Answer:
[tex]y" + 2y' + 2y = 0[/tex]
Step-by-step explanation:
Given
[tex]y=c_1e^{-x}cosx+c_2e^{-x}sinx[/tex]
Required
Determine a homogeneous linear differential equation
Rewrite the expression as:
[tex]y=c_1e^{\alpha x}cos(\beta x)+c_2e^{\alpha x}sin(\beta x)[/tex]
Where
[tex]\alpha = -1[/tex] and [tex]\beta = 1[/tex]
For a homogeneous linear differential equation, the repeated value m is given as:
[tex]m = \alpha \± \beta i[/tex]
Substitute values for [tex]\alpha[/tex] and [tex]\beta[/tex]
[tex]m = -1 \± 1*i[/tex]
[tex]m = -1 \± i[/tex]
Add 1 to both sides
[tex]m +1= 1 -1 \± i[/tex]
[tex]m +1= \± i[/tex]
Square both sides
[tex](m +1)^2= (\± i)^2[/tex]
[tex]m^2 + m + m + 1 = i^2[/tex]
[tex]m^2 + 2m + 1 = i^2[/tex]
In complex numbers:
[tex]i^2 = -1[/tex]
So, the expression becomes:
[tex]m^2 + 2m + 1 = -1[/tex]
Add 1 to both sides
[tex]m^2 + 2m + 1 +1= -1+1[/tex]
[tex]m^2 + 2m + 2= 0[/tex]
This corresponds to the homogeneous linear differential equation
[tex]y" + 2y' + 2y = 0[/tex]
What happens to a 44-degree angle if you rotate it 90 degrees counterclockwise? Explain your answer.
Answer:
it would melt
Step-by-step explanation:
at 40 degrees, the angle will stay in its natural shape. if increased to 90 degrees on the counter, and with the wisdom of mr. clock, the angle will start to warp, and lose its shape. evidently, if the angle is heated at a steady 90 degrees, the melting process will occur, and it will make a mess on your counter. thats why, when melting angles, I recommend putting it in a container, so as to not make too big of a mess.
Gavin needs to buy candy for the 11 students in his class plus himself. Gavin and each student will get one bag of candy. He uses $20 to buy two different types of candy. Gavin buys x bags of gummy bears that cost $1.50 per bag and y bags of chocolates that cost $2.00 per bag. The system of equations used to represent this situation is graphed, as shown.
Answer:
20=1.50(6)+2.00(4)
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
When Lila conducted an experiment on citywide pond water, all of her samples came from the pond in her uncle's backyard. Explain her error.
Her area of study is too narrow. There are other sources of water in the city that she is not considering. So her sample is too biased leaning toward the Uncle's pond water, and that leaves out every other source. We say that the Uncle's source of water is over-represented while the other sources are completely under-represented.
Let's put it this way: We have a hypothetical city that has 100 acres of pond water either in or surrounding the city limits. If the Uncle's pond only represents 1% of this, then she's ignoring the other 99% of the ponds.
What Lila needs to do to to fix this error is to draw up a map of each major pond and mark those ponds with numbers 001,002,...998,999. In this example, there are 999 ponds. Then she needs to either use a random number table or computer software to help randomly generate values to help select the ponds. Doing so will ensure that she spans a good portion of the city and not stay focused on just the narrow area of her Uncle's backyard.
The reason why she needs to enlarge her area of study is because the results of her Uncle's pond study may lead to the wrong conclusion of the city overall. Let's say his pond is contaminated somehow, and it's only his pond that's the unfortunate one. She would likely see the pond is contaminated and conclude that the whole city's water is ruined as well, which isn't the case. Or we could have nearly the entire city's pond water in trouble, but her Uncle's pond is one of the lucky ponds not to get contaminated. We can see that Lila would likely conclude that no action needs to be taken to clean up the city's water sources, which is also not the case.
If Lila only cared about her Uncle's pond, then that pond (and perhaps immediate close surrounding area) would be her population of study. However, her study is about citywide pond water which is why she needs to extend to other places in the city or in the outer surrounding areas.
please help i will give extra points
Answer: 1
Step-by-step explanation:
4b-5a
4(4)-5(3)
16-5(3)
16-15
1
Answer:
1
Step-by-step explanation:
4 x 4 - 5 x 3
16 - 15 = 1
Emily has 437 pennies in a
piggy bank. Round the number
of pennies Emily has to the
nearest ten.
Answer:
437 to the nearest ten is 440, hope this helps
simplify 45÷3+2×8-12+43
Answer:
62
Step-by-step explanation:
divide, then multiply, then calculate the sum or difference and you should get 62
Answer:
Many ways
Step-by-step explanation:
One of them being:
1. 15 + 16 -12 +43
Answer is 62 if wondering
(Brainliet?)
First, divide 45 by 3 which is 15
Then, multiply 2 and 8 which is 16
Add 15 and 16 which is 31
Subtract 12 and get 19
Add 43 adn get 62
How is math used in making murals?(subject:Collage and Career readiness)
identify the coefficeient following expression
6a+7
Answer:
6
Step-by-step explanation:
The coeffecient is the number next to the variable. Boom. Done.
Answer:
6
Step-by-step explanation:
a coefficient is a number in front (behind) the variable (ex. the coefficient in 2x is 2, and the variable is x)
i hope this helps :)
I aould appreciate if someone helped
Choose the sentence that does not have any errors in spelling or punctuation.
Someone who sells tickets is always in the ticket wagon, which is stationary in spite of its wheels.
Someone who sells tickets is always in the ticket wagon, which is stationery in spite of its wheels.
Someone, who sells tickets, is always in the ticket wagon which is stationary in spite of its wheels.
Someone, who sells tickets, is always in the ticket wagon which is stationery in spite of its wheels.
Answer: Someone who sells tickets is always in the ticket wagon, which is stationery in spite of its wheels.
Step-by-step explanation: Do usage of the comma in answers C , and D are incorrect , so that leaves us with answers A and B , in option A stationery is miss spelled so your answer would be : Someone who sells tickets is always in the ticket wagon, which is stationery in spite of its wheels.
On Saturday and Sunday jarrod went running and burned a total of 6475 calories he burned 320 of those calories on Saturday which addition equation could be used to find the number of calories c jarrod burned on Sunday
A 647.5+c=320
B. 320 + c = 647.5
C. 320 + 647.5=c
D. 647.5 + 320 =c
Answer:
The answer is B.
Step-by-step explanation:
It is saying that 647.5 calories is the total amount and 320 is a part of it. so when you do 647.5-320, it becomes 327.5 and that is c. You can only do this with the equation that letter B is saying.
An electronics store is having a 15% off sale. Suppose the sale price(p) of a laptop is $495. Which statement are true for this stuation
A. P+ 0.15p represents the sales price
B. P- 0.15p represent the sales price
C. 0.85p represents the sales price
D. The sale price is 420.75
E. The sale price is 569.25
Answer:
The answer to the Question is D
Answer:
B, C, D
Step-by-step explanation:
If the sales price is 15% off, then the the price is .85(100-15%) of the price so c is true
this also makes b true. (100-15%) is p-.15
495 x .85 (100-15%)=420.75 so d is true
a triangle has angles that measure 64 degrees and 55 degrees what is the measure of the third angle
Answer:
61
Step-by-step explanation:
the angles of any triangle combined equal 180 therefore take the known angles and subtract them from 180 getting 61
Draw a quadrilateral with two pairs of parallel sides, with one side measuring 5 centimeters, one side measuring 3 centimeters, and one angle measuring 45 what is the name of the figure you drew?
Answer:
a trapezoid
Step-by-step explanation:
Answer is parallelogram.
Parallelogram:
A two-dimensional geometrical shape, figure with four sides whose opposite sides are parallel and equal.
Here,
It is given that the quadrilateral have two pairs of parallel sides.
It cannot be rectangle as the angles in rectangle should be 90 degrees.
Answer is parallelogram.
Learn more about parallelogram here:
https://brainly.com/question/18137045?referrer=searchResults
#SPJ2
help w all please!!! i dont even know where to plot lol
I need help sooo please HELP ME :’) ill give good points because its my last question:
When is the multiplicative relationship used? Select all that apply.
options (more than 1):
1.When multiplying the same amount to an x-value.
2.When subtracting the same amount to an x-value.
3.When dividing the same amount to an x-value.
4.When adding the same amount to an x-value.
Answer:
1 and 3
Step-by-step explanation:
What are the values of x and y?
Answer:
All of the angles are 60!
Step-by-step explanation:
the sum of all angles will be 180. the angles are conguent....180-60=120
120/2=60
The 20,000 seats available at Madison Square Garden for a popular concert sold out in just 12
minutes. If the tickets sold at a constant rate, how many tickets sold in 5 minutes (min)? Round
the answer to the nearest whole number.
Answer:
8333 tickets.
Step-by-step explanation:
If you take 20,000 and divide it by 12 you get 1666.66
You then take 1666.66 and times it by 5.
The answer you get is 8333.33 but the instructions say to round it to the nearest whole number which would be 8333. Hope this helps!!
a person on a 2500 calorie diet states that they are healthier because they eat more veggies. explain why this is not accurate?
Step-by-step explanation: because they need to have atleast 2500 calories a day
Complete the equation for the horizontal line that passes through (5-7)
Answer:
The point (a,b) is (5,7) . Therefore, the equation of the line is y=7 .
Hopefully this helps!
Step-by-step explanation:
The following data are the daily number of minutes of smartphone use for a random sample of 8 students at your institution: 117, 156, 89, 72, 116, 125, 101, 100.
(a) Test the null hypothesis according to which the true mean is 100 min against the alternative that it is different than 100. Use a significance level of 5% (state the null and the alternative hypothesis, the test statistic and the conclusion). (10 points)
(b) Compute a 95% confidence interval for the true mean number of minutes per day a student uses his or her smartphone. Is your finding consistent with your answer in (a) (Explain why or why not)?
Step-by-step explanation:
Number of students = 8
Mean of sample = 876/8
= 109.5
We solve for standard deviation using formula:
S = √(Xi -barX)/n-1
S = 25.3264
A.
H0: u = 100
H1: u not equal to 100
T test = barX - u/s/√n
t = 109.5-100/(25.3264/√8)
= 9.5/8.9542
= 1.0609
Df = 8-1 = 7
P value = 0.953141 at 5% significance level. P-value > 0.05 so we fail to reject H0
Conclusion: insufficient evidence that mean = 100
B.
95% = bar x +-t*s/√n
t = 2.365 at 95% and df = 7
109.5 +- 2.365(25.3264/√8)
= 109.5 +- 2.365(8.9542)
= 109.5-21.1768, 109.5+21.1768
= (88.3232, 130.6768)
In conclusion true mean is in the confidence interval, so it is consistent.
How many joules of gravitational potential energy are stored in an object that has a mass of 8.5 kilograms and is held 2 meters above the surface of earth?
Answer:
I believe the answer is 166.6 Joules or (if rounding to the nearest whole number) 167 Joules.
Step-by-step explanation:
Here is the formula to find the gravitational potential energy of an object:
U = m * g * h (potential energy equals mass times gravitational acceleration * the height)
The mass is 8.5 kilograms, the height is 2 meters, and Earth's gravitational acceleration is always, no matter the other values or earthly situations, 9.8 m/s.
Now we solve:
8.5 * 9.8 * 2 = 166.6 which is rounded to 167 Joules.
Please can someone help
ramon makes a spinner with 4 colors. he colors 25% of the spinner red, 15% blue, 40% orange, and the rest green. ramon then spins the spinner. which outcome would be most likely to happen?
a. the spinner landing on green or red
b. the spinner landing on green or blue
c. the spinner landing on orange or red
d. the spinner landing on orange or blue
Answer:
c. the spinner landing on orange or red
Step-by-step explanation:
So first you find how much is green
25 + 15 + 40 = 80
100 - 80 = 20
So the amount green is 20%
Then you choose the color that has the biggest percentage because it has a higher change of being chosen
25% is red
15% is blue
40% is orange
20% is green
orange and red is the biggest amount/ has the biggest percentage
c is your answer
Write 8 1/5 as a fraction
Answer:
8.2
Step-by-step explanation:
let me know if its wrong
please Answer Please answer ASAP illg ive brainliest
Answer:
Speed = 100/Time
Step-by-step explanation:
(a). Speed is a function of time : As seen from equation (1) Speed of the students varies according to the value of time. So, This a true statement.
(b). Time is a function of distance : Distance is not varying in the equation (1), it is fixed to be 100. So, time is not a function of distance because here the distance is made constant. So, This is false statement.
(c). Speed is a function of number of students racing : Speed is not depending on the number of students racing so sped is independent of the number of the students racing. Therefore, Speed is not a function of number of students racing. This is False statement.
(d). Time is a function of speed : As seen from equation (1) Time of the students varies according to the value of their speed. So, This a true statement.
Hence, the true statements are (a) and (d)
Need help plz and thank u
Answer:
20%
Step-by-step explanation:
12/60 (divided) makes 0.2, converted to a percent is 20%
I WILL GIVE BRAINIEST IF ANSWERED WITH EXPLANATION ASAP
Answer: 9 inches.
Step-by-step explanation:
Use a proportion for this problem
2/3=6/x
Cross multiply
2x=18
Simplify
x=9
Answer:
9
Step-by-step explanation:
you find the scale factor by using the new shapes number which would be 3 and its corresponding value from the old shape which would be 2
3/2 is equal to 1.5 so thats the scale factor ud need to use
6*1.5 is 9 so thats the answer
find the variable h+ 1/2 = 3 1/4
Answer:
h=2 3/4
Step-by-step explanation:
2 3/4+1/2=
you can convert 1/2 into 2/4 so they have like denominators
2 3/4+2/4= 2 5/4 which is also equal to 3 1/4
a. Create a real world scenario of a study with a population mean and a population standard deviation. Include the information that a random sample of a given size (greater than 30) was selected from the population.
b. Check the conditions for the assumptions about the sampling distribution.
c. Draw, label and describe the sampling distribution in context.
Answer:
The t-score has the same interpretation as the z-score. It measures how far in standard deviation units \stackrel{-}{x} is from its mean μ. For each sample size n, there is a different Student’s t-distribution. The degrees of freedom, n – 1, come from the calculation of the sample standard deviation s. Remember when we first calculated a sample standard deviation we divided the sum of the squared deviations by n − 1, but we used n deviations \left(x-\stackrel{-}{x}\text{values}\right) to calculate s. Because the sum of the deviations is zero, we can find the last deviation once we know the other n – 1 deviations. The other n – 1 deviations can change or vary freely. We call the number n – 1 the degrees of freedom (df) in recognition that one is lost in the calculations. The effect of losing a degree of freedom is that the t-value increases and the confidence interval increases in width.
Properties of the Student’s t- Distribution 0.05, 95% level of confidence, we find the t-value of 1.96 at infinite degrees of freedom.
Step-by-step explanation: