Answers
Step-by-step explanation:
Given:
[tex]x = e^{-t}\sin t[/tex]
Taking the 1st and 2nd derivatives of the above expression,
[tex]\dfrac{dx}{dt} = -e^{-t}\sin t + e^{-t}\cos t[/tex]
[tex]\dfrac{d^2x}{dt^2} = e^{-t}\sin t - e^{-t}\cos t -e^{-t}\cos t[/tex]
[tex]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- e^{-t}\sin t[/tex]
[tex]\:\:\:\:\:\:\:\:\:= -2e^{-t}\cos t[/tex]
Therefore,
[tex]\dfrac{d^2x}{dt^2} + 2\dfrac{dx}{dt} + 2x[/tex]
[tex]= -2e^{-t}\cos t + 2(-e^{-t}\sin t + e^{-t}\cos t)[/tex]
[tex]\:\:\:\:+ 2e^{-t}\sin t[/tex]
[tex]= -2e^{-t}\cos t - 2e^{-t}\sin t + 2e^{-t}\cos t + 2e^{-t}\sin t[/tex]
[tex]= 0[/tex]
This shows that [tex]x = e^{-t}\sin t[/tex] is the solution to the differential equation
[tex]\dfrac{d^2x}{dt^2} + 2\dfrac{dx}{dt} + 2x = 0[/tex]
Related Questions
Mr jones rolls a 6 sided cube mumbered 1,2,3,4,5,6, what is the probability he rolls a three.
Answers
Answer:1.5
Step-by-step explanation:
a number t is less than 7
Answers
Answer:
6 or 5 or 4...........
Step-by-step explanation:
Answer:
x=N :x<7
Step-by-step explanation:
123456
hope it's helpful
(Kind of urgent!) Using the figure below, find the value of a. Enter your answer as a simplified radical or improper fraction (if necessary)
Answers
Answer:
15/4
Step-by-step explanation:
sin60 =z/15
z=15sin60 =(15√3)/2
cos30 =b/z
b = zcos30 = (15√3)/2 * √3/2 = 45/4
a = 15-b = 15-45/4 = 15/4
The value of a is 15/4
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
According to the given figure,
Here is a right triangle
Let, The hypotenuse = 15
perpendicular = z and base = 15 = a + b
⇒ sin60 = perpendicular/hypotenuse = z/15
⇒ z = 15sin60 = (15√3)/2
⇒ cos30 = base/hypotenuse = b/z
⇒ b = zcos30 = (15√3)/2 * √3/2 = 45/4
⇒ a + b = 15
Substitute the value of b in the above equation,
⇒ a = 15-b = 15-45/4 = 15/4
Hence, the value of a is 15/4.
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The total number of branches in a tree diagram will be which of the following values?
the probability of an event occurring
the denominator of a probability
the numerator of a probability
Answers
Answer:
The total number of branches = total possibilities = the denominator of a probability.
So the second choice is correct.
Let me know if this helps!
Answer:
Step-by-step explanation: answer B (the denominator of a probability)
de la
QUESTION 8
The hospital has allotted 120 days of inservice for every 15 departments. How many days of inservice can each department use?
I
Answers
Answer:
in 8 days
Step-by-step explanation:
soln
given,
total days=120
department=15
we know,
120/15
=8
•°•8days are given to each department.
calculate the effective yearly rate if an investment offers a nominal interest rate of 9.5% compounded quarterly
Answers
Answer:
9.725%
Step-by-step explanation:
(1.0475)^2 =1.09725
one year 2 periods 4.75% per period
a shopkeeper gains #1.75 by selling an article for #6.25. what is the percentage gain.
Answers
Answer:
≈ 38.89%Step-by-step explanation:
The cost is:
6.25 - 1.75 = 4.50Percentage gain:
1.75/4.50*100% ≈ 38.89%if a/b = 3 and a + b = 2, what is a - b
Answers
Answer:
1
Step-by-step explanation:
a/b=3------equation 1
a+b=2-----equation 2
from equation 2
b=2-a
substitute b=2-a in equation 1
a/2-a=3
a=3(2-a)
a=6-3a
a+3a=6
a=6/4
a=3/2
substitute a=3/2 in equation 2
3/2+b=2
3+2b=4
2b=1
b=1/2
a-b=3/2-1/2
a-b=(3-1)/2
a-b=2/2
a-b=1
What is 3.24 ( 4 repeating) as a fraction?
Answers
Answer:
81/25
Step-by-step explanation:
change 3.24 into faction
324 over 100 because there are two decimal points .
simplfy into the smallest fraction
the answer is 81 over 25
Solve for
x. Round to the nearest tenth of a degree, if necessary.
Answers
Answer:
[tex]\displaystyle x \approx 30.8[/tex]
Step-by-step explanation:
Note that the figure is a right triangle, and that we are given the length of the side adjacent to x and the hypotenuse of the triangle.
Therefore, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 8.5 and the hypotenuse is 9.9. Therefore:
[tex]\displaystyle \cos x = \frac{8.5}{9.9}[/tex]
We can take the inverse cosine of both sides:
[tex]\displaystyle x = \cos^{-1} \frac{8.5}{9.9}[/tex]
Use a calculator. Hence:
[tex]\displaystyle x \approx 30.8[/tex]
In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.
Answers
Answer:
plato screenshot!
Step-by-step explanation:
I don't personally know *how* to find the answers, but here's the screenshot of the suggested answer on Plato
Answer:
A B Slope of C Slope of Line Through C
(−5,4) (−1,−1) −1.25 (1,2) 0.8
(−5,4) (−3, 5) 0.5 (−2, 1) −2
(−4, 1) (−3, 5) 4 (−2, −2) −0.25
(−5, −2) (−1, 1) 0.75 (−4, 3) −1.33
(−5, −2) (1, −1) 0.17 (−3, 1) −6
Step-by-step explanation:
that way you can copy and paste each one but Plato
A plumber can do a job in 4 hours. When he and his 2 helpers do the job, they can finish it in 2 hours. If both helpers work at the same rate, how many hours would each helper take to do the job alone?
Answers
cross multiply
4x2/2
Please help me with this someone
Answers
9514 1404 393
Answer:
79 23/24 yards
Step-by-step explanation:
10 5/8 +24 5/6 +44 1/2 = (10 +24 +44) +(5/8 +5/6 +1/2)
= 78 +(15/24 +20/24 +12/24) = 78 +47/24 = 79 23/24 . . . yards
_____
Express the fractions over a common denominator, add, and convert back to a mixed number. Here, the fraction cannot be reduced.
47/24 = 1 23/24
What is the order of rotational symmetry for the figure?
A. 4 or more
B. 2
C. 1
D. 3
Answers
Đại biểu ĐBTQ lần thứ VIII (1996) của Đảng, xác định “phát huy nguồn lực con người là yếu tố cơ bản cho sự phát triển nhanh và bền vững trong quá trình CNH,HĐH đất nước”, anh/chị hãy phân tích quan điểm này và liên hệ thực tiễn Việt Nam hiện nay?
Answers
What is the probability of rolling a 2 and 3 with 2 die
Answers
the probability of rolling a 2 is 1/6 and the probability of rolling a 3 is 1:6 to find the final probability you need to multiply the two
find the value of x and y
Answers
Answer:
x=50 and y=80
Step-by-step explanation:
ATQ, x+50+y=180 and y+2x=180. x=50 and y=80
Two lines, A and B, are represented by equations given below:
Line A: y = x − 2
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(−3, −5), because the point does not lie on any axis
(−3, −5), because the point satisfies both equations
(−4, −8), because the point satisfies one of the equations
(−4, −8), because the point lies between the two axes
Answers
9514 1404 393
Answer:
(b) (−3, −5), because the point satisfies both equations
Step-by-step explanation:
Any solution to a system of two equations must satisfy both equations. The only reasonable explanation of "why" is the one associated with the answer shown above.
Help! Please? Dont understand
Answers
Solve 5x + 3 = -7x + 21
Answers
x = 3/2
Step-by-step explanation:
5x + 3 = -7x + 21
5x - -7x = 21 - 3
12x = 18
x = 18/12
x = 3/2
Find the missing side length. Leave your answers radical in simplest form. PLEASE HURRY
Answers
Answer:
the answers for x and y are both 12
After the release of radioactive material into the atmosphere from a nuclear power plant at Chernobyl (Ukraine) in 1986, the hay in Austria was contaminated by iodine 131 (half-life 8 days). If it is safe to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay?
Answers
Given the data provided, it follows that the farmers must wait for 26 days before feeding the hay to cows.
What is half life?The term half life is defined as the time taken for half of the original amount of the radioactive sample to remain.
Now we know that;
half life = 8 days
Original amount = No
Amount left after t days = 0.1No
time taken = t days
Hence;
0.693/8 = 2.303/t log (No/0.1No)
0.087 = 2.303/t
t = 2.303/0.087
t = 26 days
Learn more about radioactivity: https://brainly.com/question/14356798
a new automobile cause 11300 which is 100 more than 25 times a certain number what is the number
Answers
Answer:
25x + 100 = 11300
25x = 11200
448 = x
Step-by-step explanation:
the certain number is 448
What is the volume of the prism below?
19.80 cubic units
553.02 cubic units
84.17 cubic units
42.09 cubic units
Answers
The volume of prism is,
⇒ V = 42.09 cubic units
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Base = 5.12
height = 4.11
Lenght = 4
Now, We can formulate;
The value of volume of prism is,
⇒ V = 1/2 (b x h) l
⇒ V = 1/2 (5.12 x 4.11) 4
⇒ V = 42.09 cubic units
Thus, The volume of prism is,
⇒ V = 42.09 cubic units
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Use the graph of ƒ to find ƒ(2).
0.5
–8
–0.5
Does not exist
Answers
Answer:
Step-by-step explanation:
When you're looking to find things like f(2) and f(4) and f(-3000), etc. the number inside the parenthesis is an x value. Look to the graph, find that x value, and locate the y value that corresponds to it. f(2) = -8. f(-1) = 4. f(1) = -4. See?
Answer:
does not exist
Step-by-step explanation:
that what i put hope it helps
Change the word phrase to an algebraic expression. Use x as the variable to represent the number.
16 subtracted from a number
Let x = the number.
16 subtracted from a number can be written as…
Answers
Answer:
I think the answer is
x-16
since 16 is subtracted from x.
I hope this helps
For what values are 2x^2=10x
Answers
[tex]\\ \sf\longmapsto 2x^2=10x[/tex]
Take to to right[tex]\\ \sf\longmapsto x^2=\dfrac{10x}{2}[/tex]
[tex]\\ \sf\longmapsto x^2=5x[/tex]
Cancel a x from both sides[tex]\\ \sf\longmapsto x=5[/tex]
QUESTION 9
Convert 0.85 decimal to a fraction (do not reduce)
Answers
Answer:
85/100
Step-by-step explanation:
0.85 from a decimal is equal to 85/100 in fractions
100 x 20 + 30 help me
Answers
[tex]\boxed{\underline{\bf \: Answer}}[/tex]
[tex] \sf100 \times 20 + 30[/tex]
First multiply 100 & 20 together.
[tex] \sf= 2000 + 30[/tex]
Now add 2000 & 30. You'll get :-
[tex]= \boxed{ \bf 2030}[/tex]
____
Hope it helps.
RainbowSalt2222
[tex]\\ \rm\longmapsto 100\times 20+30[/tex]
[tex]\\ \rm\longmapsto (100\times 20)+30[/tex]
Solve bracket[tex]\\ \rm\longmapsto 2000+30[/tex]
[tex]\\ \rm\longmapsto 2030[/tex]
What is the area of the trapezoid?
Answers
Answer:
A=a+b
2
Step-by-step explanation:
To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
