Solve the given initial-value problem.
y''' − 2y'' + y' = 2 − 24ex + 40e5x, y(0) =
1
2
, y'(0) =
5
2
, y''(0) = −
11
2
the values for the first 3 derivatives derivatives of y are 1/2, 5/2, -11/2 respectively
The given differential equation:
y''' − 2y'' + y' = 2 − 24ex + 40e5x,
y(0) = 1/2, y'(0) = 5/2, y''(0) = −11/2
Therefore, the next solution is 13/2
Differential Equation:
In mathematics, a differential equation is an equation relating one or more unknown functions to their derivatives. In applications, functions usually represent physical quantities, derivatives represent rates of change, and differential equations define the relationship between them. These relationships are common.
Now,
Given differential equation is
y''' - 2y'' +y' = 2- 24eˣ +40e⁵ˣ ------------ (1)
Auxiliary equation is m³ - 2m² +2m = 0
Now,
m(m² - 2m +2) = 0
⇒ m(m-1)² = 0
Therefore, m = 0,1,1
Therefore,
[tex]y_{c} = c_{1}+ c_{2} e^{x} + c_{2}x e^{x}[/tex]
Now, we have to find the particular solution by method of undetermined coefficient.
[tex]y'_{y} = a + b(x^{2} e^{x} +2xe^{x} ) +5ce^{x}[/tex]
⇒ [tex]y''_{p} = a + bx^{2} e^{x} +2bxe^{x} +5ce^{x}[/tex]
⇒ [tex]y''_{p} = b(x^{2} e^{x} +2xe^{x}) + 2b(ex^{x}+ e^{x} +25ce^{x}[/tex]
⇒ [tex]y'''_{p} = bx^{2} e^{x} +6bxe^{x} +6be^{x} +125ce^{5x}[/tex]
Putting these values in differential equation (1), we get:
y'''(0) = 13/2
Complete Question:
Solve the given initial-value problem. y''' ? 2y'' + y' = 2 ? 24ex + 40e5x, y(0) = 1 2 , y'(0) = 5/ 2 , y''(0) = ? 13/ 2
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helpppp ASAP.
1. What is the height of the cone? Explain how you found the height. (4 points)
2. Now that you have the height of the cone, how can you solve for the slant height, s? (3 points)
3. How far does the ant crawl to get from the base of the cone to the top of the hill? Show your work. (3 points)
1. The height of the cone is, 22.18 mm.
2. The slant height is, 28.14 mm.
3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.
What is Volume?In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.
The volume of cone V = (1/3)πr²h
Given that,
The volume = 8792 mm³
1. by using the formula to solve for h,
we get h = (3V)/(πr²).
Plugging in the values given,
we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.
Therefore, the height of the cone is approximately 22.18 mm.
2. it is known that, from the Pythagoras theorem
s² = h² + r²,
where s is the slant height, h is the height, and r is the radius.
Plugging in the values we found in part 1,
we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².
Taking the square root of both sides, we get s ≈ 28.14 mm.
Therefore, the slant height is approximately 28.14 mm.
3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.
Using the value we found in part 2,
the length of the slant height is approximately 28.14 mm.
Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.
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There are 32 computers in a computer lab—some are laptops, and some are desktops. If there
are 8 more laptop computers than desktop computers, how many of each type of computer are
in the lab?
Answer:
There are 12 desktop computers and 20 laptop computers.
Step-by-step explanation:
32:2=16
8:2=4
16-4=12
16+4=20
Based on historical data, your manager believes that 32% of the company's orders come from first-time customers. A random sample of 80 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is less than 0.33?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's
approach and calculations.
(Enter your answer as a number accurate to 4 decimal places.)
The probability that the sample proportion is less than 0.33 is approximately 0.7422.
How to model sample proportion?The sample proportion of first-time customers can be modeled by a normal distribution with mean p, the true proportion of first-time customers, and standard deviation [tex]\sqrt{\frac{p(1-p)}{n}}[/tex], where n is the sample size.
In this case, p = 0.32, n = 80, and we want to find [tex]P(\hat{p} < 0.33)[/tex].
The standardized version of [tex]\hat{p}[/tex] is given by:
[tex]z = \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
Substituting the values, we get:
[tex]z = \frac{0.33-0.32}{\sqrt{\frac{0.32(1-0.32)}{80}}} \approx 0.6579[/tex]
Using a standard normal distribution table (or a calculator or statistical software), we find that the probability of z being less than 0.6579 is approximately 0.7422.
Therefore, the probability that the sample proportion is less than 0.33 is approximately 0.7422.
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The three graphs represent the progress of three runners in a 500-meter race.
The red solid line represents runner A. The purple dotted line represents runner B.
The blue dashed line represents runner C.
Options: Runner A, Runner B, Runner C, 0, 20, 55, 90.
The answers include the following:
Runner B ran at a constant rate throughout the race.Runner C stopped running for a while and it occurred between 20 to 55.Runner A also sprinted at different speeds.Runner A won the race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
From the graph, we can deduce that Runner A won the race because it attained a greater distance when compared to the time for all the other runners.
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On the following composite figure, the longer edge length is 14 millimeters. The shorter edge length is 8 millimeters. The width of the figure, at its longest point, is 11.3 millimeters. Find the area of the figure. Explain or show how you got your answer. Note: Lines that look parallel are parallel, and angles that look like right angles are right angles.
The area of the given composite figure with a side length of 14mm and an edge length of 8mm is 158.2 mm².
What is a composite figure?
A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. A variety of forms that we encounter every day are composite figures that can be created from two or more fundamental figures.
The figure is given below.
From the figure, we can see that the sides of a triangle at the top and bottom are the same.
So the triangle cut from the bottom is placed at the top of the figure.
When the cut triangle is placed back at the bottom, we get a rectangle of length 14 mm and breadth 11.3 mm, as given below.
So the area of the given composite figure is the same as the area of the rectangle.
The area of the rectangle = length * breadth = 14 * 11.3 = 158.2 mm²
Therefore the area of the given composite figure is 158.2 mm².
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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.4 mmHg (millimeters of mercury) for a sample of size 686 and a sample standard deviation 5.5 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 90% confidence.
What is the 90% confidence interval to estimate the population mean? Round your answer to one decimal place.
Answer:
{30.1,30.7}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]
Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.
Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]
How do I solve for side a and b and angle B when when side c equals 968m, angle a is 33 degrees abs 25 minutes and angle c is 90 degrees
Answer:
Step-by-step explanation:
Calculated based on 2 given angles and 1 given side.
∠B = 180° - A - C = 0.99484 rad = 57°
∠B = 57°
a = c·sin(A)/sin(C) = 527.21059
b = c·sin(B)/sin(C) = 811.83311
Whats the correct answer answer asap for brainlist
A quotation isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2.
The option (a) is correct.
What is quote?Famous people who discuss their opinions on a given subject often employ quotation marks around their words. The brief nature of a quotation allows it to share individuality. The citation served as a means of sharing ideas and serving as a source of historical information.
The quotation, which is sometimes referred to as "quote vomit," was cut off from the remainder of the text.
The sentences are directed at their objective. Understanding how the universe functions and how we fit into it can be done through the metaphor of weaving.
As a result, the quote isolated from the rest of the writing - sometimes called "quote vomit" type of quote is Sample #2. Therefore, option (a) is correct.
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A scientific model is used to predict the average global high
temperature on earth by anaylizing the data from previous
years. In 1940, the temperature was 55° F However, the
temperature has grown to 59.5° F in 1990.
A) Find an equation in the form T = ax + b, where x is the
number of years since 1940 and T is the average gobal high
temperture on Earth.
Answer:
chapter 1
Step-by-step explanation:
A local high school has 1,152 students with 391 freshmen, 351 sophomores, 208 juniors, and 202 seniors. What is the
relative frequency of sophomores at this high school?
The relative frequency of sophomores at this high school is 39/128.
How to find the relative frequency?
Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).
We are given that;
Total students=1152
Freshmen=391
Sophomores=351
Juniors=208
Seniors=202
Now, to find frequency of sophomores
=number of sophomores/total number of students
=351/1152
=117/384
=39/128
Therefore, the relative frequency will be 39/128.
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What is the size, in degrees, of the missing angle?
45
65°
Solve the equation. 15 - 2x = -4(x + 1) + 9
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
x = -5
Step-by-step explanation:
15 - 2x = -4(x+1) + 9
-4(x+1) can be distributed and simplified to -4x - 4
15 - 2x = -4x - 4 + 9
15 - 2x = -4x +5
-2x + 4x = 5 - 15
2x = -10
x = -5
Answer:
[tex]x=-5[/tex]
Step-by-step explanation:
Given
[tex]15-2x=-4(x+1)+9[/tex]
Simplify the right side by applying the distributive property.
[tex]15-2x=(-4*x)+(-4*1)+9[/tex]
[tex]15-2x=-4x-4+9[/tex]
Add [tex]-4[/tex] and 9.
[tex]15-2x=-4x+5[/tex]
Add [tex]4x[/tex] to both sides of the equation.
[tex]15-2x+4x=5[/tex]
Add [tex]-2x[/tex] and [tex]4x[/tex].
[tex]15+2x=5[/tex]
Subtract [tex]15[/tex] from both sides of the equation.
[tex]2x=-10[/tex]
Divide both sides of the equation by [tex]2[/tex].
[tex]x=-5[/tex]
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That are a valid decomposition of c (x )such that c equals f ring operator g g (x )equals x squared f (x )equals cube root of x plus 1 end root g (x )equals x squared plus 1 f (x )equals cube root of x g (x )equals x plus 1 f (x )equals cube root of x squared end root g (x )equals cube root of x plus 1 f (x )equals x squared
By using the composition of functions, we can find valid decompositions of c(x) using f(x) = [tex](x+1)^{1/3}.[/tex] and g(x) = x²
A function is a rule that takes an input value and produces an output value.
One way to do this is to use the composition of functions. The composition of two functions f(x) and g(x) is denoted as f(g(x)). This means that we first apply g(x) to the input, and then apply f(x) to the output of g(x). In other words, we first evaluate g(x), and then plug that result into f(x) to get the final output.
Using this concept, let's look at the first set of functions. We are given
=> c(x) = f ◦ g (x) = (x²) f(x) = [tex](x+1)^{1/3}.[/tex]
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x², and f(x) = [tex](x+1)^{1/3}.[/tex] This is a valid decomposition of c(x).
Similarly, in the second set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x² + 1.
This means that c(x) is the composition of two functions, f(x) and g(x). We can see that g(x) = x² + 1, and [tex](x+1)^{1/3}.[/tex] This is also a valid decomposition of c(x).
In the third set of functions, we have
=> c(x) = f ◦ g (x) = [tex](x+1)^{1/3}[/tex] g(x) = x + 1, and f(x) = [tex](x^2)^{1/3}=x^{2/3}[/tex]
This is another valid decomposition of c(x).
Finally, in the fourth set of functions, we have
=> c(x) = f ◦ g (x) = x² g(x) = [tex](x+1)^{1/3}[/tex], and f(x) = [tex]x^{2/3}[/tex].
This is yet another valid decomposition of c(x).
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Question 4 (10 points)
(03.06 MC)
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work. (10 points
The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.
Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³
Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³
The volume of this cylinder is 1.5 times that of the cone
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Please help me with this question
Answer:
= 7022cm
Step-by-step explanation:
The Perimeter of a rectangle =
[tex] = 2(l) + 2(w)[/tex]
From the question
L= 15.47m
w= 19.64m
therefore perimeter of a rectangle
=
[tex] = 2(15.47) + 2(19.64) \\ = 30.94 + 39.28 \\ = 70.22 m[/tex]
Also since rectangle are in centimetres
than if. 1 m = 100cm
than 70.22m = ?
therefore 70.22/1 = 100cm
=7022cm
therefore the Perimeter of a rectangle = 7022
Write this ratio as fraction in lowest terms. 8.64 to 37.76
The ratio 8.64 : 37.76 as a fraction will be 27/118.
What precisely is ratio?
Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.
In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.
As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2.
Now,
Given ratio is 8.64 : 37.76
we can write this as 8.64/37.76
=864/3776
=432/1888
=216/944
=54/236
=27/118
Hence,
The ratio 8.64 : 37.76, as a fraction will be 27/118.
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Which one of the following items is not necessary in preparing a statement of cash flows?
O Determine the cash provided by operations
O Determine cash from financing and investing activities
O Determine the cash in all bank accounts
Determine the change in cash
The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
What is meant by statement cash flows?In financial accounting, a cash flow statement, often called a statement of cash flows, is a financial statement that breaks down the analysis into operating, investing, and financing operations. It illustrates how changes in balance sheet accounts and income effect cash and cash equivalents.
A cash flow statement lists all of an organization's cash inflows from current operations and outside investment sources. The cash flow statement shows the cash the business has generated from operations, investments, and financing. Net cash flow is the name given to this sum.
Functionally speaking, cash flows are categorized according to the nature of the underlying transaction. The statement's main goal is to give pertinent details about the agency's cash inflows and outflows during a given time period.
Therefore, the correct answer is option d) Determine the change in cash.
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What are the slopes and lengths?
Answer:
KL - slope 6/5 , length 7.8
LM - slope -5/6 , length 7.8
MN - slope 6/5 , length 7.8
NK - slope -5/6 , length 7.8
Step-by-step explanation:
square :3
What are the line segments in this rectangle?
a rectangle with the vertices labeled Q, R, S, and T
Answer:
qr rs st qt are the line hope it helped
Find the sum of the numbers. Express your answer in scientific notation.
(6.94 times 10 Superscript negative 7 Baseline) + (2.7 times 10 Superscript negative 8)
7.21 × 10⁻⁷
Step-by-step explanation:
(6.94 × 10⁻⁷) + (2.7 × 10⁻⁸) = 7.21 × 10⁻⁷
A hole in a steel plate has a diameter of 1.166 cm
at 23.00 ∘C
At what temperature is the diameter of the hole equal to 1.164 cm
?
will give brainliest
So here we have a hole in a steel plate with a diameter of 1.166 cm. So we need to find the temperature at what temperature is the diameter of full equal to 1.165 cm. So you're given is D. I. That is equal to initial diameter. That is equal to 1.166 cm. and temporary Germany shirt temperature is equal to 23°C and DF is equal to 1.165 m. This is the final diameter. So you only need to find the value of P. F. So we know that whole diameter very nice linearly with And nature. So here we can say DFS equal to D. I multiplied by one plus alpha. They're dirty. Yeah, I'll find that coefficient of thermal expansion. So here we can say it this is for steel And the value of alpha is equal to 13, multiplied by 10, raised to -6. So D F. Is equal to B. I multiplied plus the I'm multiplied by alpha, multiplied by delta T. So here we can see it D F minus D. I. That is the initial final diameter minus initial diameter divided by D. I. Alpha. That is equal to delta P. So this will be where to tell 30. That is equal to -6.59717. multiplied by 10° to -5 divided by And there's do -6. So here the key Is equal to -65.9717 degree. So here P f minus T I is equal to minus 65.9717 degree. The T.F will be equal to 23 -65.9717. So therefore final temperature that this T.F is equal to -42.8717 degrees Celsius. So therefore this is the answer to the question. So here we can say hands, final temperature Is equal to -42.8717°C.
If the market price is below the equilibrium price, which of the following will occur?
Answer:
Shortage
Step-by-step explanation:
If the market price of a product is set below the equilibrium price, it will create a shortage of the product because the demand exceeds the supply.
_____
which two integers is between /-83
The two integers that are between -83 and +83 are -82 and +82.
What is integers ?
In mathematics, integers are a set of whole numbers that include positive numbers, negative numbers, and zero. Integers do not include fractional or decimal parts, they are the numbers in the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Integers are commonly used in many areas of mathematics, including arithmetic, algebra, and number theory.
There are multiple pairs of integers that are between -83 and 83.
Here are two examples:
-50 and 50: These are integers that are between -83 and 83. Any integer between -83 and -50, or between 50 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -50 0 50 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
-75 and 75: These are also integers that are between -83 and 83. Any integer between -83 and -75, or between 75 and 83, is also between -83 and 83. We can represent this range on a number line as follows:
-83 -75 0 75 83
|----------------|----------------|----------------|----------------|
The integers between -83 and 83 are represented by the shaded portion of the number line.
In general, any pair of integers that are equidistant from 0 and within a range of 83 from 0 will be between -83 and 83.
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A= (x| x es un mes del año ayúdeme a resolver no le entiendo
The elements of the set A are given as follows:
A = {January, February, March, April, May, June, July, August, September, October, November, December}.
How to obtain the elements of the set A?The set A in the context of this problem is defined as follows:
A = {x | x is a month of the year.}
Hence the set A is composed by 12 elements, which are all the months of an year, as follows:
A = {January, February, March, April, May, June, July, August, September, October, November, December}.
TranslationThe problem asks for all the elements of the set A, given as follows:
A = {x | x is a month of the year.}
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1196 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 13°. At some later time, the crew measures the angle of elevation from point B to be 3 ° . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B measures is 1,269.9 feet.
What are the six trigonometric ratios?Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
The slant side is called hypotenuse.
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle (suppose its measure is θ),
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\[/tex]
Given;
The horizontal distance= 1196ft
Angle of elevation to the lighthouse’s=13°
Angle of elevation from point B =3 °
Now,
Distance from A to B = D;
D = Horizontal distance from B to LH - Horizontal distance from A to LH
Distance from A to B = 2237.9 feet - 968 feet ≈ 1269.9 feet;
Therefore, by the trigonometric ratios the distance from point A to point B, D will be 1,269.9feet;
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A. 188.5in²
B. 94.25in²
C. 133.5in²
D. 149.25in²
Answer:B
Step-by-step explanation:
area of triangle is (10*11)/2=55
area of semicircle is
[tex]d=2r\\r=10/2=5\\s=\pi r^{2} /2=25\pi /2=39.25\\39.25+55=94.25[/tex]
2. Чему равна разность? Сравните результаты.
Answer:
[tex] \frac {3}{8} + \frac{2}{8} = \frac{5}{8} = 1 \frac{3}{8} [/tex]
[tex] = \frac{5}{ \\ 8} = 1 \frac{3}{8} [/tex]
someone help me please
The value of summation of ( x-2)² is 973
What is summation?A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
if
x (x-2) ( x-2)²
15 13 169
13 11 121
13 11 121
4 2 4
19 17 289
12 10 100
6 4 16
5 3 9
14 12 144
Therefore the summation of (x-2)²
= 169+121+121+4+289+100+16+9+144 = 973
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Answer:answer
Step-by-step explanation:
The value of summation of ( x-2)² is 973
