
= -6 × -2/3 + (-6) × 2x
= 4 - 12x
help please :) A, B , C , or D?
Answer:
the answer is 120 degree
Answer:
(A) 30 degree
Step-by-step explanation:
Just subtract 180 with 120 = 60
then add 60 and 90 = 150
after that 180 - 50 = 30
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Have a great day, be safe and healthy
Thank u
XD
no The sum of two angles in a triangle is 150 degrees. What is the supplement of the third angle of the 2 of 4 triangle? (a) 150 (b) 10 (c) 30 (d) 85
The measure of the third angle, C, is 30 degrees. So, the correct answer is (c) 30.
Let's assume the three angles of the triangle are A, B, and C, where A, B, and C are measured in degrees.
We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:
A + B + C = 180
The obtain of two angles is 150 degrees, we can set up another equation:
A + B = 150
To obtain the measure of the third angle, which we'll call C, we can subtract the sum of the other two angles from 180:
C = 180 - (A + B)
Substituting the value of the sum of two angles (150 degrees), we have:
C = 180 - 150
C = 30
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Which expression is equivalent to (-3)x+(3)(-12)?
Answer:
Step-by-step explanation:
(-3)x + (3)(-12)
= -3x -36
or -3(x + 12)
Answer:
Step-by-step explanation:
(-3)x + 3(-12) = (-3) (x + 12)
(-3) is both the two terms. So we can take (-3) as common
HELPPPPPPPPP
What is the value of x in the figure at the right?
Answer:
Answers is D
Step-by-step explanation:
2x = 60° because they are vertically opposite angles.
x=60÷2=30°
2. Write a ratio expressing the slope of the line through each pair of points.
(-6, 1) and (-2, 0)
Answer:
Step-by-step explanation:
m = [tex]\frac{-1}{4}[/tex]
An element with a mass of 840 grams decays by 22.9% per minute. To the nearest minute, how long will it be until there are 70 grams of the element remaining?
Answer:10
Step-by-step explanation:believe me bro
To the nearest minute, it will be 10 minutes until there are 70 grams of the element remaining.
How to find the time it took for an element to decay to a certain mass?The time the element took to decay can be found by using the following formula:
[tex]F=P(1-r)^{t}[/tex]
Where:
F is the remaining mass.P is the original mass of the element.r is the rate at which the element is decaying.t is the time it took for the element to decay.We can find the answer by substituting the values.
[tex]F=P(1-r)^{t}\\\Rightarrow 70=840(1-0.229)^{t}\\\Rightarrow \frac{70}{840} =(1-0.229)^{t}\\0.0833=(1-0.229)^{t}\\t=9.56\\\approx10 \text{ minutes}[/tex]
Therefore, we have found that the element will take around 10 minutes to have 70 grams remaining.
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A glass is formed by rotating the shaded region shown above about the y axis. The curve that forms the inside of the glass is the graph of y = x^4/2. Length units in the figure are cm.
(a) What is the volume of the glass? (That is, what is the volume of the solid formed when the shaded region is rotated about the y axis?)
To find the volume of the glass formed by rotating the shaded region about the y-axis, we can use the method of cylindrical shells.
The volume of a solid of revolution using cylindrical shells is given by the integral:
V = ∫[a,b] 2πx * f(x) * dx
In this case, the function representing the curve that forms the inside of the glass is y = x^4/2. We need to find the limits of integration, a and b, which correspond to the x-values where the shaded region begins and ends.
From the graph, it appears that the shaded region begins at x = -1 and ends at x = 1. So, the limits of integration are -1 to 1.
Now, we can calculate the volume of the glass using the integral formula:
V = ∫[-1,1] 2πx * [tex](x^4/2) * dx[/tex]
V = π * ∫[-1,1] [tex]x^5 dx[/tex]
Using the power rule of integration, we integrate x^5:
V = π * [x^6/6] from -1 to 1
V = π * [[tex](1^6/6) - (-1^6/6)][/tex]
V = π * [(1/6) - (1/6)]
V = π * 0
Therefore, the volume of the glass is 0 cubic units.
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Find the value of x and y.
Answer:
Step-by-step explanation:
Please help me guys, do not give me the wrong answer please explain it to me please, please.
Answer:
Where is ur question??
plss put ur question I will give correct answer
Select the correct answer from each drop-down menu.
Consider the equation below.
x^3 - 3x^2 - 4 = 1/x-1 +5
The solutions to the equation are approximately x =
0.91 and x= *blank*
Answer:
The solution is x = + 0.77 , -0.77
Step-by-step explanation:
The equation is
[tex]x^3 - 3x^2 - 4 = \frac{1}{x} -1 +5\\x^4 -3x^3 -4x = 1-4x\\x^4 - 3x^3 = 1\\x^3 (x-3) = 1\\\\x^4 -3x^3 -1 = 0\\x^4 -3x^3 -1[/tex]
The solutions to the equation is
x = + 0.77 , -0.77
Answer:
0.91 and 3.69
Step-by-step explanation:
School: Your future depends on me
Me: Nahhhhh, I'll spend my time on Brianly making s.tupid questions
Answer:
lol same facts though
Step-by-step explanation:
Answer:
Your future doesn't really depend on school to be honest, but school is one of the options to a great future. Even college and etc dropouts become successful.
Given a set of linear equalities in several variables, we know that we can find a satisfying assignment in polynomial time. For example, given the equalities 211X1 + 212X2+...+ almxm = 221X1 + a22x2+...+ a2mdm = C2 an1X1 + An2x2+...+ AnmIm = Cn we know that we can solve this (i.e. find a set of xis so that all the equalities are satisfied) in polynomial time in n and m. ?. Suppose we now have a set of linear inequalities 211X1 + 212X2+...+ alm&m < 221X1 + A2222+...+ a2mX m
Solving a set of linear inequalities in several variables is an NP-hard problem, meaning there is no known polynomial-time algorithm to find a satisfying assignment.
Unlike linear equalities, solving a set of linear inequalities in several variables is an NP-hard problem. This means that there is no known polynomial-time algorithm to find a satisfying assignment for all instances of such problems. The complexity arises from the fact that there are infinitely many potential solutions, making it challenging to determine whether a feasible assignment exists or not. To find a satisfying assignment for linear inequalities, algorithms typically use heuristics or approximation techniques that do not guarantee optimality or completeness. Various methods, such as linear programming or constraint satisfaction algorithms, can be employed, but they may have exponential time complexity in the worst case. Therefore, solving a set of linear inequalities generally requires more computational resources and time compared to solving linear equalities.
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Draw the pipeline diagram (on the next page) for the following programs. Please note whether it
is a multi cycle CPU or a single cycle CPU
Program 1
Given a Single Cycle CPU where each stage is fixed at 200 ps (a 1000ps clock cycle), draw the pipeline diagram for the program below data
num: .word 12 .text
la $s0, num
lw $t0, 0($s0)
addi $t1, $t0, 3
Program 2
Given a Multi Cycle CPU where each stage is fixed at 200 ps (a 1000ps clock cycle), draw thepipeline diagram for the program below data
num: .word 12
.text
la $s0, num
lw $t0, 0($s0)
addi $t1, $t0, 3
1. What is the total length of time to run Program 1?
2. What is the total length of time to run Program 2?
3. What hazards, if any, exist in Program 1?
4. What hazards, if any, exist in Program 2?
The steps to draw a pipeline diagram for a given program are:
Understand the CPU architecture Identify the instructions in the programAssign cycle numbers Draw the pipeline stagesRepresent the pipeline stages Represent the instructions Handle hazards (if applicable)Review and finalizeWhat is the process?Understand the CPU architecture: This involves knowing pipeline stages, their durations, and relevant instructions/hazards. Step 2: Identify program instructions. Each instruction goes through pipeline stages.
Assign cycle numbers sequentially to each instruction. Visualize pipeline progress over time. Draw pipeline stages. Draw a horizontal line divided into cycles to represent time. Each cycle = 1 clock cycle duration. Place cycle numbers below the line.
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Is rolling a 5 on a traditional number cube
1. Impossible
2. Unlikely
3. Likely
4. Certain
Answer:
3. Likely
Step-by-step explanation:
⚠️⚠️⚠️⚠️⚠️help⚠️⚠️⚠️⚠️⚠️
Answer:
u have it right it increases by 1:75 per time
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
it is A because it is increasing by 1.75 each week
Home Internet Access According to a study, 76% of adults ages 18-29 years had broadband Internet access at home in 2011. A researcher wanted to estimate the proportion of undergraduate college students (18-23 years) with access, so she randomly sampled 180 undergraduates and found that 157 had access. Estimate the true proportion with 99% confidence. Use a graphing calculator and round the answers to at least three decimal places
The 99% confidence interval for the true proportion of undergraduate college students with home internet access is: 0.872 ± 0.057 or (0.815, 0.929).
To estimate the true proportion of undergraduate college students (18-23 years) with home internet access, we can use a confidence interval.
The point estimate for the proportion is 157/180 = 0.872. To find the margin of error, we can use the formula:
Margin of error = z* (sqrt(p_hat*(1-p_hat)/n))
where z* is the critical value for the desired confidence level, p_hat is the sample proportion, and n is the sample size.
For a 99% confidence level, the critical value is 2.576. Plugging in the values, we get:
Margin of error = 2.576 * (sqrt(0.872*(1-0.872)/180)) = 0.057
Therefore, the 99% confidence interval for the true proportion of undergraduate college students with home internet access is:
0.872 ± 0.057 or (0.815, 0.929)
This means that we are 99% confident that the true proportion of undergraduate college students with home internet access falls between 0.815 and 0.929.
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12 pumpkins cost 24.60 how much will it cost for 8 pumpkins also
I can run 5 laps in 1 1/4 hours how many laps could I run in a day
Answer:
the second one is 20 i think
Step-by-step explanation:
which properties are being used to solve the question
Answer:
Both commutative and associative
please help its for a grade!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
2x+4y=56; 5x+2y=64adult: $10; child: $7budget is not high enoughStep-by-step explanation:
See the attached.
a rational expression is undefined whenever its denominator is zero.T/F
True. A rational expression is undefined whenever its denominator is zero. This is because division by zero is not defined.
In mathematics, a rational expression is defined as the quotient of two polynomials, where the denominator represents the divisor. When the denominator of a rational expression becomes zero, it results in division by zero, which is undefined. Division by zero is not a valid operation in mathematics, and it leads to an undefined value. Therefore, to determine if a rational expression is undefined, we need to check if its denominator evaluates to zero. If the denominator is zero, the rational expression is undefined. Also there is division by zero, or related concepts in mathematics.
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last one
Mosquitoes are just dirty used needles that can fly
Jericho has m paintings and n drawings. He sold his paintings for $x each and drawings for $y each. His earnings for one day are
represented by the expression given below.
x(m) + y(m- 12)
Which statement best describes the term (m - 12)?
A. It is the number of paintings sold, which was 12 more than the number of drawings sold.
B. It is the number of drawings sold, which was 12 more than the number of paintings sold.
C. It is the number of paintings sold, which was 12 less than the number of drawings sold.
D. It is the number of drawings sold, which was 12 less than the number of paintings sold.
Answer:
b
Step-by-step explanation:
One customer purchases 8 bags of cat food and 2 bags of dog food. The total weight of the purchase is 44 pounds. Another customer purchases 5 bags of cat food and 2 bags of dog food. The total weight of the purchase is 35 pounds.
A. You write the following system of linear equations to represent this
situation. Is your answer correct?
8x + 2y = 44
5x + 2y = 35
B. Your answer for the next step is 13 79, x = which is incorrect. Explain
the error.
Answer:
answer is x=3 and y=10
Step-by-step explanation:
Forgot to isolate y and x and simplify
Show me the work to 4x-4<8 and 9x+5>23. The answer is already shown. (Geometry )
Answer:
transpose -4 to left
and 5 to left
subtract and and after transpose you will have a sign change
then you can divide
12/4,18/9
so,
x<2,x>3