Find the function y(x) satisfying d^{2}y/dx^2 = 4 -36x, y'(0)=5, and y(0) = 4.
Answers
The function y(x) that satisfies the given differential equation and initial conditions is:
\(y(x) = 2x^2 - 6x^3 + 5x + 4.\)
To find the function y(x) satisfying the given conditions, we need to integrate the differential equation twice.
First, we integrate both sides with respect to x:
\(d^2y/dx^2 = 4 - 36x\)
Integrating once gives:
\(dy/dx = 4x - 18x^2 + C\)
where C is a constant of integration.
Next, we integrate again:
\(y = 2x^2 - 6x^3 + Cx + D\)
where D is another constant of integration.
We can use the initial conditions y'(0) = 5 and y(0) = 4 to solve for C and D.
Using the first initial condition, we have:
y'(0) = 5 = 0 + 0 + C
so C = 5.
Using the second initial condition, we have:
y(0) = 4 = 0 + 0 + 0 + D
so D = 4.
Therefore, The function y(x) that satisfies the given differential equation and initial conditions is:
\(y(x) = 2x^2 - 6x^3 + 5x + 4.\)
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Related Questions
y= x-v/b
Solve for x
Answers
Answer:
x = y*b + v
Step-by-step explanation:
y=(x-v)/b
Multiply by b on both sides,
y*b = x-v
Add v on both sides,
x = y*b + v
If you need work lemmme know.
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answers
The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data
How to explain the informationThe answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.
In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.
Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.
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The average number of cans of creamed peas produced each day at the processing plant is 30,000 with a standard deviation of 3,200. Assuming a normal distribution, answer the following questions: 1. What is the probability of producing more than 36,000 cans per day
Answers
The probability of producing more than 36,000 cans per day is approximately 0.0319 or 3.19%.
To calculate the probability of producing more than 36,000 cans per day, we need to use the concept of standard deviation and the normal distribution.
First, we calculate the z-score, which tells us how many standard deviations a value is from the mean. To calculate z-score :
z = (x - μ) / σ
Where:
- x is the value we want to find the probability for (36,000 in this case)
- μ is the mean (30,000 in this case)
- σ is the standard deviation (3,200 in this case)
The following formula can be used to determine the z-score:
z = (36,000 - 30,000) / 3,200 = 6,000 / 3,200 ≈ 1.875
Next, we may determine the probability attached to the z-score using a calculator or a conventional normal distribution table. The region on the standard normal distribution curve to the right of the z-score represents the possibility of manufacturing more than 36,000 cans each day.
Looking up the z-score of 1.875 in a standard normal distribution table, we find that the probability is approximately 0.0319 or 3.19%.
Therefore, the probability of producing more than 36,000 cans per day is approximately 0.0319 or 3.19%.
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please help me solve this: solve for x
Answers
Answer:
x = 100
Step-by-step explanation:
You have to use the equation 15x + 10 = 6x - 6 + 70. This equation finds out that x = 6. Then, you would multiply 6 by 15. This gets 90. Finally, add 10 to that.
a basket is filled with an unknown number of eggs. when eggs are removed from the basket 2,3,4,5,or6atatime,oneeggisleftoverattheend. butnoeggsareleftoverwhentheyare removed 7 at a time. what is the smallest number of eggs that could have been in the basket?
Answers
The smallest number of eggs that could have been in the basket = 301
Given that the basket is filled with an unknown number of eggs.
Let N be the smallest number of eggs in the basket.
When eggs are removed 2, 3, 4, 5, or 6 at a time, one egg is left over at the end which means (N-1) is divisible by 2, 3, 4, 5, or 6, i.e. (N-1) is the least common multiple of 2, 3, 4, 5, and 6.
Since LCM (2, 3, 4, 5, 6) = 60
So, (N-1) should be a multiple of 60, then only (N-1) will be divisible by 2, 3, 4, 5, and 6. Therefore N is of the form 60k+1 (where k is an integer).
Since no egg is left over when they are removed 7 at a time, N should be a multiple of 7. Smallest multiple of 7 that is of the form 60k+1 (where k is an integer) is 301.
Hence the smallest number of eggs that could have been in the basket = 301.
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Please solve this ASAP! I WILL GIVE 20 points!
Answers
Answer:
15 parts
Step-by-step explanation:
Sugar: 20/4=5 you are doing five times the recipe because your using 5 times as much sugars. So for the flour 3*5=15
pls help me fill in the blank
Answers
Answer:
only a brainliest can answer this question
Step-by-step explanation:
sry i cant
Work out the base of a square with area,
A
= 64cm2.
Answers
Answer:
32
Step-by-step explanation:
because 64 divided by 2 is 32
A company has a multi-tier investment. They have $40 million in operating expenses each year and a cost of capital of 12%. They can invest $12 million in new technology for their plant. There is a 40% chance that the new equipment reduces expenses by 15%, a 30% chance it reduces expenses by 10%, and a 30% chance it reduces expenses by 5%. Shareholders will view the results after 3 years and vote on continuing or abandoning the project. Abandoning costs the company $5 million. If expenses drop 15%, there is a 95% chance the vote is yes, to continue for another 3 years, If they drop 10%, the vote has a 75% chance to be yes. If expenses only drop 5%, there is a 40% change the shareholders vote to continue the project. Draw out the timeline, decision tree, and calculate the probabilities for all six possible scenarios.
Answers
The probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.
To analyze the given scenario and calculate the probabilities for all six possible scenarios, let's create a decision tree and timeline to visualize the information provided.
Timeline:
Year 1: Initial investment of $12 million in new technology.
Year 2: Results evaluated by shareholders.
Year 3: Final decision made by shareholders.
Decision Tree:
``` ┌─── Continue (95%)
│
15% ─────┼─── Continue (75%)
│
$12 million ─────┼─── Continue (40%)
investment │
│
10% ─────┼─── Abandon ($5 million cost)
│
│
5% ─────┼─── Abandon ($5 million cost)
│
└─── Abandon ($5 million cost)
```
Now, let's calculate the probabilities for each scenario:
1. New equipment reduces expenses by 15% (40% probability):
Probability = 40% * 95% = 0.4 * 0.95 = 0.38 (38%)
Outcome: The shareholders vote to continue for another 3 years.
2. New equipment reduces expenses by 10% (30% probability):
Probability = 30% * 75% = 0.3 * 0.75 = 0.225 (22.5%)
Outcome: The shareholders vote to continue for another 3 years.
3. New equipment reduces expenses by 5% (30% probability):
Probability = 30% * 40% = 0.3 * 0.4 = 0.12 (12%)
Outcome: The shareholders vote to continue for another 3 years.
4. New equipment does not reduce expenses (10% probability):
Probability = 10%
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
5. New equipment reduces expenses by 15%, but shareholders vote to abandon (5% probability):
Probability = 15% * (1 - 95%) = 0.15 * 0.05 = 0.0075 (0.75%)
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
6. New equipment reduces expenses by 10%, but shareholders vote to abandon (5% probability):
Probability = 10% * (1 - 75%) = 0.1 * 0.25 = 0.025 (2.5%)
Outcome: The shareholders vote to abandon the project, incurring a $5 million cost.
To summarize, we have calculated the probabilities for all six possible scenarios based on the given information. The likelihood of each scenario and its respective outcome have been determined by multiplying the probabilities of the relevant events.
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Kira paid $15. 60 for 19. 5 centimeters of wire.
Find the unit price in dollars per centimeter.
If necessary, round your answer to the nearest cent.
HELP PLEASE!!! ASAP!!!
Answers
The unit price in dollars per centimeter is 80 cents.
:: Total wire length = 19.5 cm
:: Total amount paid = $15.60
Per unit price = [ (total amount paid) / (total wire length) ]
Per unit price = (15.60 / 19.5) $/cm
Per unit price = 0.8 ($/cm)
And as we know, $1 = 100 cents,
So,
$0.8 = 0.8 x 100 cents = 80 cents.
Therefore, the unit price in dollars per centimeter is 80 cents.
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HELP PLEASE!!!!! THIS IS DUE TODAY!!!!
Answers
Answer:
nonlinear
Step-by-step explanation:
it's a parabola
Amy and Vince want to save $18,000 so that they can take a trip to Europe in five years. How much must they save at the beginning of each month to have the money they need if they can get 5.5% interest in their savings account?
Group of answer choices
$435.39
$260.13
$323.45
$224.22
Answers
Amy and Vince must save approximately $323.45 at the beginning of each month to have the $18,000 they need for their trip to Europe in five years if they can get 5.5% interest in their savings account.
We know that Amy and Vince want to save $18,000 in five years and can earn 5.5% interest in their savings account, we need to adjust the interest rate to a monthly rate.
First, let's calculate the monthly interest rate (r) from the annual interest rate:
r = (1 + annual interest rate)^(1/12) - 1
= (1 + 0.055)^(1/12) - 1
= 0.0045107
Next, let's calculate the number of periods (n) in months:
n = 5 * 12
= 60 months
Using the future value of an ordinary annuity formula, we can solve for the monthly savings (PMT):
PMT = FV / [((1 + r)^n - 1) / r]
where:
FV = Future Value (desired savings amount)
r = Monthly interest rate
n = Number of periods
FV = $18,000
PMT = 18,000 / [((1 + 0.0045107)^60 - 1) / 0.0045107]
≈ $323.45
Therefore, Amy and Vince must save approximately $323.45 at the beginning of each month to have the $18,000 they need for their trip to Europe in five years.
Therefore, the correct option is $323.45.
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In ΔPQR, r = 60 inches, ∠Q=104° and ∠R=43°. Find the length of q, to the nearest inch.
Answers
Answer:
it's 85
Step-by-step explanation:
deltamath
If in ΔPQR, r = 60 inches, ∠Q=104° and ∠R=43° then the length of 80 inches.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.
a/sin A = b/sin B = c/sin C
where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.
Using this formula, we can solve for the length of side q as follows:
q/sin Q = r/sin R
q/sin 104° = 60/sin 43°
q = (60 sin 104°)/sin 43°
q = 79.9 inches
Therefore, the length of q, to the nearest inch, is 80 inches.
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15-7 x 2 x 2 to the 3rd power
Answers
Answer:
5832
Step-by-step explanation:
15 - 7 = 8
8 × 2 = 16
16 + 2 = 18
18 × 18 × 18 = 5832
In the figure, OAPB is a quadrant of a circle and OAP is a sector. If | AOP = 30° and the area of the shaded region is 462 cm2, then find the length of the arc PB. A P B
Answers
By answering the above question, we may state that As a result, the arc's expressions PB length is around 20.45 cm.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
Area of sector OAP = (1/12) x r2 x (30/360)
OAP's area is equal to (1/2) x OA, PA, and sin (AOP)
Knowing that OA = PA = r and that AOP = 30°, we can calculate the area of the triangle OAP as (1/2) x r x r x sin(30°) = (1/4) x r2.
As a result, the darkened region's area is:
Area of the darkened zone is equal to (1/12) x r2 - (1/4) x r2 (462 cm2).
When we simplify this equation, we obtain:
\((\pi/3 - 1) x r^2 = 1848\)
The result of dividing both sides by (/3 - 1) is:
\(r^2 = 1848 / (π/3 - 1) = 378.9\)
When we square the two sides, we obtain:
\(r ≈ 19.47\\PB = (1/6) x 2r = (1/3) x r = 20.45 cm\), where
As a result, the arc's PB length is around 20.45 cm.
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Jamiya's family is going shopping. There are three
people, including her, that need new school clothes. The
total amount they can spend is $618.36. If Jamiya had
another sibling how much more money would the family
need to go shopping?
Answers
What is the longest version of pi? Please type the whole thing.
Answers
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198938095257201065485863278865936153381827968230301952035301852968995773622599413891249721775283479131515574857242454150695950829533116861727855889075098381754637464939319255060400927701671139009848824012858361603563707660104710181942955596198946767837449448255379774726847104047534646208046684259069491293313677028989152104752162056966024058038150193511253382430035587640247496473263914199272604269922796782354781636009341721641219924586315030286182974555706749838505494588586926995690927210797509302955321165344987202755960236480665499119881834797753566369807426542527862551818417574672890977772793800081647060016145249192173217214772350141441973568548161361157352552133475741849468438523323907394143334547762416862518983569485562099219222184272550254256887671790494601653466804988627232791786085784383827967976681454100953883786360950680064225125205117392984896084128488626945604241965285022210661186306744278622039194945047123713786960956364371917287467764657573962413890865832645995813390478027590099465764078951269468398352595709825822620522489407726719478268482601
Find the ordered triplet (x,y,z) for the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7
Answers
The ordered triplet (x, y, z) or the following system of equations: x+3y + 2z = 1, 03x+y+5z=10, -2x-3y+z=7 is (-170/127, -89/127, 282/127).
Start with the first equation:
x + 3y + 2z = 1
Isolate x by subtracting 3y and 2z from both sides:
x = 1 - 3y - 2z
Substitute this expression of x into the second equation:
0.3x + y + 5z = 10
Substitute the value of x found in step 2 into this equation:
0.3(1 - 3y - 2z) + y + 5z = 10
0.3 -0.9y -0.6z + y + 5z = 10
0.1y + 4.4z = 9.7
y + 44z = 97
Solve for y by isolating it:
y = 97 - 44z
Substitute this expression of y into the first equation:
x + 3(97 - 44z) + 2z = 1
x + 291 - 132z + 2z = 1
Solve for x:
x = 130z - 290
Substitute this expression of x into the third equation:
-2(130z - 290) - 3(97 - 44z) + z = 7
-260z + 580 - 291 + 132z + z = 7
Solve for z:
127z = 282
z = 282/127
Substitute this value of z into the expression of y:
y = 97 - 44(282/127)
= -89/ 127
Substitute the values of z into the expression of x:
x = 130(282/127) - 290
= - 170/ 127
So the solution of the system of equations is: x = -170/127, y = -89/127, z = 282/127.
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What is a complex root of a polynomial?
Answers
The roots of a polynomial are the values of x for which the polynomial evaluates to 0.
A complex root is a root for which the real and imaginary parts are not both 0. If a polynomial has a complex root, that means that there is at least one value of x for which the polynomial evaluates to 0.
This can happen in two ways: either the polynomial has a real root and an imaginary root, or it has two complex roots. In either case, the complex roots must be found in order to determine the polynomial's factorization.
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Klein reads 30 pages of a book on Monday and 1/8th of the book on tuesday.He completed the remaining 1/4th jf gbe book on Wednesday. How many pages are there in the book?
Answers
How many pages are there in the book: The total number of pages in the book is 48.
Give the total number of pages accessing the book = x.
On Monday, he read 30 pages.
On Tuesday, he read 1 / 8 the total pages i.e. x / 8
On Wednesday, he read the excess 1 / 8 of the total pages i.e. x / 4
In this way, we have a relationship,
30 + x /8 + x / 4= x
i.e. 240 + x + 2x / 8 = x
i.e. 240 + 3x = 8x
i.e. 5x = 240
i.e. x = 48
Subsequently, the total number of pages in the book is 48.
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A normal population has a mean of $85 and standard deviation of $15. You select random samples of 40.
a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n = 40. What condition is necessary to apply the central limit theorem?
b. What is the standard error of the sampling distribution of sample means? (Round your answer to 2 decimal places.)
c. What is the probability that a sample mean is less than $84? (Round z value to 2 decimal places and final answer to 4 decimal places)
d. What is the probability that a sample mean is between $84 and $86? (Round z value to 2 decimal places and final answer to 4 decimal places)
e. What is the probability that a sample mean is between $86 and $87? (Round z value to 2 decimal places and final answer to 4 decimal places) f. What is the probability that the sampling error ( x¯ − μ) would be $1.50 or less? (Round z value to 2 decimal places and final answer to 4 decimal places)
Answers
a. Necessary cοnditiοn tο apply the central limit theοrem is that sample shοuld be randοmly selected and shοuld nοt cοntain high οutliers.
b. standard error = 2.3717
c. The probability that a sample mean is less than $84 is 0.3372.
d. The probability that a sample mean is between $84 and $86 is 0.3256.
e. The probability that a sample mean is between $86 and $87 0.1367.
f. The probability that the sampling error (x−μ) would be $1.50 or less is 0.4714.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
a)
since sample size is larger than 30 ;necessary cοnditiοn tο apply the central limit theοrem is that sample shοuld be randοmly selected and shοuld nοt cοntain high οutliers.
b)
std errοr=σx=σ/√n=15/√40 =
2.3717
c)
prοbability = P(X<84)
=(Z<(84-85)/2.372)
=P(Z<-0.42)
=0.3372
d)
prοbability = P(84<X<86)
=P((84-85)/2.372)<Z<(86-85)/2.372)
=P(-0.42<Z<0.42)
=0.6628-0.3372
=0.3256
e)
prοbability =P(86<X<87)
=P((86-85)/2.372)<Z<(87-85)/2.372)
=P(0.42<Z<0.84)
=0.7995-0.6628
=0.1367
f)
prοbability =P(83.5<X<86.5)
=P((83.5-85)/2.372)<Z<(86.5-85)/2.372)
=P(-0.63<Z<0.63)
=0.7357-0.2643
=0.4714
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what's 4x + 3 = 2x + 17
Answers
Answer:
x=7
Step-by-step explanation:
Move all terms containing x to the left side of the equation.
2x+3=17
Move all terms not containing x to the right side of the equation.
2x=14
Divide each term by 2 and simplify.
x=7
Need help with school
Answers
Answer:
x=9
Step-by-step explanation:
Answer:
Dont we all
Step by step Explanation
In ΔGHI, the measure of ∠I=90°, GH = 8.5 feet, and IG = 4.7 feet. Find the measure of ∠G to the nearest tenth of a degree.
Answers
Answer:
4.7
Step-by-step explanation:
Identify the length, width, and height of the figure formed.
WHOEVER ANSWERS FIRST GETS BRILLIANT
Answers
Answer:
216 units
Step-by-step explanation:
lenght x width x height
∠A=angle, A, equals
^\circ
∘
degrees
Round your answer to the nearest hundredth.
\
Answers
Answer:
What are you asking?
Step-by-step explanation:
∠A=angle, A, equals ^\circ ∘ degrees Round your answer to the nearest hundredth. \
Give the geometric representation of 2x+ 1= x-4 as an equation in (a) one variable (b) two variables
please help
Answers
Answer:
Step-by-step explanation:
2x+1=x-4
2x-x= -4-1
1x=-5
x=-5when finding a minimum in a linear programming problem, it is possible to find more than one minimum value. yes or no
Answers
The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.
In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'
We need to state whether it is true or false.
We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.
Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.
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What is the length of the shortest side if the perimeter of the rectangle is 56 inches?
Answers
Answer:
12
Step-by-step explanation:
3x + 3x + 5x - 4 + 5x - 4 = 56
16x - 8 = 56
16x = 64
x = 4
3(4) = 12
Hope this helps! Pls give brainliest!
Answer:
area= 5x(5x-4)
Step-by-step explanation:
perimiter= 2(5x-4) + 2(5x-4)
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answers
Answer:
9/13
Step-by-step explanation:
rise = y₂ - y₁ = -1 - (-10) = -1 + 10 = 9
run = x₂ - x₁ = 9 - (-4) = 9 + 4 = 13
Step-by-step explanation: