Answer:
[tex]9u" + 2304u = 160cos(6t)[/tex]
[tex]u(0) = \frac{5}{12}ft[/tex] and [tex]u'(0) =0[/tex]
Step-by-step explanation:
Given
[tex]w =9lb[/tex] --- weight
[tex]L = 1.5in[/tex] --- stretch
[tex]u(0) =5in[/tex] --- initial position
[tex]u'(0) =0[/tex] --- initial velocity
[tex]\gamma =0\ lbs/ft[/tex] --- no damping
[tex]F(t) = 5cos(6t)\ lb[/tex] -- External force
Required
Solve the initial value problem
The initial value problem is calculated using:
[tex]mu" + ku = F(t)[/tex]
First, convert all lengths to ft
[tex]L = 1.5in[/tex]
[tex]L = \frac{1.5}{12}ft[/tex]
[tex]L = \frac{1}{8}ft[/tex]
[tex]u(0) =5in[/tex]
[tex]u(0) = \frac{5}{12}ft[/tex]
Weight is calculated as:
[tex]w = mg[/tex] and [tex]w = kL[/tex]
Where
[tex]g = 32fts^{-1}[/tex]
Make m the subject in [tex]w = mg[/tex]
[tex]m = \frac{w}{g}[/tex]
[tex]m = \frac{9}{32}[/tex]
Make k the subject in [tex]w = kL[/tex]
[tex]k = \frac{w}{L}[/tex]
[tex]k = \frac{9}{1/8}[/tex]
[tex]k = 72[/tex]
Recall that: [tex]mu" + ku = F(t)[/tex]
[tex]\frac{9}{32}u" + 72u = 5cos(6t)[/tex]
Multiply through by 32
[tex]9u" + 2304u = 160cos(6t)[/tex]
[tex]u(0) = \frac{5}{12}ft[/tex] and [tex]u'(0) =0[/tex]
I think of a number, add on 15 and my answer is 8
Answer:
The number is -7
Step-by-step explanation:
x + 15 = 8
Answer:
the number is -7
Step-by-step explanation:
do the opposite( sum-number added)
8-15=-7
Plz helppp I will mark brainless
Answer:
168
Step-by-step explanation:
34 + 58 + 100 = 192
360 - 192 = 168
Solve by elimination:
3x + 4y = 0
5x-3y = -58
A (6, -8)
B (-6, -8)
C (-8, 6)
D ( 8, 6)
Answer:
x=−8
y=6=
Step-by-step explanation:
3x+4y=0
5x−3y=−58
In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
3x+4y=0,5x−3y=−58
To make 3x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 3.
5×3x+5×4y=0,3×5x+3(−3)y=3(−58)
Simplify.
15x+20y=0,15x−9y=−174
Subtract 15x−9y=−174 from 15x+20y=0 by subtracting like terms on each side of the equal sign.
15x−15x+20y+9y=174
Add 15x to −15x. Terms 15x and −15x cancel out, leaving an equation with only one variable that can be solved.
20y+9y=174
Add 20y to 9y.
29y=174
Divide both sides by 29.
y=6
Substitute 6 for y in 5x−3y=−58. Because the resulting equation contains only one variable, you can solve for x directly.
5x−3×6=−58
Multiply −3 times 6.
5x−18=−58
Add 18 to both sides of the equation.
5x=−40
Divide both sides by 5.
x=−8
The system is now solved.
x=−8,y=6
Coordinates are: (-8,6)
Graph:
find the value of x cubed minus 2x squared minus 7x + 5 of x=1/2-√3
9514 1404 393
Answer:
3
Step-by-step explanation:
For f(x) = x^3 -2x^2 -7x +5 and x=1/(2-√3), we have ...
f(x) = ((x -2)x -7)x +5
and ...
x = 1/(2-√3) = (2+√3)/(2^2 -3) = 2+√3
Then ...
f(2+√3) = ((2 +√3 -2)(2 +√3) -7)(2 +√3) +5
= (3+2√3 -7)(2+√3) +5
= 2(√3 -2)(√3 +2) +5 = 2(3 -4) +5 = -2 +5
f(1/(2 -√3)) = 3
_____
If you really mean x = (1/2) -√3, then f(x) = (42√3 -3)/8.
Plz help
.
X
X
X
X
D
E
D
D
D
Answer:
radius by 2 ye this will be the correct answer d=r/2
Colton finished his math homework at 8:27. He spent 32 minutes working
on it. What time did Colton start his homework?
Please i need extreme help
Answer:
90
Step-by-step explanation:
the formula to find the area of any right triangle is:
a=leg 1
b=leg 2
(a*b)/2
(15*12)/2
180/2
90
Answer:
90
Step-by-step explanation:
Is the sequence 7, 9, 12, 16 geometric
Answer:
The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term.
Kiana is saving for a new computer that cost $499. So far, she has earned 68 percent of the cost of the computer. How much more must Kiana earn.
Answer:
159.68
Step-by-step explanation:
68% of 499 is 339.32
499 -339.32=159.68
hope this helps
ill mark brainlist plss help
Answer:
option 1 is correct
Step-by-step explanation:
Can I plz have brainliest. thx :-)
Have a nice day!
Answer: Quadrilateral parallelogram, trapezoid; trapezoid
Step-by-step explanation:
A trapezoid has four sides so that makes it a quadrilateral, a parallelogram has at least two parallel sides (top and bottom), a lastly a it's a trapezoid and trapezoid has only one pair of parallel sides.
find the area of triangle CDE the length of the square is 24 meters;
Answer:
288
Step-by-step explanation:
If you didnt know a triangle has the area of a square/2
so basically what im saying is the area of that square/2 equals the area of the triangle
to find the area of the square you take 24 and square it
24^2=576
finally we divide that by 2
576/2=288
so the area of the triangle is 288
have a great day :D
Electrical circuit has a voltage of 60 v and resistance of 5 ohms that is the current?
Answer:
The current or I = 12.
Step-by-step explanation:
Ohm's law requires you to divide 60 volts by 5 ohms, hence giving you 12.
A text book publisher wants to estimate the number of sentences per paragraph in a history textbook. The publisher count the number of sentences in 150 randomly selected paragraphs. The results are shown in the table. Based on the data what is the mean number of sentences per paragraph in the textbook?
A. 4
B. 5
C. 10
D. 15
Using the weighed mean, it is found that the mean number of sentences per paragraph in the textbook is given by:
B. 5
What is the weighed mean?The weighed mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
In this problem:
The sum of the values multiplied by it's weights is: 1 x 0 + 2 x 3 + 3 x 20 + 4 x 43 + 5 x 36 + 6 x 25 + 7 x 10 + 8 x 8 + 9 x 2 + 10 x 3 = 750.Considering that there are 150 books, we have the mean is:
M = 750/150 = 5.
Hence option B is correct.
More can be learned about the weighed mean at https://brainly.com/question/24398353
Tom hits golf balls at the driving range every 3 days, practices putting every 4days, and goes golfing every 6 days. If he did all three activities today, in how may days will he do all three activities again?
Answer:
12 days
Step-by-step explanation:
Trust me I did the work.
A boat travels 102 miles in 5
hours (with a constant speed).
How far can it travel in 12 hours
(with the same speed)?
bvcdrtStep-by-step explanation:
Any idea on what the answer might. Be if u can explain would help alot
Answer:
pythagorean theorem!
Step-by-step explanation:
a²+b²=c² (normal)
a²=c²-b² (to find a)
[tex]a { = \sqrt{c {}^{2} } } - b ^{2} [/tex]
[tex]a = 38 ^{2} - 27 ^{2} [/tex]
[tex]a = \sqrt{1444 - 729} [/tex]
[tex]a = \sqrt{715} [/tex]
[tex]a = 26.7394839142[/tex]
help pls thank you
....
Answer:
m+n=2n+8
m=n+8
n=m-8
2k=m+n
Step-by-step explanation:
What combination of transformations is shown below
Answer:
rotation ,then reflection
Please help! I will mark brainlist!
Answer: A
Step-by-step explanation:
At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill.
How much would the sales tax be on a $66 meal?
Please show work.
Answer:
It is 5.61
Step-by-step explanation:
22×3=66
1.87×3=5.61
Find the domain and range of the relation.
{(3,-2) (2,1) (-1,0) (1,3)}
Please help this is due TODAY
Calculate the unknown variable value .
Do not answer with a one answer, blank or a ridiculous answer please this is serious.
Answer:
x=75°and y=x= 75°
Step-by-step explanation:
Reason: opposite angles are equal and how I got 75 is by drawing an extension line and finding the other angle (i.e. angle on a straight line=180) so 180-105=75.
please help me with this where do I put capitalization?????
Answer: At the beginning of the quotes. I hope this helps!
Answer: beginning
Step-by-step explanation:
This is a long question so look at the picture thank
you
Answer:
2 students
Step-by-step explanation:
.............
Plz help I will give you 40 points and Brainly
Answer:
sorry i don't knowe this, i realy want to help you
can someone help me pleasee ??
Factor out the coefficient of the variable.
The expression 4h−3 factored is
Answer:
4
Step-by-step explanation:
because the variable is h and the constant is 3
There are 7 red marbles, 7 blue marbles, 7 yellow marbles, and 7 green marbles in a bag. If a person randomly selects 1 marble from the bag, what is the probability that the person selects a blue marble? (HOW DID YOU GET YOUR ANSWER, PLEASE SHOW ME YOUR WORK!!)
A. 0.75
B. 0.5
C. 0.25
D. 0.0625
Answer:
0.25
Step-by-step explanation:
You have 4 options:
1/4: red
1/4: blue
1/4: green
1/4: yellow
Combined equals a whole, so each one of them equals 0.25
What is the square root of 23
Answer:
No real solution
Step-by-step explanation:
The simplest form is √23
Answer:
4.79583152331
Step-by-step explanation:
.................
...
I NEED HELP ASAAP SOMEONE!!
Answer:
5x4x3=60 3x4x5=60
Step-by-step explanation: