1. Consider a damped spring-mass system with m = 1kg, = 2
kg/s^2 and c = 3 kg/s. Find the general solution. And solve the
initial value problem if y(0) = 1 and y′(0) = 0.
Answers
The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).
The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/\(s^2\).
To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get \(r^2\) + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.
The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).
By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.
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Related Questions
I need help! Please!!!
Answers
Answer:
with what
Step-by-step explanation:
Answer:
Yes I would be truly willing to help u so what do u need help with
Step-by-step explanation:
what two numbers add up to 6 but multiply to -72?
Answers
Answer:
12 x -6 is -72 and -6 + 12 is 6 so 12 and -6 is the answer
Step-by-step explanation:
Answer:
-6 and 12.Step-by-step explanation:
Equations to check:
-6 + 12 = 6.-6 * 12 = -72.The 2 numbers that add up to 6, but multiply to -72 are - 6 and 12.
Brainliest please.
A sequence is defined by the term-to-term rule
Un+1 = U²₁ + 5
Given that u, = 1,
a) find u₁
b) find u₂
c) find u
Answers
Answer:
Step-by-step explanation:
a) To find u1, we can use the term-to-term rule given in the problem:
Un+1 = U²₁ + 5
We know that u1 = 1, so we can substitute that into the equation:
u2 = 1² + 5 = 1 + 5 = 6
b) To find u2, we can use the same term-to-term rule and substitute the value of u1 (which is 6) into the equation:
u3 = 6² + 5 = 36 + 5 = 41
c) To find un, we can use the term-to-term rule and substitute the value of un-1 into the equation.
un = un-1² + 5
It's important to note that the value of n is not given so we can't calculate the value of un.
Therefore, u1 = 6, u2 = 41, and we can't calculate un without knowing the value of n.
what is the number of the parking space 16, 06, 68
Answers
The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.
To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.
When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.
Therefore, the number formed by the digits 16, 06, and 68 is 160668.
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PLSS HELP NEED RIGHT ANwSER
Answers
Answer:
(-2,-2)
Step-by-step explanation:
Answer:
(-2, -2)
Step-by-step explanation:
The solution is the point where the two lines intersect.
From inspection of the graph, we can see that the two lines intersect at point (-2, -2)
someone help please
the options are
1. y = 2x + 4
2. y = 1/2 x + 4
3. y = -1/2x + 4
4. y = -2x + 4
Answers
Answer:
2. y = 1/2x + 4
Step-by-step explanation:
This is the only equation that moves in a positive slope the way the graph shows it, hope this helps.
to maximize its profit, a monopolist would choose which of the following outcomes? a. q = 45 and p = 45 b. q = 60 and p = 30 c. q = 30 and p = 30 d. q = 30 and p = 60
Answers
To maximize its profit, a monopolist would choose option d: q = 30 and p = 60.
To maximize profit, a monopolist would choose the outcome that corresponds to the highest profit level.
Profit is calculated as total revenue minus total cost.
Let's analyze each option:
a. q = 45 and p = 45:
In this case, the monopolist produces a quantity of 45 units and sets the price at $45.
To determine if this is the optimal choice, we need to compare the revenue and cost associated with this outcome with the other options.
b. q = 60 and p = 30:
Here, the monopolist produces a higher quantity of 60 units but sets a lower price of $30.
c. q = 30 and p = 30:
This option represents a lower quantity of 30 units and a price of $30.
d. q = 30 and p = 60:
In this scenario, the monopolist produces a lower quantity of 30 units but sets a higher price of $60.
To determine the optimal outcome, we need to consider the monopolist's cost structure.
Without information about costs, we cannot definitively identify the optimal choice.
The monopolist would consider both revenue and cost implications to maximize profit.
However, we can make some general observations:
Option a (q = 45 and p = 45) and option c (q = 30 and p = 30) result in the same price and may have similar revenue implications.
The choice between these options would depend on the cost structure and profit margins.
Option b (q = 60 and p = 30) could result in higher revenue due to the higher quantity sold, but the lower price may affect profit margins.
Option d (q = 30 and p = 60) may result in higher prices and potentially higher profit margins, but the lower quantity sold may affect revenue.
Ultimately, the monopolist would need to assess the revenue, cost, and profit implications of each option to determine the optimal outcome for maximizing profit.
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how to solve inequations
Answers
Answer:
When solving an inequality: you can add the same quantity to each side •you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.
you can add subtract multiply and divide the quantity to each side
But if you’re doing any of those with a negative quantity, the inequality symbol must be reversed
3 x -8> 29
3 x -8 < 29
In the equation 6x − 2 = −4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct?
Answers
Answer: Both Technically, Look Below
Step-by-step explanation:
This is a very interesting problem they are technically both not wrong. You can choose to subtract the 6x first if you want or add 4x. Both technically work and will end up with the same value for x. Which I will show here. Although both work adding 4x can be the easier way as there is less negatives to deal with.
Adding 4x:
6x - 2 = -4x + 2
10x - 2 = 2
10x = 4
x = 4/10
x = 2/5
Subtraction 6x:
6x - 2 = -4x + 2
-2 = -10x +2
-4 = -10x
4/10 = x
2/10 = x
Answer:
Both are correct in their order of steps. In does not matter which you subtract or add as long as you are eliminating something from each side. However, in order to keep the equation positive, the most preferred step would be to add 4x.
Find the measure of the missing angle 71 a
Answers
The measure of the missing angle in the quadrilateral is given as follows:
x = 129º.
How to obtain the missing angle?The sum of the measures of the internal angles of a polygon of n sides is given by the equation presented as follows:
S = (n - 2) x 180º.
The number of sides of a quadrilateral is given as follows:
n = 4.
Then the sum of the measures of the internal angles of the quadrilateral is of:
S = (4 - 2) x 180º
S = 360º.
From the image given at the end of the answer, the angle measures are given as follows:
71º.48º.112º.x.Then the measure of the missing angle x is obtained as follows:
71 + 48 + 112 + x = 360
x = 360 - (71 + 48 + 112)
x = 129º.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Need help with this pls
Answers
Answer:
num 1 is answer...
plz help will give brainliest
Answers
Answer:
the right is the answer :>
Step-by-step explanation:
MATH SUFACE AREA OF PYRAMIDS
WILL GIVE YOU MY LAST 10 POINTS!!!! AND BRAINLYIST!!
Answers
Step-by-step explanation:
the surface areas are always the sum of the areas of the individual sides and base area.
so, all we need to do here is calculating the areas of triangles, rectangles (actually squares) and a hexagon.
the area of a triangle is
baseline × height / 2
or with Heron's formula when we have all sides
s = (a+b+c)/2
area = sqrt(s×(s-a)×(s-b)×(s-c))
the area of a rectangle is
length × width
for a square that is then
side × side = side²
and the area of a regular hexagon can be created again as sum of multiple sub-shapes. but ultimately it is
3 × sqrt(3) × side² / 2
1.
square base area : 10×10 = 100 cm²
lateral areas :
one triangle is 10×13/2 = 65 cm²
4 triangles are then 4×65 = 260 cm²
total surface area :
100 + 260 = 360 cm²
2a.
3 lateral triangles :
3 × 8×10/2 = 120 units²
base area (Heron's, as all 3 sides are 8 units) :
s = 3×8/2 = 12
area = sqrt(12×4×4×4) = sqrt(3×4×4×4×4) = 16×sqrt(3)
total surface area :
120 + 16×sqrt(3) = 147.7128129... units²
2b.
4 lateral triangles :
4 × 8×10/2 = 160 units²
base area : 8×8 = 64 units²
total surface area :
160 + 64 = 224 units²
2c.
6 lateral triangles :
6 × 8×20/2 = 480 units²
base area :
3×sqrt(3)×8²/2 = 96×sqrt(3)
total surface area :
480 + 96×sqrt(3) = 646.2768775... units²
2d.
base area : 16² = 256 units²
4 lateral triangles. but we need to get their height first.
Pythagoras :
(16/2)² + 24² = height²
8² + 24² = height²
64 + 576 = height²
height² = 640
height = sqrt(640) = sqrt(64×10) = 8×sqrt(10)
4 triangles are
4 × 16×8×sqrt(10)/2 = 256×sqrt(10) units²
total surface area :
256 + 256×sqrt(10) = 256×(1 + sqrt(10) = 1,065.543081... units²
Angles jhi and gjh are inscribed angles. we have that m∠jhi = one-half b and m∠gjh = one-halfa by the . angle jhi is an exterior angle of triangle . because the measure of an exterior angle is equal to the sum of the measures of the remote interior angles, m∠jhi = m∠jgi m∠gjh. by the , one-halfb = m∠jgi one-halfa. using the subtraction property, m∠jgi = one-halfb – one-halfa. therefore, m∠jgi = one-half(b – a) by the distributive property.
Answers
This can be used to find the measure of angle JGI if the measures of angles JHI and GJH are known.
There does not seem to be a question here, but the given statements can be summarized as follows:
Angles JHI and GJH are inscribed angles.
m∠JHI = 1/2 b and m∠GJH = 1/2 a.
Angle JHI is an exterior angle of triangle JGI.
By the exterior angle theorem, m∠JHI = m∠JGI + m∠GJH.
Therefore, 1/2 b = m∠JGI + 1/2 a.
Using the subtraction property, m∠JGI = 1/2 b - 1/2 a.
By the distributive property, m∠JGI = 1/2 (b - a).
This can be used to find the measure of angle JGI if the measures of angles JHI and GJH are known.
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Answer:
1. inscribed angle theorem
2. GJH
3. substitution property
Rebecca is calculating her expected expenses for her week long trip to Thailand. Her plane ticket costs 22,885 baht, her lodging costs 15,307 baht, and she has set aside 29,071 baht for food and spending money. What is Rebecca’s total expense? a. 128,071 baht b. 67,263 baht c. 21,493 baht d. 9,121 baht.
Answers
Answer:
The answer is B because you add up the 3 expenses
Step-by-step explanation:
Add the three expenses
The total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht
How to calculate total expense?Total expense shows the overall expense for the thing we're expending for. We add all the expenses to get the total expense.
For this case, we're given that:
Cost of plane tickets = 22,885 bahtCost of lodging = 15,307Cost for food and other expenses = 29,071So, total expected expense is sum of all these expenses.
Total expected expense = 22885 + 15307 + 29071 = 67263 baht
Thus, the total expected expense of Rebecca for her week long trip to Thailand is given by: Option B: 67,263 baht
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find the surface area of the following cylinder. Round your answers to the nearest tenth.
Answers
Answer:
233
Step-by-step explanation:
2=33=2=
Greg’s parents bought a $350.00 savings bond when he was born. When he turns 3030, the bond’s value will have increased 125%. How much will the savings bond be worth on Greg’s thirtieth birthday?
Answers
Using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
What is the percentage?In mathematics, a quantity or ratio known as A% stands for a percentage of 100.
There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.
To represent percentages, the symbol "%" is typically written after the number.
So, we know that:
The bond is $350.
The return is 125% when Greg turns 30.
Then, the amount after she turns 30 will be as follows:
350/100 * 125
437.5
Bonds value: 437.5 + 350 = $787.5
Therefore, using percentages we know that the savings bond will be worth $787.5 on Greg's 30th birthday.
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please help
marking brainlist
the answer is not C
Answers
Answer:
it is most definitely d because that's where they intercept
Answer:
(-3, 2)
Step-by-step explanation:
Point (-3, 2) represents the solution to the pair of equations. Because, this is the point where both the lines are intersecting each other.
Woof chow dog food company believes that it has a market share of 25 percent. it surveys n100 dog owners and ask whether or not woof chow is their regular brand of dog food, and 23 people say yes. based upon this information, what is the critical value if the hypothesis is to be tested at the 0.05 level of significance?
Answers
On solving the provided question, we can say that Considering that the test statistic inside the lower tail the rejection zone, the null hypothesis should be rejected.
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
\(H0:p=0.25\) (null hypothesis)
\(H0:p \neq 0.25\) (alternative hypothesis)
Do not reject the null because the test statistic\((-1.2) is >\) \(the critical value (-1.7531)\)
Considering that the test statistic is inside the lower tail of the rejection zone, the null hypothesis should be rejected.
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Juan worked 2.5 hours and earned $37.00. Lisa was paid $42.00 for 3 hours of work. Which of the following statements is true?
Juan made a lower rate of pay because he made less money.
Lisa made a better rate of pay because she made more money.
Lisa said she made a better rate of pay because her rate was $14 an hour.
Juan said he made a better rate of pay because he was paid $14.80 an hour.
Answers
Answer:
Juan said he made a better rate of pay because he was paid $14.80 an hour.
Step-by-step explanation:
Juan made more because he makes $14.80 an hour, whereas Lisa makes only $14 an hour.
Enjoy your day! :D
HELPPP ME PLEASEEEEEE
Answers
Answer:
I would think the answer is 0
Step-by-step explanation:
this is a sort of division and any number divided by itself is always 0
What is the solution of x + 1/5 (x - 1) = 1?
Answers
Answer:
1
Step-by-step explanation:
x-1+ 1 /5*( x-1)=0
(x-1)*6/5=0
x=1
My mom was at the store with a 15% off coupon. She spent $25.00 with 7% sales tax. How much is the total?
Answers
Answer:
The answer is $22.74
Step-by-step explanation:
Mr Gleasons math class lasts for 40 minutes. Math class starts at 9;55 AM. At what time does math class end?
Answers
Answer:
Math class ends at 10:35 AM.
Step-by-step explanation:
To find the answer, you need to add 40 minutes to the timestamp if 9:55 AM. There are 60 minutes in an hour, so you add five minutes to get to 10:00. 40-5=35. Now add 35 minutes to 10:00. The answer is 10:35 AM.
Answer:
The answer is 10:35 AM.
Step-by-step explanation:
Given;Mr Gleasons math class lasts for 40 minutes.Math class starts at 9:55 AM.To Find;At what time does math class end.Here, we know that in one hour there's 60 minutes.
1 hour = 60 minutes.
So, add 40 minutes in 9:55
9:55 + 40 minutes = 10:35 AM
Thus, Mr Gleasons math class will end at 10:35 AM.
Hamid has gained weight he is now 88k which is 10% more than what he use to be what was his original weight
Answers
Answer:
79.20 and
The difference is 8.80
Answer:
79.2
Step-by-step explanation:
88*0.10 = 8.8
88-8.8 = 79.2
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481.5712 Find the digits in the tens place, in the tenths place, and in the ten thousandths place for the following number.
Answers
Answer:
Tens place: 8
Tenths place: 5
Ten thousandths place: 2
Answers:
tenths place = 5
ten-thousandths place = 2
======================================================
Explanation:
Refer to the place value chart shown below.
The 5 is in the tenths place which is one spot to the right of the decimal point. The ten-thousandths place is four spots to the right of the decimal point.
Please answer correctly! I will Mark you as Brainliest!
Answers
Answer:
Try 8 if it's wrong sorry
Step-by-step explanation:
Evaluate the expression under the given conditions, cos 2theta; sin theta = - 8/17, theta in Quadrant III Write the product as a sum. sin 5x cos 6x
Answers
Evaluating the expression under the conditions: cos 2theta; sin theta = - 8/17, theta in Quadrant III -
sin 5x cos 6x can be expressed as sin 11x / 2.
To evaluate the expression cos 2θ, we need to find the value of θ first.
We have,
sin θ = -8/17 and θ is in Quadrant III.
Since sin θ = -8/17, we know that the opposite side of the triangle is -8 and the hypotenuse is 17. Using the Pythagorean theorem, we can find the adjacent side:
adjacent^2 = hypotenuse^2 - opposite^2
adjacent^2 = 17^2 - (-8)^2
adjacent^2 = 289 - 64
adjacent^2 = 225
adjacent = 15
Now, we can use the definition of cosine to evaluate cos θ:
cos θ = adjacent / hypotenuse
cos θ = 15 / 17
Since cos 2θ is a double-angle identity, we can use the formula:
cos 2θ = cos^2 θ - sin^2 θ
Plugging in the values we found, we get:
cos 2θ = (15/17)^2 - (-8/17)^2
cos 2θ = 225/289 - 64/289
cos 2θ = (225 - 64) / 289
cos 2θ = 161/289
Therefore, cos 2θ is equal to 161/289.
To express sin 5x cos 6x as a sum, we can use the double-angle identity for sine:
sin 2θ = 2sin θ cos θ
Let's rewrite sin 5x cos 6x using the double-angle identity:
sin 5x cos 6x = (2sin 5x cos 6x) / 2
= sin (5x + 6x) / 2
Simplifying further:
sin (5x + 6x) / 2 = sin 11x / 2
Therefore, sin 5x cos 6x can be expressed as sin 11x / 2.
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What is the zero of 2x + 3y = 12
Answers
Answer:
6
Step-by-step explanation:
2x=-3y+12
x=-3/2x+6
6 is zero
Answer:
x/the zero=6
Step-by-step explanation:
Make the y zero
2x+3(0)=12
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then you're left with 2x=12
dived from both sides
x=6
a normalized binary number consists of three parts. these are:
Answers
Main Answer: A normalized binary number typically consists of three parts:
Sign bitExponentMantissaSupporting Question and Answer:
What is a sign bit in a normalized binary number?
The sign bit is the leftmost bit of a normalized binary number and indicates whether the number is positive or negative .A value of 0 indicates a positive number, while a value of 1 indicates a negative number.
Body of the Solution: A normalized binary number typically consists of the following three parts:
Sign bit: This is the leftmost bit of the number and indicates whether the number is positive or negative. A value of 0 indicates a positive number, while a value of 1 indicates a negative number.Exponent: This is the next set of bits that represent the exponent of the number in binary form. The exponent represents the power to which the base (2) is raised to obatain the actual value of the number. Mantissa: This is the remaining bits that represent the fractional part of the number in binary form. The mantissa contains the significant digits of the number, which are multiplied by the base raised to the exponent power to obtain the actual value of the number.Final Answer: A normalized binary number typically consists of three parts:
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