Given equation is y''' + 343y = 0 which is a third-order linear differential equation. To find the general solution of the equation, we can use the characteristic equation of the differential equation as follows;
Let y = erx be the trial solution of the differential equation, where e is the exponential function and r is an unknown constant to be determined. Substituting the trial solution into the differential equation, we have; y''' + 343y = 0 y' = rerx, y'' = rerx, y''' = rerx. Substituting into the differential equation, we have;r³erx + 343erx = 0. Factorizing out erx, we have erx(r³ + 343) = 0For erx ≠ 0;r³ + 343 = 0r³ = -343r = (-343)¹/³ = -7 (r = -7, since we are working with real forms of the equation). Therefore, the general solution of the third order linear differential equation is;
y = c₁e^-7x + c₂e^-7x cos(12.124x) + c₃e^-7x sin(12.124x) where c₁, c₂, and c₃ are arbitrary constants.
To know more about Laplace Transform, click here:
https://brainly.com/question/30759963
#SPJ11
Yezenia is filling up her outdoor swimming pool to get ready for summer time. She leaves the garden hose running for 1000 minutes in order to fill the pool, which has a volume of 15,460 gallons. What is the approximate rate at which water leaves the garden hose?
Answer:
15.46 gallons per minutes
Step-by-step explanation:
Garden hose was running for 1000 minutes
Volume of the pool = 15,460 gallons
What is the approximate rate at which water leaves the garden hose?
Rate at which water leaves the garden hose = Volume of the pool / running time of the hose
= 15,460 gallons / 1000 minutes
= 15.46 gallons per minutes
Rate at which water leaves the garden hose = 15.46 gallons per minutes
Someone please help me.
Felipe's age is ≥ 5
Step-by-step explanation:
Difference of F's age and 4: f - 4
Twice: 2 (f -4) ≥ 2
2f - 8 ≥ 2
2f ≥ 10
f ≥ 5
Answer:
Step-by-step explanation:
residents of the town smithfield like to consume pizzas, but each pizza requires 10 people to produce it and takes a month. if the town has a total of 100 people, what is the maximum amount of pizza the residents can consume in a year?
The number of pizzas the people of the town will produce in a year, obtained using the simple mathematical operations, is 120 pizzas.
What are mathematical operations?Mathematical operations include operations of additions, subtraction, division, and multiplication.
The number of pizzas produced in a year can be obtained using mathematical operations as follows;
The number of people required to produce one pizza in a month = 10 people
The number of people in the town = 100 people
The number of pizza'a that the people in the town can produce in a month is therefore;
Number of pizza's produced in a month = 100/10 = 10
The number of months in a year = 12 months
The number of pizzas the people in the town can produce in a year = 10 × 12 = 120 pizzas
Learn more on mathematical operations here: https://brainly.com/question/1794851
#SPJ1
A map has a scale of 1 inch : 40 miles. Use the given map distance to find the actual distance.
1.) 12 inches
2.) 1 foot
Answer:
480 miles
Step-by-step explanation:
If one inch equals 40 miles, then 12 times that would be 4800 miles.
1 Inch 12 Inches
---------- = ------------------
40 Miles 480 Miles.
Let p, q, and r be the propositions You get an A on the final exam. You do every exercise in this book. You get an A in this class. p 9: r: (3 pts) Express as an English sentence: q-p b) (p) Express as an English sentence: ar - (-p A-q) Pe 2 c) (4 pts) Write the proposition below using the propositions p, q or r as well as logical connectors (including negation): "To get an A in this class or get an A on the final exam, you need to do every exercise in the book." 7. (pt) Use truth table to determine whether [-p Apv q)] →q is a tautology. (you may not need to use all the rows and columns available below.) 8. (4 pts) Use truth table to determine whether [(pv q) Apr)^(q→r)] →r (you may not need to use all the rows and columns available below.) is a tautology.
q - p can be expressed as "If you do every exercise in this book, then you get an A on the final exam."
¬(p ∨ ¬q) can be expressed as "You need to do every exercise in this book and not get an A on the final exam."
The proposition "To get an A in this class or get an A on the final exam, you need to do every exercise in the book" can be written as "(r ∨ p) → q."
q - p: This proposition states that if you do every exercise in this book (q), then you get an A on the final exam (p).
¬(p ∨ ¬q): This proposition states that you need to do every exercise in this book (q) and not get an A on the final exam (¬p).
"(r ∨ p) → q": This proposition expresses that to get an A in this class (r) or get an A on the final exam (p), you need to do every exercise in the book (q). It is a conditional statement, where the antecedent is (r ∨ p) and the consequent is q.
For the truth table analysis:
[-p ∨ (p ∧ ¬q)] → q: The truth table should be constructed using the propositions p, q, and r, along with logical connectors. However, the given proposition doesn't involve the proposition r, so it cannot be analyzed using the truth table.
[(p ∨ q) ∧ r) ∧ (q → r)] → r: The truth table should be constructed using the propositions p, q, and r, along with logical connectors. However, the given proposition doesn't involve the proposition p, so it cannot be analyzed using the truth table.
Learn more about antecedent click here;
brainly.com/question/28845527
#SPJ11
EASY POINTS!!
PLS ADD A DISC!!
All interior angle degrees must add up to 180 degrees.
the little square means that it is a right angle (90 degrees)
30 + 90 = 120
Y = 60
A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure below. Of the following, which is closest to the volume of the grain silo, in cubic feet?
A) 261.8
B) 785.4
C) 916.3
D) 1047.2
Answer:
A. 261.8
Step-by-step explanation:
espero ayudar sorry
Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.
Answer:
2/4 quarts of juice is 0.125 Gallons of juice for
Step-by-step explanation:
Please Give Brainliest
Answer:
He divided instead of using multiplication
Step-by-step explanation:
Can someone please respond to this
Answer:
that's easy, use the 6969 equation, with a some 420's and that will do it
The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool, they moved 2 feet to the right and 4 feet up to create the center of their formation (Point C). From the center of their formation, they then formed a circle that goes through a point 3 feet to the left and 4 feet up (Point D). What is the equation of the circle?
Answer:
The equation of the circle is;
(x - 2)² + (y - 4)² = 5²
Step-by-step explanation:
We note that the general equation of a circle is given as follows;
(x - h)² + (y - k)² = r²
Where;
(h, k) = The coordinates of the center of the circle
r = The radius of the circle
The given parameters are;
The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool
The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation
Taking the center of the pool as the origin of the coordinate plane system, we have;
The coordinate of the center of the circle = The coordinate of their motion from the center of the circle
∴ The coordinate of the center of the circle = (2, 4)
∴ (h, k) = (2, 4)
h = 2, k = 4
The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)
∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5
r = 5
The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;
(x - 2)² + (y - 4)² = 5².
WXYZ is a parallelogram. Find the measure of angle Z
Given:
The figure of a parallelogram.
To find:
The measure of angle Z.
Solution:
We know that, the consecutive interior angles of a parallelogram are supplementary angles, it means there sum is 180 degrees.
In the given figure angle W and angle Z are supplementary angle. So,
[tex]m\angle W+m\angle Z=180^\circ[/tex]
[tex](18b-11)^\circ+(9b+2)^\circ=180^\circ[/tex]
[tex](27b-9)^\circ=180^\circ[/tex]
[tex](27b-9)=180[/tex]
Adding 9 on both sides, we get
[tex]27b=180+9[/tex]
[tex]27b=189[/tex]
[tex]b=\dfrac{189}{27}[/tex]
[tex]b=7[/tex]
Now,
[tex]m\angle Z=(9b+2)^\circ[/tex]
[tex]m\angle Z=(9(7)+2)^\circ[/tex]
[tex]m\angle Z=(63+2)^\circ[/tex]
[tex]m\angle Z=65^\circ[/tex]
Therefore, the correct option is C.
What is the product of 2b(b+11)? Show your work.
Answer:
25
Step-by-step explanation:
Answer:
2b^2 + 22
Step-by-step explanation:
2b(b + 11)
2b ×b + 2 × 11
2b^2 + 22
8-2(4×3-5)
does this equal -4?
Answer:
-6
Step-by-step explanation:
Answer:
No -6
Step-by-step explanation:
Jeremy wants to determine the number of solutions for the equation below without actually solving the equation. -3(x+1)+3x=-3(x-1)+3 Which method should Jeremy use? Determine whether the equation has the form a = a, and if it does, the equation has infinitely many solutions. Determine whether the equation has the form a = b, and if it does, the equation has no solution. Determine whether the equation has the form x = a, and if it does, the equation has one solution. Determine whether the equation has the form x = 0, and if it does, the equation has no solution.
Answer:C
Step-by-step explanation:
I have taken a test and it was right sorry if it isn’t right
Answer:
C
Step-by-step explanation:
determine whether the equation has the form x=a, and if it does, the equation has one solution
What additional information could be used to prove that the triangles are congruent using AAS or ASA? Check all that apply. B ≅ P and BC ≅ PQ A ≅ T and AC = TQ = 3. 2cm A ≅ T and B ≅ P A ≅ T and BC ≅ PQ AC = TQ = 3. 2 cm and CB = QP = 2. 2 cm
Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:
Option 1: B ≅ P and BC ≅ PQ
To prove that two triangles are congruent using AAS (Angle-Angle-Side) or ASA (Angle-Side-Angle) postulates, we need specific conditions met. Let's examine the given options:
1. B ≅ P and BC ≅ PQ:
This condition satisfies the AAS postulate since we have two angles and a corresponding side that are congruent.
2. A ≅ T and AC = TQ = 3.2 cm:
This condition satisfies the ASA postulate since we have two angles and the included side that are congruent.
3. A ≅ T and B ≅ P:
This condition alone does not satisfy either the AAS or ASA postulate, as we need to have at least one side congruent or an included side congruent to prove congruence.
4. AC = TQ = 3.2 cm and CB = QP = 2.2 cm:
This condition alone does not satisfy either the AAS or ASA postulate, as we need to have congruent angles as well.
Based on the given options, the additional information that could be used to prove congruence using AAS or ASA is:
- Option 1: B ≅ P and BC ≅ PQ
This satisfies the AAS postulate, and with the given information, we can conclude that the triangles are congruent.
For more questions on congruence
https://brainly.com/question/29789999
#SPJ8
Please help asap I’ll give Brainly to whoever gets it right.
Consider the inequality -20.2 > 0y. Which of the following must be true? Check all that apply.
You cannot divide by zero.
The inequality is equivalent to -20.2 > 0, which is false.
The solution is y > 0.
The solution is 0 > y.
The solution is y = 0.
Determine the integral of 8 (3x − 2)³ dx
The integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C, where C is the constant of integration.
To find the integral of 8(3x - 2)³ dx, we can apply the power rule of integration. According to the power rule, the integral of xⁿ dx is (xⁿ⁺¹ / (n + 1)) + C, where n is a constant and C is the constant of integration.
In this case, we have (3x - 2)³ as the integrand. We can rewrite it as 8(3x - 2)³ to simplify the expression. Since 8 is a constant multiplier, it can be factored out of the integral.
Using the power rule, we integrate each term separately. The integral of (3x - 2)³ is [(3x - 2)⁴ / 4] + C, where C is the constant of integration. Multiplying by the constant 8, we get 8[(3x - 2)⁴ / 4] + C.
Simplifying further, we can simplify the expression to 2(3x - 2)⁴ + C, where C is the constant of integration.
Therefore, the integral of 8(3x - 2)³ dx is 2(3x - 2)⁴ + C.
Learn more about integration here:
https://brainly.com/question/31744185
#SPJ11
A line passes through the points (-1, 10) and (3, 2). Which shows the graph of this line?
8
8
4
2
- 108
2
46
8 10
X
12
-8
-10
10
6
Answer:
C
Step-by-step explanation:
EDGE 2021
Find a85 of the sequence 4,9,14,19,….
Answer: 424
Step-by-step explanation:
The lifetime of an electronical component is to be determined; it is assumed that it is an ex- ponentially distributed random variable. Randomly, users are asked for feedback for when the component had to be replaced; below you can find a sample of 5 such answers (in months): 19,23,21,22,24.
Fill in the blanks below.
(a) Using the method of maximum likelyhood, the parameter of this distribution is estimated to λ = ________WRITE YOUR ANSWER WITH THREE DECIMAL PLACES .
(b) Let L be the estimator for the parameter of this distribution obtained by the method of moments (above), and let H be the estimator for the parameter of this distribution obtained by the method of maximum likelyhood. What comparison relation do we have between L and M in this situation? Use one of the symbols
< = or > to fill in the blank. L ________M
(a) Using the method of maximum likelihood, the estimated parameter of the exponential distribution is λ = 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we have L < M.
(a) The maximum likelihood estimation involves finding the parameter that maximizes the likelihood function based on the given data. In this case, using the sample of replacement times (19, 23, 21, 22, 24), the estimated parameter λ of the exponential distribution is calculated to be 0.050.
(b) Comparing the estimators obtained by the method of moments (L) and the method of maximum likelihood (M), we can determine the relationship between them. In general, the method of maximum likelihood tends to provide more efficient and precise estimators compared to the method of moments. Therefore, we have L < M, indicating that the estimator obtained by the method of maximum likelihood (M) is expected to be greater than the estimator obtained by the method of moments (L) in this situation.
To learn more about maximum likelihood (M), click here: brainly.com/question/30625970
#SPJ11
Consider the following argument by analogy.
Some doctors recommend that people over the age of 40 should get a physical every year. As one physician argued, "People take their car in for servicing every few months without complaint. Why shouldn’t they take similar care of their bodies?" [U.S. News & World Report, Aug. 11, 1986]
Analyze and evaluate this argument by doing the following: 1) Identify the two things being compared (A and B) and the property P attributed to B in the conclusion. 2) Identify the (unstated) properties (S) that are supposed to make A and B similar. 3) Analyze the argument into its inductive and deductive elements. The deductive step with be a valid syllogism with a universal major premise. 4) Evaluate the inductive generalization in the inductive step: a) Consider its initial plausibility given our other knowledge; b) Look for additional positive instances besides the one stated; c) Look for counterexamples.
The argument draws an analogy between car servicing and regular physicals for people over 40, highlighting the need for preventive care and maintenance. The deductive step is a valid syllogism with a universal major premise, and the inductive generalization is plausible given the potential benefits of regular check-ups, although individual circumstances may vary.
1) In this argument by analogy, two things are being compared: A) taking a car in for servicing every few months, and B) getting a physical every year for people over the age of 40. The property P attributed to B in the conclusion is the need for regular care or check-ups.
2) The unstated properties (S) that are supposed to make A and B similar include the idea that both cars and bodies require regular maintenance to ensure proper functioning and longevity. The argument assumes that just as neglecting car maintenance can lead to breakdowns and costly repairs, neglecting regular physical check-ups can lead to health problems and potential medical issues.
3) The deductive step of the argument can be formulated as follows:
Major premise: Cars need regular servicing to prevent breakdowns and maintain optimal performance.
Minor premise: Bodies are similar to cars in the sense that they require regular check-ups to prevent health issues and maintain optimal well-being.
Conclusion: People over the age of 40 should get a physical every year.
4) The inductive generalization in the argument relies on the plausibility of the comparison between car maintenance and physical check-ups. To evaluate its validity, we can consider the following:
a) The initial plausibility of the generalization: Given our knowledge that regular check-ups can help detect health problems early and promote overall well-being, it is reasonable to argue that regular physicals are beneficial, similar to regular car servicing.
b) Additional positive instances: We can find support for the generalization by examining medical recommendations and practices that emphasize the importance of regular check-ups for preventive care.
c) Counterexamples: While some individuals may not experience health issues or see the need for frequent physicals, the argument assumes that the general population will benefit from regular check-ups.
To know more about argument, refer to the link below:
https://brainly.com/question/9392384#
#SPJ11
The population of a city and 2005 was 18,000. By 2010, the cities population has grown to 32,800. It’s a population grows flow a linear model, what is the projected population for 2015?
Answer:
47,600
Step-by-step explanation:
The rate is (32,800 - 18,000) = 14,800 per 5 years
therefore :
in 2015 = 2010 + 5 years
the pop. will be :
32,800 + 14,800 = 47,600
The answer is 47,600.
Hope this helped :)
Find the perimeter of a square with a side length of 10 meters
side length of square=10
Now,
perimeter of square =4l
=4×10
=40m
Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.
WILL MARK BRAINLIEST IF ITS RIGHT!!! PLEASE HELLPP!!!!!
Answer:
114
Step-by-step explanation:
To find - Find the sum of all the two-digit numbers that divide 170 with a remainder of 5.
Proof -
The 2 digit number is 11
170 = 11(15) + 5
The two digit number is 15
170 = 15(11) + 5
The two digit number is 33
170 = 33(5) + 5
The two digit number is 55
170 = 55(3) + 5
∴ we get
The two digit numbers are
11, 15, 33, 55
Their sum is equals to
11 + 15 + 33 + 55 = 114
Solve for z.
x + y + z = 4
4x - y - z = 1
x + z = 2
Answer:
z= 4-x-y
z= -1+4x-y
z= 2-x
Step-by-step explanation:
z = 2-x
y = -1-z +4x
substitute
x -1 -2+x +4x + 2 -x = 4
-1 + 5x = 4
5x = 5
x = 1
z = 1
1+y+1 = 4
y = 2
LOOK RIGHT HERE! HELP FASSST EMERGENCY! Don't go past go to this question right here and no Decimal answers plz. Thanks the answer is not 144 BTW. Thank you.
Answer: 140cm^3
Step-by-step explanation:
PLSS HELPPP NO BOTS OR I WILL REPORT BUT PLS HELP ASAPP!! The graphs below of a function true or false?
Does anyone know about this question I give brainless If you answer this correctly
Answer:
Side x = 2.12132 = 3√2/2
Step-by-step explanation:
I used a triangle calculator to find side x
How is the dispersion of a Normal distribution compare to the dispersion of a T - distribution, Normal Distribution is more dispersed than the T distribution Normal Distribution is less dispersed than the T distribution Normal Distribution is dispersed in the same way as the T distribution
The dispersion of a Normal distribution is less dispersed than the T-distribution.
The dispersion of a distribution is measured by the standard deviation (or variance) of the distribution.
For a Normal distribution, the standard deviation is always known.
On the other hand, for a t-distribution, the standard deviation of the population is not known and is estimated using the sample standard deviation.
This means that the t-distribution has more uncertainty, which leads to more dispersion compared to the Normal distribution.
The t-distribution is often used when the sample size is small or when the population standard deviation is unknown. As the sample size increases, the t-distribution approaches the Normal distribution.
Therefore, for large sample sizes, both distributions become more or less similar.
In conclusion, the Normal distribution is less dispersed than the t-distribution.
To learn more about Normal distribution
https://brainly.com/question/12892403
#SPJ11
payment stream consists of three payments: $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today. What single payment, 80 days from today, is economically equivalent to the payment stream if money can be invested at a rate of 5%? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places.)
To find out the single payment that is economically equivalent to the payment stream of $2,500 due today, $3,000 due 100 days from today, and $3,500 due 240 days from today, we have to follow the below-given steps:
Step 1: Calculate the Future Value (FV) of each payment. Let's assume that "P" is the single payment we need to find out and "i" is the annual interest rate (5%)P = FV × [1 / (1 + i/365)^n] where n is the number of days between today and the payment date. For the first payment of $2,500 that is due today, the future value is $2,500 because it is already available today. Hence, no calculation is required for it. For the second payment of $3,000 that is due 100 days from today, Future Value (FV) = $3,000 × [1+(0.05/365)]^100 ≈ $3,093.29For the third payment of $3,500 that is due 240 days from today, Future Value (FV) = $3,500 × [1+(0.05/365)]^240 ≈ $3,701.85
Step 2: Calculate the Present Value (PV) of the payment stream by discounting each FV to 80 days from today. The formula for the present value of a future amount is PV = FV × [1 / (1 + i/365)^n] where "n" is the number of days between the date of the future amount and the date on which it is to be discounted. Here, we need to discount all three payments to 80 days from today. The number of days between today and 80 days from today is 80. So, we put n = 80 in the above formula.
For the first payment of $2,500 that is already available today, there is no need for any discounting. Hence, its present value is the same as its future value, i.e., $2,500.For the second payment of $3,093.29 that is due 100 days from today, Present Value (PV) = $3,093.29 × [1 / (1 + 0.05/365)^80] ≈ $2,893.16For the third payment of $3,701.85 that is due 240 days from today, Present Value (PV) = $3,701.85 × [1 / (1 + 0.05/365)^80] ≈ $3,243.11
Step 3: Add up the present values of all three payments to find the present value of the payment stream Present Value of the payment stream = $2,500 + $2,893.16 + $3,243.11 = $8,636.27
Step 4: Calculate the single payment that is economically equivalent to the payment stream by calculating its future value at the end of 80 days. FV = PV × (1 + i/365)^n where n = 80, i = 0.05, and PV = $8,636.27FV = $8,636.27 × (1 + 0.05/365)^80 ≈ $9,040.07Therefore, the single payment that is economically equivalent to the payment stream is $9,040.07.
Learn more about economically equivalent:
https://brainly.com/question/2599759
#SPJ11