Find the general solution of the differential equation y" – 7y' – 18y = –26t + 36t². NOTE: Use t as the independent variable. Use c₁ and c₂ as arbitrary constants. y(t) = ...
Answers
The general solution is the sum of the complementary and particular solutions: y(t) = c1e9t + c2e-2t + (3t² - 2t)
To find the general solution of the differential equation y" – 7y' – 18y = –26t + 36t², we have to follow the given steps: First, let us write the auxiliary equation associated with the given differential equation as (m - 9) (m + 2) = 0. We get m = 9 and m = -2.
Hence, the general solution of the given differential equation is given by:y(t) = c1e9t + c2e-2t + (3t2 - 2t). Therefore, y(t) = c1e9t + c2e-2t + (3t² - 2t) is the general solution of the given differential equation.
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Related Questions
The zoo has 12 Emperor penguins, which makes up 24% of all penguins at the zoo. How many penguins live at the zoo?
Answers
Answer:
\(50\) penguins
Step-by-step explanation:
Let \(p\) = number of penguins at the zoo
\(24\%p=12\) (Is given that 12 Emperor penguins at the zoo make up 24% of total penguins)
\(0.24p=12\)
\(p=12\div0.24\)
\(p=50\)
∴ There are \(50\) penguins at the zoo
Hope this helps :)
(PLEASE HELP QUICK) A high school has 4.5 times as many students as the middle school. If the high school has 2934 students, how many students are in the middle school
Answers
pls help asap if you can!!!!
Answers
The statement that proves that angle XWY is equal to angle ZYW is
A. If two parallels are cut by a transverse, then alternate interior angles are congruent
What are alternate interior anglesAlternate interior angles are a pair of angles that are formed on opposite sides of a transversal line when two parallel lines are intersected by the transversal.
When a transversal intersects two parallel lines, it creates eight angles. Among these angles, the alternate interior angles are located on the inside of the parallel lines and on opposite sides of the transversal.
In a parallelogram, the two opposite sides are parallel to each other hence the line crossing them will lead to formation of alternate interior angles
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3/10 divided divided by 6 =
Answers
Answer:
.05 or 1/20
Step-by-step explanation:
If you meant 3/10 divided by 6 then the answer is .05 aka 1/20
May I have brainliest if this helped you?
Hope this helped!!
Bella was here :)
You either meant the fraction 3/10 by 6 or 3 divided 10 divided by 6
Since I am not sure which one, I will do the work for both
1. 3/10 / 6
Convert 6 into a fraction
6 = 5 10/10
5 10/10=50/10
3/10 / 50/10
3/10 * 10/50 = 30/500
30/500= 3/50
3/50
2. 3 divided by 10 divided by 6
3 divided by 10 = 0.3
0.3 divided by 6 = 0.05
0.05
Hope this helps
what is the area of the following circle
Answers
Answer:
25π
Step-by-step explanation:
The area of a circle is calculated with the following formula :
π r²
r(radius) is given as 5 so the area is
π*5^2 = 25π
please help mee!!! tia
Answers
Answer:
D. 3y + 1
Step-by-step explanation:
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option D) \(3y + 1\)
»»————- ★ ————-««
Here’s why:
The phrase for the expression is 'one more than three times a number', where 'y' is the unknown number.⸻⸻⸻⸻
\(\boxed{\text{Breaking The Phrase Down:}}\\-------------\\! - \text{Three times a number 'y'} \rightarrow \text{the product of 3 and y} \rightarrow \boxed {3y}\\! - \text{One more than....}\rightarrow \boxed{ + 1}\\--------------\\\boxed{\text{Putting it all together:}}\\\\!-\text{One more than three times a number 'y'} \rightarrow \boxed{3y+1}\\\\\text{The correct answer should be }\boxed{\text{Option D}}.\)
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Assume you deposit $1,000 every three months at a 3 percent
annual rate, compounded quarterly. How
much will you have at the end of 5 years?
Answers
The future value of the deposits at the end of 5 years is approximately $6,138.74.
To calculate the future value of the deposits, we can use the formula for compound interest:
FV = P(1 + r/n)^(nt)
Where: FV is the future value
P is the principal amount (initial deposit)
r is the annual interest rate (3% in this case)
n is the number of times interest is compounded per year (quarterly in this case)
t is the number of years
In this case, the principal amount is $1,000, the annual interest rate is 3% (or 0.03), the number of times interest is compounded per year is 4 (quarterly), and the number of years is 5.
Plugging in these values into the formula, we get: FV = $1,000(1 + 0.03/4)^(4*5)
Calculating this, the future value of the deposits at the end of 5 years is approximately $6,138.74.
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Shawn wrote down the activities for his day on Saturday. In which situation will his activity result in a final value of zero?
1 point
A. Shawn places four quarters in a jar of quarters which contains four quarters.
B. In the morning, Shawn added six hard candies to a jar which contained four hard candies. By the end of the day he ate ten candies from this jar.
C. Shawn starts out on the ground and then climbs ten feet on a ladder.
D. Shawn travels east ten feet and then travels south ten feet
Answers
The situation in which Shawn's activity will result in a final value of zero is Shawn travels east ten feet and then travels south ten feet. The correct option is D.
This is because when Shawn travels east ten feet, he moves horizontally to the right of his starting point. When he travels south ten feet after that, he moves vertically downwards from his previous position, cancelling out the horizontal movement he made earlier.
The displacement caused by Shawn's movement in the east direction is equal in magnitude but opposite in direction to the displacement caused by his movement in the south direction.
The net displacement of Shawn's movement is zero, and he ends up back at his starting point. Options A, B, and C do not involve any movements that result in a net displacement of zero.
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What is the value of x in the triangle at the right?
Answers
Answer:
x=20
Step-by-step explanation:
To find x use the fact that all triangle's angles sum to 180. This means that if you add all of the angles together, they will always equal 180 degrees. So, create an equation to represent this.
The equation looks like this:2x+65+75=180
Then, combine the like terms2x+140=180
Next, subtract 140 from both sides2x=40
Finally, divide both sides by 2x=20
This means that the missing angle is 40 degrees.
If 6 cakes cost $96, how much will 11 cakes cost?
Answers
Answer:
the answer is 176.
Step-by-step explanation:
you would divide 96 by 6 which is 16. and 16 is how much each cake cost. so then multiply 16 by 11 and you'll get 176. :)
Scenario 1A Calculate the following amounts for a participating provider who bills Medicare and has no deductible left. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Coinsurance amount (20% paid by) $ Medicare payment (80 percent of the PFS) $ Provider write-off $ Scenario 1B Calculate the following amounts for a participating provider who bills Medicare and remaining annual deductible for the patient. Submitted charge (based on provider’s regular fee) $650 Medicare participating physician fee schedule (PFS) $450 Patient pays $100 remaining on their deductible $ Remaining amount for Insurance and patient to pay $ (PFS - $100) Coinsurance amount (20% of remaining amount) $ Total paid by patient (deductible & 20% of remaining) $ Medicare payment (80 percent of the remaining amount) $ Provider write-off $
Answers
Scenario 1A:
Coinsurance amount is $90
Medicare payment is $360
Provider write-off is $290
Scenario 1B:
Remaining amount for Insurance and patient to pay is $350
Coinsurance amount is $70
Total paid by patient is $170
Medicare payment is $280
Provider write-off is $370
Scenario 1A:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Coinsurance amount (20% paid by patient): $
Medicare payment (80% of the PFS): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Coinsurance amount (20% paid by patient):
Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)
Coinsurance amount = 0.2 * $450 = $90
Medicare payment (80% of the PFS):
Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)
Medicare payment = 0.8 * $450 = $360
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $360 = $290
Scenario 1B:
Submitted charge: $650
Medicare participating physician fee schedule (PFS): $450
Patient pays $100 remaining on their deductible
Remaining amount for Insurance and patient to pay: $
Coinsurance amount (20% of remaining amount): $
Total paid by patient (deductible & 20% of remaining): $
Medicare payment (80% of the remaining amount): $
Provider write-off: $
To calculate the missing amounts, we can use the provided information:
Remaining amount for Insurance and patient to pay:
Remaining amount for Insurance and patient to pay = PFS - remaining deductible
Remaining amount for Insurance and patient to pay = $450 - $100 = $350
Coinsurance amount (20% of remaining amount):
Coinsurance amount = 20% of the remaining amount
Coinsurance amount = 0.2 * $350 = $70
Total paid by patient (deductible & 20% of remaining):
Total paid by patient = remaining deductible + coinsurance amount
Total paid by patient = $100 + $70 = $170
Medicare payment (80% of the remaining amount):
Medicare payment = 80% of the remaining amount
Medicare payment = 0.8 * $350 = $280
Provider write-off:
Provider write-off = Submitted charge - Medicare payment
Provider write-off = $650 - $280 = $370
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What is the area of the triangle?
4
:10
2
units
Answers
Answer:
Your answer is 20
Step-by-step explanation:
as the formula 1/2*4*10=20.
hope it help you if yes then please make me the brainiest.
Thank you
parshv
Consider a hypothetical closed economy in which the marginal propensity to consume (MPC) is 0.5 and taxes do not vary with income (that is, taxes are fixed rather than variable and the income tax rate t=0 ). The following graph shows the aggregate demand curves ( AD1 and AD2 ), the short-run aggregate supply (AS) curve, and the long-run aggregate supply curve at the potential GDP level. The economy is currently at point A.
Answers
The economy is currently experiencing gap of hundred billion. To close this gap, one option would be for the government to decrease government purchases by $ 125 billion (assuming net taxes do not change) billion. If the government kept its purchases constant, it could also close the gap by increase net taxes (taxes minus transfers) by $ 125 billion.
We have a graph present in above figure. Graph shows the following
aggregate demand curves are represented by ( AD1 and AD2 ),the short-run aggregate supply (AS) curve,the long-run aggregate supply curve at the potential GDP level. The economy is currently through at point A.Marginal propensity to consume (MPC)
= 0.5
There is an expansionary gap, since AD1 and short run aggregate supply, SRAS meet right side of LRAS. The gap is for $100 billion, because the corresponding horizontal axis gives values 700 and 600; the difference becomes (700 – 600 =) $100 billion.
Government purchase (G) is a component of AD. IF G decreases AD would shift to the left side; this reduces the gap $125 is chosen, because it will reduce the lowest money supply [$125 / (1 – MPC) = 125 / 0.5 = $250 billion], which shifts AD1 to the left and reduces the gap.
Tax (T) reduces AD. Therefore, AD would shift to the left side; this reduces the gap. $125 is chosen, because it will reduce the lowest money supply [$125 / (MPC/MPS) = 125 / 1 = $125 billion], which shifts AD1 to the left and reduces the gap.
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Complete question:
The above figure complete the question.
Consider a hypothetical closed economy in which the marginal propensity to consume (MPC) is 0.5 and taxes do not vary with income (that is, taxes are fixed rather than variable and the income tax rate t=0 ). The following graph shows the aggregate demand curves ( AD1 and AD2 ), the short-run aggregate supply (AS) curve, and the long-run aggregate supply curve at the potential GDP level. The economy is currently at point A.
The economy is currently experiencing gap of____ billion. Government purchases by ___$ billion (assuming net taxes do. To close this gap, one option would be for the government to not change) billion. If the government kept its purchases constant, it could also close the gap by ____net taxes (taxes minus transfers) by ___$
(Hint: In this case, since taxes do not vary with income, the formula for the multiplier for a change in fixed taxes is(- MPC/ 1- MPC).
8^1/6 multiply 2^x = 32^1/2 Work out the exact value of x. WILL GIVE BRAINLIEST FOR CORRECT ANSWER!!!
Answers
Answer:
x=2
Step-by-step explanation:
8^1/6 x 2^x = 32^1/2
Divide by 8^1/6
2^x= 32^42/8^y6
2^x=4
but 4= 2^2
2^x= 2^2
x=2
I hope helps you and if you consider and want you can give me a Brainly crown
Answer:
\(\huge\boxed{x=2}}\)
Step-by-step explanation:
\(8^\frac{1}{6}\cdot2^x=32^\frac{1}{2}\\\\(2^3)^\frac{1}{6}\cdot2^x=(2^5)^\frac{1}{2}\qquad|\text{use}\ (a^n)^m=a^{nm}\\\\2^{3\cdot\frac{1}{6}}\cdot2^x=2^{5\cdot\frac{1}{2}}\\\\2^{\frac{1}{2}}\cdot2^x=2^\frac{5}{2}\qquad|\text{use}\ a^n\cdot a^m=a^{n+m}\\\\2^{\frac{1}{2}+x}=2^\frac{5}{2}\iff\dfrac{1}{2}+x=\dfrac{5}{2}\qquad|\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\x=\dfrac{4}{2}\\\\x=2\)
what is the rate of change for the function y= 5x+ 25
Answers
Answer:
5
Step-by-step explanation:
rate of change = slope = 5
Which relation is a function?
A {(-1,3), (-2,6), (0,0), (-2,-2)}
B {(-2,-2),(0,0), (1, 1), (2, 2)}
C {(4,0), (4,1),(4,2), (4,3)}
D
{(7,4), (8,8), (10, 8), (10, 10)}
Answers
Answer: B is a function
Step-by-step explanation:
All the x cordinates in (x,y) are different.
The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
Answers
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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57 is 0.3% of what number? Use pencil and paper. Would you expect the answer to be a lot less than
57, slightly less than 57, slightly greater than 57, or a lot greater than 57? Explain.
Answers
Answer:
57 is 0.3% of 19000
Step-by-step explanation:
57 = 0.3x (rewrite it into an equation!)
57/0.003 = x (solve)
x = 19000
tadah!
Marcle is registering for her college classes Which cost 105 per unit. If each classes, can she take to have a maximum cost of 1,365?
Answers
If each unit costs 105 dollars and Marcle wants to spend a maximum of 1,365 dollars on classes, then she can take up to 13 classes.
To calculate the maximum number of classes Marcle can take, we need to divide the maximum cost she is willing to spend by the cost of each unit. So, we have:
Maximum cost Marcle is willing to spend = $1,365
Cost of each unit = $105
Number of classes Marcle can take = Maximum cost Marcle is willing to spend / Cost of each unit
Number of classes Marcle can take = $1,365 / $105
Number of classes Marcle can take ≈ 12.98
Since Marcle cannot take a fraction of a class, we round down to the nearest whole number to get the maximum number of classes she can take without exceeding her budget. Therefore, Marcle can take up to 13 classes.
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Which one of the following best defines the notion of the significance level of a hypothesis test?
Answers
The probability of committing type 1 error best describes notion of significance level of hypothesis test.
What is probability?
Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.
Complete Question:
Which one of the following best describes the notion of the significance level of a hypothesis test?
i) the probability of committing a type 1 error
ii) the probability of committing a type 2 error
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6th Grade Math:
A 5-pound bag of cat food costs $11. What is the unit price of the cat food?
Answers
Answer:
The unit rate is 2.20. For a single pound of cat food it would cost $2.20
There are GCF of two numbers is three and the LCM is 180. If one of the numbers is 45,what is the other number ?
Answers
Answer:
The other number is 12
Step-by-step explanation:
There are GCF of two numbers is three and the LCM is 180. If one of the numbers is 45,what is the other number ?
Let us represent the other number as x
There are GCF of two numbers is three and the LCM is 180.
Therefore:
45 × x = 3 × 180
45x = 3 × 180
x = 3 × 180/45
x = 12
Therefore, the other number is 12
what is 0.3, 2., 0.321, 2.52 ordered from least to greatest
Answers
Answer:
0.321 ,0.3 ,2, 2.52
Step-by-step explanation:
Pay attention in class child
0.3, 0.321, 2, 2.52
Explanation:
Not sure how to explain, but it’s correct.
Item 7 the random variable x has mean 12 and standard deviation 3. the random variable w is defined as w=7 2x. what are the mean and standard deviation of w?
Answers
The random variable x has a mean of 12 and a standard deviation of 3. The random variable w is defined as w = 7 + 2x. We need to find the mean and standard deviation of w.
To find the mean and standard deviation of the random variable w, we can use properties of linear transformations of random variables. In this case, w is a linear transformation of x, given by the equation w = 7 + 2x.
Mean of w:
The mean of w can be found by substituting the mean of x into the equation for w. Since the mean of x is 12, we have:
Mean of w = 7 + 2(12) = 7 + 24 = 31.
The standard deviation of w:
The standard deviation of w can be found using the property that the standard deviation of a linear transformation of a random variable is equal to the absolute value of the coefficient of the random variable multiplied by the standard deviation of the original random variable. In this case, the coefficient of x in the equation for w is 2.
Standard deviation of w = |2| * standard deviation of x = 2 * 3 = 6.Therefore, the mean of w is 31 and the standard deviation of w is 6.
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The Bureau of Labor Statistics compiles and makes publicly available data from a range of different sectors of the economy. One value that is reported is a weighted average of the costs of certain goods, called the Consumer Price Index (CPI). The CPI is related to the price but is not a dollar amount. The rise in prices is used as a metric of inflation. To make the metric more reliable, a chained CPI was created. The regular CPI does not update the types of goods it averages often enough to reflect the market trends, like a switch from apples to oranges resulting from a rise in apple prices. The chained CPI is a measure of price that takes this into account, and there are several bills that are tied to the chained CPI index in order to determine the payout the bill allots each year. The monthly average chained CPI for urban apparel for all urban consumers for 10 consecutive months is provided below. The data are not seasonally adjusted. Construct a box and whisker plot using a TI-83, TI-83 Plus, or TI-84 graphing calculator to choose the correct plot below. All plots have the following window settings: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Answers
Answer:
I can provide guidance on how to create a box and whisker plot on a TI-83, TI-83 Plus, or TI-84 graphing calculator using the given data.
To create a box and whisker plot:
Enter the data into a list on the calculator. For example, L1={90.1, 91.1, 91.5, 92.2, 92.5, 93.1, 94.0, 94.6, 96.1, 98.3}.
Press STAT, then go to Edit.
Select L1, then press STAT again and select CALC.
Choose 1-Var Stats and press Enter. This will generate a list of statistics for the data set.
Press 2nd, then Y= (STAT PLOT).
Select Plot1, then turn it on.
Choose Box Plot as the plot type.
Select L1 as the data list.
Set the X list to any unused list (e.g. Xlist: L2).
Make sure the frequency is set to 1.
Set the window settings as follows: Xmin=88, Xmax=100.5, Xscl=0.5, Ymin=−0.5, Ymax=3.5, Yscl=1, Xres=1.
Press GRAPH to view the box and whisker plot.
Note: If the plot does not display properly, try adjusting the Ymax and Ymin values until the plot is visible.
If two events, event a with probability p(a) and event b with probability p(b) are complementary events then __________.
Answers
If two events, event A with probability P(A) and event b with probability P(B) are complementary events then the sum of the probability of events A and B will be one.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
When one event happens if and only if the other one doesn't, two occurrences are said to be complimentary. The odds of two complementary events equal one.
P(A) + P'(A) = 1
The chance of events A and B added together will equal one if events A with probability P(A) and event B with probability P(B) are complementary occurrences.
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Find the hourly rate of pay for each of the following jobs: a) Tamara owns a salon and earns R1050 for 6 hours and 15 minutes of work.
Answers
Answer:
₹168 per hour
Step-by-step explanation:
The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.
HoursWe know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...
(15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h
Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.
Hourly rateThe pay per hour is found by dividing pay by hours.
₹1050/(6.25 h) = ₹168/h
Tamara's hourly rate of pay is ₹168 per hour.
You swam the length of the pond shown below. How far did you swim? If necessary, round your answer to the nearest foot.
Answers
Answer:
The answer is 25 feet.
Step-by-step explanation:
You have to apply Pythagoras Theorem :
\( {c}^{2} = {15}^{2} + {20}^{2} \)
\( {c}^{2} = 625\)
\(c = \sqrt{625} \)
\(c = 25 \: feet\)
What is 900 times 900
Answers
Answer:
810000 is your answer
Step-by-step explanation:
9x9=81 and the 4 0's
what was the approximate number of mobile cellular subscriptions per 100 people in zimbabwe in 2003? the display gives the result of performing an exponential regression on a data set where the inputs are years since 2000 and the outputs are the corresponding mobile cellular subscriptions per 100 people in zimbabwe.
Answers
The number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is 4.
Exponential model that shows the number of mobile cellular subscriptions per 100 people in Zimbabwe since 2000,
Exponential model is a mathematical function which express in the form of a = \(e^{x}\) where, x is power and the function is increasing exponentially.
\(y = ab^{x}\)
Where,
a=1.067905095,
b=1.501755837,
y = \(1.067905095(1.501755837 )^{x}\)
Thus, for finding the number of subscriptions in 2003,
x = 3,
Hence, the number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is
y = \(1.067905095(1.501755837 )^{3}\) = 4
The number of mobile cellular subscriptions per 100 people in Zimbabwe in 2003 is 4.
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The given question is incomplete the complete question is :
Answer:4
Step-by-step explanation: