Answers
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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Related Questions
Please help me with this question.
Answers
The radius of the circle having an equation x²+ y²-10x+6y-47 = 0 is 9 units.
What is the radius of a circle?The radius is defined as a line segment joining the center of the circle or a sphere to its circumference or boundary.
Given the general form of the equation of circle described as
x²+ y²-10x+6y-47 = 0, we need to find it radius,
The given equation is;
x²+ y²-10x+6y-47 = 0
Complete the squares so add 25 and 9 on both sides of the equation
x²+ y²-10x+6y-47+25+9 = 34
(x-5)² + (y+3)² -47 = 34
(x-5)² + (y+3)² = 81
(x-5)² + (y+3)² = 9²
Comparing with the standard form of the equation of a circle is (x - h)² + (y - k)² = r²,
r² = 9²
r = 9
Hence, the radius of the circle having an equation x²+ y²-10x+6y-47 = 0 is 9 units.
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Drag each sentence to the correct category.
Determine the type of account that each description applies to.
If no deposits or withdrawals
are made, money held in this
account may increase or
decrease.
There is no risk of losing any
money put in this account.
Interest income is the only
way to earn money in this
type of account.
This account may generate
income from a variety of
sources.
Answers
Saving Account : Option B and Option C
Investment account : Option A and Option D.
Explain the terms Saving Account and Investment account?The savings account is an account of deposit account at which money you deposit earns interest. Savings accounts are trustworthy and secure given that they are insured accounts.An account that can store both cash and other investments that can be purchased and traded for financing is characterized as an investment account.Savings Account:
In this account, there is no chance that any money would be lost. An interestThe only method to make money in this kind of account is through income.Investment Account:
Money maintained in this account could rise or fall if no deposits or withdrawals are made.A number of sources may produce money for this account.To know more about the Saving Account, here
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The correct question is:
The table given in a similar question sourced on the site is presented as follows;
Saving Account || investment account
The options are;
A. If no deposit or withdrawals are made, money held in this account may increase or decrease
B. There is no risk of losing any money put in this account
C. Interest income is the only way to earn money in this type of account
D.This account may generate income from a variety of sources
A clock lost 2 minutes and 36 seconds in 78 days. How many seconds did it loose per day?
Answers
Answer: 2
Because with your Hint all you had to do was solve the problem and you should have gotten 2 soooo, the day lost 2 seconds per day.
Answer:
the clock lost 2 seconds per day
Exit Ticket: At many county and state fairs, you must purchase
tickets if you wish to go on the rides. Different rides require
different numbers of tickets. The Ferris wheel, for example,
might require three tickets, while the bumper cars might require
two. Before you buy any tickets, it might be helpful to know
which rides you plan to ride, and how many tickets you will need.
Write about it! Each ride requires 3 tickets. If a ticket costs
$1.50, write an equation to find the total cost of y of x rides.
How much will it cost to ride 10 rides?
Answers
An equation to find the total cost of y of x rides is y = 3x.
The cost to ride 10 rides is equal to $15.
How to determine the total cost of y of x rides?In order to write an equation that model this situation, we would assign variables to the number of tickets and the total cost respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of tickets.Let the variable y represent the total cost.Next, we would translate the word problem into an algebraic equation based on the fact that each ride requires 3 tickets and a ticket costs $1.50 as follows;
y = 3x
For the cost of 10 rides, we have:
y = 10x
When x = 1.50, the total cost is given by:
y = 10(1.50)
y = $15.
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Use +, -, x and to write an equation which gives an answer of 7. Put in brackets if necessary. 4( )4( )4( )4( )4=7
PLEASE HELP
(10 points)
Answers
The equation that gives the answer as 7 is 4 (×) 4 (-) 4 (÷) 4 = 7.
What are mathematical operations?Subtraction and Addition
Many problems in everyday life can be resolved using addition and subtraction. Simply said, the mathematical terminology for "combining" and "taking away" are addition and subtraction. When we combine or increase, we are adding. We take away or decrease when we subtract.
Multiplication is another operation that shares the commutative characteristic. Similar to addition and subtraction, multiplication and division have opposing purposes. While division is intended to demonstrate the dividing or subdividing of a value into smaller groups, multiplication serves the purpose of representing numerous groups of a single value.
4 (×) 4 (-) 4 (÷) 4 = 7
Hence, the equation that gives the answer as 7 is 4 (×) 4 (-) 4 (÷) 4 = 7.
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Define random error. Define random error. Random error has values that are consistent with one another. Random error has no probability of being too high or too low. Random error is an error that tends to be either too high or too low. Random error has an equal probability of being too high or too low. Random error has values that are close to the true value.
Answers
Define random error: B) Random error is an error that tends to be either too high or too low.
WHAT IS RANDOM ERRORRandom error, is an error caused by factors that cannot be predicted, you could even say that these factors seem temporary.
So, it is very difficult to predict, because it is still random. One might even say, this random error occurred, while the test was being conducted. Even worse, random errors do not have to occur in the first test, it could be in the second or third test and so on.
Random error is a very small and dissimilar effect in each test implementation, for example the effect of fluctuations in the voltage, temperature or humidity conditions of the accommodation and test environment.
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HELP PLEASEEE!!!
The chef at a school cafetería asked 100 male and 100 female students whether they like peas. 58 or the makes said they like peas. 64 of the females said they dislike peas. Which two way table correctly shows these results ?
Answers
Salut/Hello!
Answer: D
Step-by-step explanation:
Total of male students: 100
Male students that like peas: 58
Male students that dislike peas: 100 - 58 = 42
Total of female students: 100
Female students that dislike peas: 64
Female students that like peas: 100 - 64 = 36
Total of people that like peas: 58 + 36 = 94
Total of people that dislike peas: 42 + 64 = 106
I hope it'll be useful! :]
Translate the following sentence into and algebraic inequality
The quotient of a number, x, and nine is less than eight more than the product of five and the same number x
Answers
the answer is
x/9 < 8 + 5x
Which point best approximates the location of 78√?
point B
point A
point D
point C
Answers
The point that best approximates the square root of 78 is a point that is between 8 and 9.
How to estimate a non-exact square root?The estimate of a non-exact square root of x is done finding these two numbers listed as follows:
The greatest number less than x that is a perfect square(i.e., it has an exact square root), which we call a.The smallest number greater than x that is a perfect square(i.e., it has an exact square root), which we call b.For this problem, we have that these two parameters are given as follows:
8² = 64 < 78.9² = 81 > 78.Hence the point that best approximates the location of the square root of 78 is a point between 8 and 9.
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how have surface processes shaped the landforms on earth? (not multiple choice)
Answers
Weathering is the process by which rock and soil are broken down by physical, chemical, and biological processes. This can create a variety of landforms, such as rock formations, canyons, and valleys.
Erosion is the movement of rock and soil by water, wind, or ice. This can create landforms such as rivers, canyons, and deltas. Erosion also plays a role in shaping mountains by removing the softer layers of rock and leaving behind the harder, more resistant rock.
Deposition is the process by which sediment is laid down by water, wind, or ice. This can create landforms such as beaches, sand dunes, and delta.
All these processes interact with each other and shape the landforms on earth, for example rivers erode the land and deposit the sediment in another place, creating a delta, and the wind can erode the rock and create natural arches, or canyons.
Additionally, tectonic forces also play a role in shaping landforms, such as the formation of mountains and valleys, and volcanic activity can create landforms such as volcanoes and lava fields.
A triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3". Find the radius of a circle with the same vertex as a center, if the arc in the triangle bisects the area of the triangle.
Answers
Answer:
To calculate the radius of the circle, you need to use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. Therefore, in your triangle, the ratio of the length of the side opposite the 60° angle to the sine of the 60° angle is the same as the ratio of the length of the other two sides to their respective sines.
Let's call the two adjacent sides of the triangle a and b, respectively. The Law of Sines states that:
a/sin(60°) = b/sin(30°)
The length of side a is 12, and the length of side b is 12 times the square root of 3. This means that:
12/sin(60°) = (12√3)/sin(30°)
We can rearrange this equation to calculate the radius of the circle:
r = 12 * sin(30°) / sin(60°)
This gives us a radius of 12√3.
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a square of area 81cm2 is cut to make 2 rectangles
Answers
Answer:
rectangle A
length = 9cm
width = 6cm
rectangle B
length = 9cm
width = 3cm
Step-by-step explanation:
Given any real number, there is a real number that is greater. a. Given any real number r, there is __________ s such that s is _______. b. For any _____, ______ such that s > r.
Answers
(a) Given any real number r, there is a real number s such that s is greater than r.
(b) For any real number r, there exists a real number s such that s > r.
(a) For some real number r, there exists another real number s such that s is greater than r.
Complete statement is, Given any real number r, there is a real number s such that s is greater than r.
(b) For real number r, there exists another real number s such that s is greater than r, represented as s> r.
Complete statement is, For any real number r, there exists a real number s such that s>r.
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Question 3
Elias ordered 6 books online for a total of $105. Each book cost the same. He applied a
$2 discount per book. What was the original cost of each book?
Let d represent the cost of each book, in dollars. Fill in the blanks to create an equation
to solve the problem:
(d-
The cost of each book was $
Answers
When purchasing 6 books online for a total of $105 and each costing the same, the starting cost of a book is $19.5.
what is unitary method ?The component technique is a way of problem-solving where you first calculate the cost of a single component, then multiply that value to get the answer. Simply expressed, a single product value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and counterpart are equivalent. (Linear Algebra, Academic Analysis, Mathematics of Matrix or Operators)
given
Step: Since the cost of all six books is $105 and they are all the same price. she paid $17.5 for each book, making
Therefore, the price she paid for the book was 17.5 + $2, which is its original price of 107 / 6 = 17.5.
When purchasing 6 books online for a total of $105 and each costing the same, the starting cost of a book is $19.5.
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Answer:
Step-by-step explanation:
u need to explain more to the question
What is the result when the number 32 is decreased by 25%?
Answers
Answer: 69 bozo LLLLLLLLLLLLLLLLLLLLLLLLLLL
Step-by-step explanation:
69
18. The numbers 1, 4, 9, 16, 25, 36...... are examples of ________________________
Answers
Step-by-step explanation:
squared numbers.
1 = 1² = 1×1
4 = 2² = 2×2
9 = 3² = 3×3
16 = 4² = 4×4
25 = 5² = 5×5
36 = 6² = 6×6
look at the image and find the answer
Answers
The value of length x is 9 units.
The value of length y is 6 units.
What are the values of x and y?
The value of length x and length y is calculated by applying congruency theory as shown below.
side of the triangle with length 12 ≡ x
side of the triangle with length 8 ≡ 6
x / 6 = 12 / 8
x = ( 6 ) x ( 12 / 8 )
x = 9
The length of side y is calculated as follows;
h / 3 = 4 / 6
h = 3 ( 4/6 )
h = 2
y = 4 + 2 = 6
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Tiffany has a goal to complete a triathlon. The race consists of a 2.4 -mile swim, a 112 -mile bike ride, and a 26.2 -mile run. In training, Tiffany can swim at an average pace of 2.2mph . She rides her bike at an average of 20.8mph and runs at 6.2mph . Estimate how long it will take her to complete the triathlon.
Answers
Answer:
10.7 hrs
Step-by-step explanation:
For each of the three legs time = distance / rate
so
2.4 / 2.2 + 112 / 20.8 + 26.2 /6.2 = 10.7 hrs
Please help me solve this
Extra points
Answers
tumor is injected with 0.92
grams of Iodine-125. After 1 day, the amount of Iodine-125 has decreased by 1.15%
.
Write an exponential decay model with A(t)
representing the amount of Iodine-125 remaining in the tumor after t
days. Enclose arguments of the function in parentheses and include a multiplication sign between terms. For example, c*ln(t)
.
Then use the formula for A(t)
to find the amount of Iodine-125 that would remain in the tumor after 8.5
days. Round your answer to the nearest thousandth (3 decimal places) of a gram.
Answers
Answer:
A(t) = 0.92e^(-0.0115t)
The amount of Iodine-125 that would remain in the tumor after 8.5 days is 0.58 grams.
Step-by-step explanation:
A(t) = 0.92e^(-0.0115t)
To find the amount of Iodine-125 that would remain in the tumor after 8.5 days, we can plug in 8.5 for t in the exponential decay model:
A(8.5) = 0.92e^(-0.0115 * 8.5) = 0.92e^(-0.097875) = 0.92 * 0.9079 = 0.832
So, the amount of Iodine-125 that would remain in the tumor after 8.5 days is approximately 0.832 grams.
Help this is urgent!!
Answers
The derivative of the function is f'(s) = 9s^2 + 2 and the values are 146 and 11
How to determine the derivative of the functionsFrom the question, we have the following parameters that can be used in our computation:
f(s) = 3s^3 + 2s
Differentiate the function
So, we have
f'(s) = 9s^2 + 2
When the values are evaluated, we have
f(-4) = 9(-4)^2 + 2 = 146
f(-1) = 9(-1)^2 + 2 = 11
Hence, the values are 146 and 11
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Amber wrapped a gift for her daughter. The gift is shapped like a rectangular prism. Its base measures 9 inches by 0.5 feet. Part A: Amberly used exactly 408 square inches of paper to wrap the gift. Explain how tall the gift is assuming the paper does not overlap
Answers
Answer:
The gift is 4.5 feet tall, since 408 square inches is equal to a rectangular prism with dimensions of 9 inches by 0.5 feet by 4.5 feet.
Step-by-step explanation:
Please help me answer this
Extra points
Answers
Step-by-step explanation:
All you have to do is distribute the 2 and -2 to the inside of the parentheses. When you multiply it out, then combine all of your like terms, but remember to include the negative sign in the second set of parentheses.
2(7x+5)-2(4x+3)
(2*7x)+(2*5)-(2*4x)-(2*3)
14x+10-8x-6
This is the correct answer, but if you want to simplify it further, the answer would be 6x+4.
Option:-
[tex] \underline{ {\boxed{ \rm{ \red{\bold{C ) 14x + 10 - 8x - 6}}}}}}[/tex]
Ans:-
[tex] \rm{14x + 10 - 8x - 6}[/tex][tex] \: [/tex]
[tex] \rm{2( 7x + 5 ) - 2 ( 4x + 3 )}[/tex][tex] \: [/tex]
hope it helps! :)
HELP I NEED ANSWER ASAP
Answers
The rule that best describes the dilation of triangle ABC to create triangle A'B'C' is given as follows:
a. (x,y) -> (2x, 2y).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Considering a scale factor of k, the rule is given as follows:
(x,y) -> (kx, ky).
The scale factor for this problem is given as follows:
k = 2.
(as the larger triangle is formed as a dilation of the smaller triangle).
Hence the rule is given as follows:
(x,y) -> (2x, 2y).
Meaning that the correct option is given by option A.
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whitch figure is showig a ray
Answers
Answer: D.
Step-by-step explanation: It is a figure with no height or length, and it has indefinite length. Two rays are needed to make an angle.
Use the example above and fill in the missing values.
Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using
standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary
interest because the total Interest to be paid is $808.13.
After the fifth month, the borrower decides to prepay the whole loan. Under a stándard amortization plan the borrower
would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of
the total interest based on two series:
((n+35)+(n+34)+(n+33)+(n+32)+(n+31))
If you add 36, 35, 34, 33, and 32, the sum is
If you sum the numbers from 1 to 36, the sum is
{(n)+(n+1)+...+(n+35)}
The fraction (the first sum / the total sum) to the nearest tenth =
total interest.
%. The lender will multiply this fraction by the
The cumulative interest = (the percentage calculated above) x ($808.13) = $
The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78
plan is: $
Answers
The sum of the numbers 36, 35, 34, 33, and 32 is 36 + 35 + 34 + 33 + 32 = 160.
The sum of the numbers from 1 to 36 is (1 + 36) * 36 / 2 = 666.
The fraction (160 / 666) to the nearest tenth is 0.237, or 23.7%.
The cumulative interest using the Rule of 78 is (0.237 * $808.13) = $191.63.
The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is ($198.28 - $191.63) = $6.65.
What is a cumulative interest?Cumulative interest is the total amount of interest that has been accumulated on a loan or an investment over a certain period of time. It is the sum of all the interest charges that have been added to the original loan amount, and it increases with each passing period as interest is charged on the increasing balance.
This means that the cumulative interest will be higher at the end of a loan period than at the beginning, as more interest will have been charged. The cumulative interest can be used to calculate the total cost of a loan, including the interest charged, as well as to compare different loan or investment options.
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A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of three popular options, air-conditioning (A), radio (R), and power windows (W), were already installed. The survey found:
15 had air-conditioning (A),
12 had radio (R),
11 had power windows (W),
5 had A and P,
9 had A and R,
4 had R and W,
3 had all three options.
A. Construct a Venn diagram to illustrate the sets.
Answers
Answer:
Step-by-step explanation:
15-12=03
3X 11 =33
33-5=28
28-9=19
19-3=16
16 divided by 4= 4
so the awser is 4
The Dell Computer Company makes its own computers and delivers them directly to customers who order them via the Internet. To achieve its objective of speed, Dell makes each of its five most popular computers and transports them to warehouses from which it generally takes one day to deliver a computer to the customer. This strategy requires high levels of inventory that add considerably to the cost. To lower these costs the operations manager wants to use an inventory model. He notes demand during lead time is normally distributed and he needs to know the mean to compute the optimum inventory level. He observes 25 lead time periods and records the demand during each period. The manager would like a 95% confidence interval estimate of the mean demand during lead time. Assume that the manager knows that the standard deviation is 75 computers. Construct and interpret the confidence Interval Estimator.
Answers
The 95% confidence interval estimate of the mean demand during lead time is given as follows:
[tex]\overline{x} \pm 29.4[/tex]
The interpretation is that we are 95% sure that the sample mean is within 29.4 computers of the population mean.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the equation presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given as follows:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameter values are given as follows:
[tex]\sigma = 75, n = 25[/tex]
Hence the interval is given as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]\overline{x} \pm 1.96 \times \frac{75}{\sqrt{25}}[/tex]
[tex]\overline{x} \pm 29.4[/tex]
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the angle of elevation to the top of a building in new york is found to be 5 degrees from the ground at a distance of 2 miles from the base of the building. using this information, find the height of the building in feet. (hint: 1 mile
Answers
The height of the building will be 897.6 feet if the angle of elevation is 5 degree and distance is 2 miles.
The height, length of angle of elevation and the base of the triangle will form the right angled triangle. Thus, to find the height, we will use the formula -
tan theta = perpendicular ÷ base, where theta is the angle of elevation.
Now, keep the values in formula to find the height of the building.
height = tan 5 × 2
Keep the value of angle
height = 0.087 × 2
Performing multiplication on Right Hand Side of the equation
height = 0.17 mile
As per the known information, 1 mile = 5280 feet
So, 0.17 mile = 897.6 feet
Thus, the height of building is 897.6 feet.
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need help please, here is screenshot
Answers
A conversion of the expression (x - 3)² + 1 to the standard form of a quadratic function is x² - 6x + 10.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.
In Mathematics, the standard form of a quadratic function is given by ax² + bx + c = 0.
By applying the following binomial expression to the given quadratic function, we have:
(a - b)² = a² - 2ab + b²
(x - 3)² = x² - 2(x)(3) + 9
x² - 2(x)(3) + 9 = x² - 6x + 9
Therefore, the given expression can be rewritten as follows;
(x - 3)² + 1 = x² - 6x + 9 + 1
(x - 3)² + 1 = x² - 6x + 10.
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