a. For what values of k does the function y = cos(kt) satisfy the differential equation 25y'' = −16y?
b. For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution.
Answer:
Step-by-step explanation:
Given y = coskt
y' = -ksinkt
y'' = -k²coskt
Substitute this y'' into the expression 25y'' = −16y
25(-k²coskt) = -16(coskt)
25k²coskt = 16(coskt)
25k² = 16
k² = 16/25
k = ±√16/25
k = ±4/5
b) from the DE 25y'' = −16y
Rearrange
25y''+16y = 0
Expressing using auxiliary equation
25m² + 16 = 0
25m² = -16
m² = -16/25
m = ±4/5 I
m = 0+4/5 I
Since the auxiliary root is complex number
The solution to the DE will be expressed as;
y = Asinmt + Bsinmt
Since k = m
y = Asinkt+Bsinkt where A and B are constants
Which activity would Descartes most likely have enjoyed in his free time? (straight up)
Answer:
Buns VI jdgsjs ssndbssbhejdjeejsgejeoe
Step-by-step explanation:
Bdnee Ded modi’s no rhenxns hi s in dndn
Answer:
Rene Descartes was a philosopher and he loved math and science. He was French.
Step-by-step explanation:
Is the figure an example of a line?
Answer:
No, Because it has 2 endpoints lines travel forever in both directions
Step-by-step explanation:
Answer:
D. No, it has two end points.
Step-by-step explanation:
A line is something that extends indefinitely in one or both directions.
Kayla measures a distance of 50 inches. She needs to find the equivalent number of meters. Which conversion factors should she use? Check all that apply.
(A) StartFraction 2.54 centimeters Over 1 inch EndFraction
(B) StartFraction 1 inch Over 2.54 centimeters EndFraction
(C) StartFraction 1 meter Over 100 centimeters EndFraction
(D) StartFraction 100 centimeters Over 1 meter EndFraction
Answer: A and C
Step-by-step explanation: :)
Answer:
A and C [: (edg 2021)
Step-by-step explanation:
I got it correct on my assignment!
Please answer correctly, I’ll give brainlest.
Answer:
[tex] \sqrt{170} [/tex]
what is the least common denominator of 1/2, 2/3 and 3/8 A. 48 B. 24 C. 16 D. 12
Answer:
B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
If y =3x-5,and x=5 then y ???
help me with thisss simplify : 6³/6⁶
#IfWrongPleaseReport
#StudyTogetherWithMe
#ILoveMath
What is the following equal to 7 times 10^3
Answer:
7000
Step-by-step explanation:
10^3=1000
1000*7=7000
7000 is answer
1000×7 = 7000
I need help ASAP thank u
Answer:
im pretty sure the answer is a
Step-by-step explanation:
and follow me plz
How do you do this question?
Answer:
bn = 1 / n
Step-by-step explanation:
We want to show the series an diverges. So we need to find a smaller function bn that diverges. That means we can eliminate options C and D, both of which converge.
an = (3 + sin(n) + e⁻ⁿ) / (2n − 1)
Sine is between -1 and +1, and e⁻ⁿ approaches 0 as n approaches infinity. So the numerator is a minimum of 2 as n approaches infinity. So we can make a new function:
an = 2 / (2n − 1)
Let's look at option B: bn = 4 / √n = 2 / (½√n).
½√n is less than 2n − 1, so bn is greater than an. We can't use that to show that an diverges.
Now let's look at option A: bn = 1 / n = 2 / (2n).
2n is greater than 2n − 1, so bn is less than an. Since bn diverges, an must also diverge.
Which equation represents a line with a slope of -3 and a y-intercept of -6?
A. y = 3x - 6
B. y = 6x + 3
C. y = - 3x +6
D. y = - 3x - 6
Answer:
D. y=-3x-6
Step-by-step explanation:
Slope is before x and since it is -3 it is -3x the y-intercept is the number without the variable and since it's -6 you get y=-3x-6
A report revealed that the average no. of months that an employee stays in a factory is 36 months. Assuming that
the no. of months of an employee tenure in the factory is normally distributed with a standard deviation of 6
months, find the probability that a certain employee will stay:
a. More than 30 months
b. Less than 24 months
c. Between 24 to 48 months
Answer:
a) P [X ≥ 30 ] = 0,8413 or 84,13%
b) P [X < 24] = 0,0228 or 2,28 %
c) P [ 24 < X < 48 ] = 0,9544 or 95,44%
Step-by-step explanation:
z = ( X - μ₀ )/σ
μ₀ the mean ( average no. of months that an employee stay in a factory)
σ standard deviation
a) P [X ≥ 30 ] = 1 - P [X < 30 ]
P [X < 30 ]
We look for z (score)
z = ( X - μ₀ )/σ ⇒ z = 30 - 36 / 6
z = - 1
From z table we get for -1
P [X < 30 ] = 0,1587
And
P [X ≥ 30 ] = 1 - P [X < 30 ] ⇒ P [X ≥ 30 ] = 1 - 0,1587
P [X ≥ 30 ] = 0,8413 or 84,13%
b) P [X < 24]
z (score) = ( 24 - 36 ) / 6
z( score) = -2
And from z table we get:
P [X < 24] = 0,0228 or 2,28 %
c) P [ 24 < X < 48 ] is P[X ≤ 48] - P[X ≤ 24]
P [X < 48]
s (score) = 48 - 36 / 6 ⇒ z = 2
P [X < 48] = 0,9772
Then
P [ 24 < X < 48 ] = 0,9772 - 0,0228
P [ 24 < X < 48 ] = 0,9544 or 95,44%
6. The store paid $2.50 for a book and sold it for $5.25. What is the profit as a percent?
What is the asymptote of the function g(x) = 5.2 3x + 4 shown on the graph?
Y=0
Y=3
Y=4
Y=5
Answer:
Y=4
Step-by-step explanation:
Answer:
Y=4
Step-by-step explanation:
Mr. Waxman is helping with deliveries for a shipping company. The graph shows a linear model for his delivery times on different days. (A) Identify two points on the line and write the coordinate pairs below. (B) Use your two points to find the slope, and make sure to show your work. (C) Use your slope from Part B and find the equation of the line in point-slope form. Show your work and work through the steps to transform the equation from point-slope form into slope-intercept form. (D) Based on the equation you found in Part C, predict how long it take Mr. Waxman to deliver his packages on Day 0. Approximately how much did his delivery time decrease per day? 2 SEE A
Answer:
See below
Step-by-step explanation:
Note: missing graph is attached
SolutionA) The two points are:
(4, 19) and (7, 7)B) Slope formula: m = (y2-y1)/(x2-x1)
m = (7 - 19)/(7-4)m = -12/3m = -4C) Point-slope formula:
y - y1 = m(x - x1)Using one of the points we get:
y - 19 = -4(x - 4)D) Delivery time on Day 0:
y - 19 = -4(0 - 4)y - 19 = 16y = 16 + 19y = 35 minutesDelivery time decreases by the value of the slope which is 4 minutes per day
PLEASE HELP ASAP ITS DUE SOON
Lines R and S are parallel Find the value of x, then find the measure of m<1 and m<2.
m<1=(70-2x)"
m<2 = (82-3x)
x=
m<1=
m<2=
m<1 and m<2 are corresponding angle
Answer:
im very confused aadly
A Cessna 172 plane that is used to transport up to four VIPs is 2 km in the air if the potential energy of the VIP plane with three VIPs on board is 860 J what is the combined mass of the Cessna and passengers
Answer:
0.0438 kg
Step-by-step explanation:
We are given;
Potential energy; U = 860 J
Height; h = 2 km = 2000 m
Formula for potential energy is;
U = mgh
Where g is acceleration due to gravity = 9.81 m/s²
Thus;
860 = m × 9.81 × 2000
m = 860/(9.81 × 2000)
m = 0.0438 kg
D) 685
Titik koordinat yang manakah berada pada garis lurus Y=X +99
A) (2,13)
B) (4,11)
C) (3,12)
D) (5,10)
Answer:
A
Step-by-step explanation:
5624/6 with a remainder
Answer:
937.333
Step-by-step explanation:
Answer:
937.33 (rounded. Real answer: 937.333333)
Step-by-step explanation:
5,624 ÷ 6 = 937.33 (rounded since the real answer was: 937.333333)
In the diagram, bisects ABC. Find mABD and mDBC
Answer:
Angle ABD = 45 degrees
Angle DBC = 45 degrees
Step-by-step explanation:
If the ray BD bisects ABC, then it divides it in two angles of equal measure. The we can write the following equality:
angle ABD = Angle DBC
9 x + 9 = 12 x - 3
solve for x by subtracting 9x from both sides,
9 = 3 x - 3
and adding 3 to both sides:
9 + 3 = 3 x
12 = 3 x
divide both side by 3 to isolate "x":
12/3 = x
x = 4
And now we can find the value of each angle:
Angle ABD = 9 x + 9 = 9 (4) + 9 = 36 + 9 = 45 degrees
Angle DBC = 12 x - 3 = 12 (4) - 3 = 18 - 3 = 45 degrees
HELP! Giving branliest to who answers!!!
Answer: A. -1.8
Step-by-step explanation: Hi there!
First, we have to see the constant rate of change in the x and y values.
For x: 2
For y: -3.6
If the slope is m=y/x
then we can do
-3.6/2
that simplifies to
-1.8/1
which is
-1.8
Hope this answer helps you!
Is .09 greater then .0003
Answer:
Yes
Step-by-step explanation:
For ease, let's multiply these by 10,000.
0.09 • 10,000 = 900.00 = 900
0.0003 • 10,000 = 3.00 = 3
900 is clearly greater than 3. Therefore, 0.09 is greater than 0.0003.
Two angles of a triangle measures 55 degrees and 20 degrees
Answer:
105
Step-by-step explanation:
55 + 20 + x = 180
Which statement best explains whether △ABC is congruent to △DEF?
△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a reflection across the y-axis followed by a translation 5 units down.
△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a rotation of 90° counterclockwise about the origin followed by a reflection across the y-axis.
△ABC is congruent to △DEF because △ABC can be mapped to △DEF by a translation 5 units down followed by a reflection across the x-axis.
△ABC is not congruent to △DEF because there is no sequence of rigid motions that maps △ABC to △DEF.
Answer: △ABC is congruent to △DEF because △ABC can be mapped to △DEF by a translation 5 units down followed by a reflection across the x-axis.
Step-by-step explanation: By moving the shape down 5 units, you are met with DEF. You then mirror it (reflect) across the y axis.
this table displays the amount of water in the bathtub as it is being drained a two-column table with four rows column one is labeled time minutes with entry 7 8 9 10 CO2 is labeled water gallons with entries 38.5 36.2 534-3175 use the table to interpret the rate of change what is the rate of change for the relationship
The rate of change for the relationship, given the data is -2.25 gallon/min
What is velocity?Velocity is simply defined as the rate of change of displacement with time. Mathematically, it can be expressed as:
Velocity = displacement / time
With the above idea in mind, we can obtain the rate of change for the given relationship. This is illustrated below:
How to determine the rate of change Column 1 i.e time (min) = 7, 8, 9, 10.Column 2 i.e Water (gallons) = 38.5, 36.25, 34, 31.75.Rate of change =?Rate = Change in gallon / change in time
Rate = (36.25 - 38.5) / (8 -7)
Rate = -2.25 / 1
Rate of change = -2.25 gallon/min
Learn more about velocity:
https://brainly.com/question/3411682
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The sixth-graders at Scott's school got to choose between a field trip to a museum and a field trip to a factory. 57 sixth-graders picked the museum. If there are 100 sixth-graders in all at Scott's school, what percentage of the sixth-graders picked the museum?
Answer:
57%
Step-by-step explanation:
because percentages go up to a hundred so 57 would be 57%.
Answer:
57%
Step-by-step explanation:
The answer is 57%. The reason is because when we are talking about percentage, it always out of 100. 57 out of 100, you would make that into a fraction so it would be 57/100. You would then divide 57/100 to get 0.57. Move the decimal two places to the right to get 57%.
Show that each conjecture is false by finding a counterexample.
1.For any integer n, n3 > 0.
2. Each angle in a right triangle has a different measure.
3.For many years in the U.S, each bank printed its own currency. The variety of different bills led to widespread counterfeiting. By the time of the Civil War, a significant fraction of the currency in circulation was counterfeit. If one soldier had 48 bills, 16 of which were counterfeit, and another soldier had 39 bills, 13 of which were counterfeit, make a conjecture about what fraction of bills were counterfeit at the time of the Civil War.
Answer:
1. [tex]n: n^3 > 0[/tex] is not true for negative integers
2. [tex]45\ and\ 45[/tex] show that all angles do not have different measure
3. [tex]Fraction = \frac{1}{3}[/tex]
Step-by-step explanation:
Solving (1):
[tex]n: n^3 > 0[/tex]
Take
[tex]n = -1[/tex]
[tex]-1^3 = -1[/tex]
[tex]n: n^3 > 0[/tex] is not true for negative integers
Solving (2):
The angles of a right angled triangle are:
[tex]45, 45\ and\ 90[/tex]
[tex]45\ and\ 45[/tex] show that all angles do not have different measure
Solving (3):
When
[tex]Bills = 48[/tex]
[tex]Counterfeit = 16[/tex]
The fraction is calculated as thus:
[tex]Fraction = \frac{Counterfeit}{Bills}[/tex]
[tex]Fraction = \frac{16}{48}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
Similarly, when
[tex]Bills = 39[/tex]
[tex]Counterfeit = 13[/tex]
[tex]Fraction = \frac{Counterfeit}{Bills}[/tex]
[tex]Fraction = \frac{13}{39}[/tex]
[tex]Fraction = \frac{1}{3}[/tex]
polynomial time............
Answer:
I'm pretty sure its b
Step-by-step explanation:
I plotted each one to make a polynomial graph and b was the one that had the x-intercepts at -6, 1, and 4.
hope this helped a little :))
What’s the ratio 217:279 simplified
Answer:
666:999
Step-by-step explanation:
olyiuuuyyiuuuuuu