The particular solution to the given differential equation, x³y' + 2y = e^(1/x²), that satisfies the initial condition y(1) = e, is y = e.
To find the particular solution of the given differential equation, we can use the method of integrating factors. Let's break down the steps to solve it:
Rearrange the equation: We rewrite the given differential equation in the standard form:
y' + (2/x³)y = (e^(1/x²))/(x³)
Identify the integrating factor: The integrating factor (IF) is determined by multiplying the entire equation by x³. This results in:
x³y' + 2xy = e^(1/x²)
Apply the integrating factor: Multiplying the equation by the integrating factor x³ gives us:
(x⁶y)' = x³e^(1/x²)
Integrate both sides: Integrating both sides of the equation gives us:
x⁶y = ∫x³e^(1/x²) dx
Evaluate the integral: Unfortunately, the integral on the right side does not have an elementary function solution. Therefore, we cannot find an explicit expression for the integral.
However, we can still find the particular solution by applying the initial condition y(1) = e.
Solve for the particular solution: Using the initial condition, we substitute x = 1 and y = e into the equation:
1⁶ * e = ∫1³e^(1/1²) dx
e = ∫e dx
e = e
Since the left side and the right side are equal, the initial condition is satisfied.
We used the method of integrating factors to solve the differential equation and obtained an integral expression. Although we couldn't find an explicit solution for the integral, we were able to confirm that the initial condition y(1) = e satisfies the differential equation. This means that y = e is the particular solution that satisfies the given initial condition.
Learn more about differential equation here:
https://brainly.com/question/32645495
#SPJ11
Hannah needs to calculate the cotangent of an angle. She uses the ratio
opposite leg
for her calculation. Did Hannah correctly calculate the cotangent of the angle?
adjacent leg
A
B.
Yes, Hannah correctly calculated the cotangent of the angle.
adjacent leg
No, Hannah should have used the ratio
opposite leg
hypotenuse
No, Hannah should have used the ratio
opposite leg
O c.
D.
No, Hannah should have used the ratio
adjacent leg
hypotenuse
Answer:
B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)
Step-by-step explanation:
✍️The formula for calculating cotangent of an angle is given as:
\( cot = \frac{adjacent}{opposite} \).
The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.
Therefore, Hannah did not calculate the cotangent of the angle correctly.
She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.
HELP ME PLEASE!!!!!!
the answer is d (the last one) 1/6.
i hope this helps.
Answer:
C
Step-by-step explanation:
Because their's 3 with 2 shaded in
The mean number of words per minute (WPM) read by sixth graders is 8989 with a standard deviation of 1616 WPM. If 6666 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 92.2592.25 WPM
The probability of obtaining a sample mean greater than 92.25 WPM is extremely small, approaching zero.
What is the probability of obtaining a sample mean greater than 92.25 WPM, given a population mean of 8989 WPM and a standard deviation of 1616 WPM?We can use the Central Limit Theorem to solve this problem, since we have a large sample size (n=6666) and a known population mean (μ=8989) and standard deviation (σ=1616).
The Central Limit Theorem states that the distribution of the sample means will be approximately normal with a mean of μ and a standard deviation of σ/√n.
So, for this problem:
The sample size is n=6666The population mean is μ=8989The population standard deviation is σ=1616We want to find the probability that the sample mean would be greater than 92.25 WPM, which we can convert to a z-score using the formula z = (x - μ) / (σ / √n), where x is the sample mean.
z = (92.25 - 8989) / (1616 / √6666) = -116.45
Now, we can use a standard normal distribution table or a calculator to find the probability that a standard normal random variable is greater than -116.45. Since this probability is extremely small (essentially zero), we can conclude that the probability of getting a sample mean greater than 92.25 WPM is also essentially zero.
Therefore, the answer to the problem is that the probability of getting a sample mean greater than 92.25 WPM is essentially zero, or very close to 0.
Learn more about Central Limit Theorem
brainly.com/question/18403552
#SPJ11
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1.7.
27
O-3
عد اس مراس
01/1/0
O 3
Answer:
hold up
Step-by-step explanation:
عد اس مراس whats this mean??
How do you find a linear slope on a table chart? -3 -8 0 -1 3 6 6 13
Answer:
Look at the x values.
Step-by-step explanation:
On the table chart, look at the x values. If there is the same number for different points, it is not a linear slope. However, if all of the x values are different, then it is a linear slope.
10. An airline estimates that the probability a randomly selected call to its reservation phone line results in a reservation being made is 0. 31. Suppose that 4 calls are randomly selected.
1. What is the probability that all 4 of the calls result in a reservation?
2. What is the probability that at least one of the calls does not result in a reservation?
1. The probability that all four of the calls result in a reservation is calculated by multiplying the individual probabilities together since the events are assumed to be independent. Therefore, the probability is 0.31^4 = 0.0303 (approximately).
The probability that at least one of the calls does not result in a reservation can be found by calculating the complement of the probability that all four calls result in a reservation. Since these events are mutually exclusive, we can subtract the probability of all reservations from 1. So, the probability is 1 - 0.0303 = 0.9697 (approximately).
To calculate the probability of all four calls resulting in a reservation, we multiply the individual probabilities together because the events are assumed to be independent. With a probability of 0.31 for each call, the calculation becomes 0.31^4, which equals approximately 0.0303.
For the probability of at least one call not resulting in a reservation, we find the complement of the probability that all four calls do result in a reservation. Since these events are mutually exclusive (either a reservation is made or not made for each call), we subtract the probability of all reservations (0.0303) from 1, resulting in approximately 0.9697.
Learn more about individual probabilities together here:
https://brainly.com/question/28103804
#SPJ11
What is m∠P?
There is a five sided polygon PQRST in which the measure of angle PQR is 132 degrees, the measure of angle QRS is (4x-10) degrees, the measure of angle RST is (5x-11) degrees, the measure of angle STP is 128 degrees and the measure of angle TPQ is (4x+2) degrees.
m∠P =
°
Answer: 94 degrees
Step-by-step explanation:
What is the height of the trapezoid?
O 3 units
o 5 units
o 10 units
12 units
Answer:
5 Units
Step-by-step expla
Answer: b
Step-by-step explanation:
Slope of (5a, b) and (2a, 2b)
Answer:
8a+4b
Step-by-step explanation:
Two of Maxwell's equations contain a path integral on the left side and an area integral on the right. The directions of the infinitesimal path element ds and infinitesimal area element dA are:
The directions of the infinitesimal path element d Vector s and infinitesimal area element d Vector A is none of the given option.
The directions of the infinitesimal path element d Vector s and infinitesimal area element d Vector A in Maxwell's equations are not fixed or predetermined to always be in the same direction, always in opposite directions, or always perpendicular to each other.
The orientations of these elements depend on the specific geometry and configuration of the electromagnetic field being considered. The direction of d Vector s is determined by the chosen path or curve along which the integration is performed.
The direction of d Vector A is determined by the orientation of the surface over which the integration is carried out. These orientations can vary depending on the specific problem and the shape of the path or surface involved.
Therefore, the correct answer is E. none of the above, as there is no fixed relationship between the directions of d Vector s and d Vector A in general.
Learn more about Maxwell's Equation here:
https://brainly.com/question/31648187
#SPJ4
The question attached here seems to be incomplete, the complete question is:
Two of Maxwell’s equations contain a path integral on the left side and an area integral on the right. The directions of the infinitesimal path element d Vector s and infinitesimal area element d Vector A are: A. always in the same direction B. always in opposite directions C. always perpendicular to each other D. never perpendicular to each other E. none of the above
Caroline and Stephen have played 44 tennis matches.
Caroline has won 23 times.
Stephen won the rest.
a) Estimate the probability that Caroline wins.
b) Estimate the probability that Stephen wins.
what's 4.54 rounded to the nearest tenth?
Answer:
4.5
Step-by-step explanation:
have a nice day :)
Answer:
4.5
Step-by-step explanation:
when rounding, if the previous number is over 5 you round up or if it's under 5, you stay the same. the tenths spot is the first after the decimal and the next number 4 so you would stay the same.
60
aº
e
Exhi
Using the information from item 14, what is the measure of angle c if angle e is equal to 115 degrees? Show your work.
gordon types 1800 words in 25 minutes. word per minute
Answer:
72
Step-by-step explanation:
words per minutes= 1800÷25=72
plz help I’m gonna be in so much trouble if I don’t do this
Which pair of numbers has a sum of 0?
1) 2 and 12
2) 2 and –12
3) 2 and –0.2
4) 2 and –2
(13/7) to the power of 2 help?
Answer: 169/49
that is your awnser
How do you solve 14p−8=22+20p ?
The value of p is -5
Simply use cross multiplication :
The process of multiplying numbers in the shape of a fraction is called cross multiplication. Cross multiplying, also known as cross multiplication, is the process of multiplying the numerator of one fraction by the denominator of the other fraction on the other side of an equal symbol. Cross multiplication is a method for comparing fractions.
Both fractions with like and unlike parts are multiplied across. When employing the cross-multiplication procedure, we multiply the denominators as well as the numerators when a fraction is dissimilar, or when the denominators of two fractions are not alike.
\(14p-8=22+20p\\or, 14p-20p=22+8\\or, -6p=30\\or, p=-\frac{30}{6} \\or, p= -5\)
To learn more about cross multiplication visit: brainly.com/question/29190202
#SPJ4
The _____ probability function is based in part on the counting rule for combinations.
a. exponential b. Poisson c. uniform d. hypergeometric
The hypergeometric probability function is based on the counting rule for combinations.
This rule states that if you have two sets of items, with one set containing n1 items and the other containing n2 items, the number of possible combination of r items that can be taken from the two sets is equal to n1+n2 choose n1. This means that you have to select n1 items from the first set, then n2 items from the second set. This function is used in probability calculations to determine the probability of selecting a certain number of items from one set, given a certain number of items from the other set. It is also used to calculate the probability of a certain event occurring when items are randomly selected from two sets.
The hypergeometric probability function can be used to calculate the probability of drawing a certain number of items from a given set. It can also be used to calculate the probability of a certain event occurring. For example, if you are playing a game where you draw 5 balls out of a bag of 20, you can use the hypergeometric probability function to calculate the probability of drawing a certain number of balls from the bag.
know more about a hypergeometric here:
https://brainly.com/question/30886423
#SPJ4
\( {( {5}^{ - 1 } \times {3}^{ - 1} })^{ - 1} \div {6}^{ - 1} \)
Pls include steps...
Step-by-step explanation:
everything can be found in the picture
It is known that a certain lacrosse goalie will successully make a save 85.6% of the time. Suppose that the lacrosse goalie atternpts to make 15 aves. What is the probabilit? that the lacronse goalie will make at least 13 saves? Let X be the random variable which denotes the number of suves that are made by the lacrosse goalie. Find the expected value and sandard devianion of the random variable. E(X)=
The standard deviation of the random variable X is approximately 1.307.
Let's calculate each probability:
P(X = 13) = C(15, 13) * (0.856)^13 * (1 - 0.856)^(15 - 13) = 0.194
P(X = 14) = C(15, 14) * (0.856)^14 * (1 - 0.856)^(15 - 14) = 0.333
P(X = 15) = C(15, 15) * (0.856)^15 * (1 - 0.856)^(15 - 15) = 0.397
Now, we can sum these probabilities to find the probability of making at least 13 saves:
P(X ≥ 13) = P(X = 13) + P(X = 14) + P(X = 15) = 0.194 + 0.333 + 0.397 = 0.924
Therefore, the probability that the lacrosse goalie will make at least 13 saves is 0.924.
To find the expected value (E(X)), we multiply the number of trials by the probability of success:
E(X) = n * p = 15 * 0.856 = 12.84
The expected value of the random variable X is 12.84.
To find the standard deviation (σ), we use the formula:
σ = sqrt(n * p * (1 - p))
σ = sqrt(15 * 0.856 * (1 - 0.856)) ≈ 1.307
Learn more about probability here : brainly.com/question/31828911
#SPJ11
Tell whether each equation is in slope-intercept, point-slope, or standard form.
b. y= -(1/4)x+9
The given equation is in slope-intercept form, on the x-y coordinate plane.
To arrive at a conclusion, we need to understand line equations in Coordinate Geometry.
In 2-D Coordinate Geometry, there are several ways in which the equations of lines can be written. All of these differ according to the parameters used to represent the equation, such as the slope, a single point, two points, intercepts, etc.
But for the same graphical representation, all forms of the line equation are supposed to be the same.
We define all three forms of line equations mentioned in the question:
1. Slope Intercept Form
For a line of slope 'm', which intersects the y-axis at a point (0,b), the line equation is as follows.
y = mx + b
2. Slope Point Form
For a line of slope 'm', which passes through a point (x₁ , y₁), the equation is as follows.
(y - y₁) = m(x - x₁)
3. Standard form:
y = mx + c
where c is a constant.
For the given equation y = (-1/4)x + 9,
If we put in x = 0, we get y = 9, which is the y-intercept of the line.
So, we can conclude that the given equation is in slope-intercept form.
For more on Line Equations,
brainly.com/question/33577446
#SPJ4
helpppppppppppppppppppppppppppppppppppp
Answer:
£120
Step-by-step explanation:
original_price = discounted_price / (1 - discount / 100)
78/(1-35/100)=120
What is the value of x in the equation 1/4(4 + x) = 4/3
The value of x in the equation 1/4(4 + x) = 4/3 is x = 4/3.
Multiply both sides of the equation by 4 to eliminate the fraction on the left-hand side:
1/4(4 + x) = 4/3
4 * 1/4(4 + x) = 4 * 4/3
Simplifying:
4 + x = 16/3
Subtract 4 from both sides of the equation:
4 + x - 4 = 16/3 - 4
Simplifying:
x = 16/3 - 12/3
x = 4/3
A fraction is a mathematical concept used to represent a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator (top number) over a denominator (bottom number), separated by a horizontal line. For example, the fraction 1/2 represents one out of two equal parts, or half of a whole. Similarly, the fraction 3/4 represents three out of four equal parts, or three-quarters of a whole.
Fractions are an essential part of mathematics and are used in a wide range of applications, including measurements, cooking, and financial calculations. They can be added, subtracted, multiplied, and divided just like whole numbers, but they require a bit more care in their manipulation due to their unique structure.
To learn more about Fraction visit here:
brainly.com/question/10354322
#SPJ4
3
Use the less than, greater than, or equal to symbol
What is this answer?
Answer:
3 and what
hope this does not help
What value of x makes the equation true?
0.2x + 0.7 = 0.8 - 0.3x
Answer:
x=0.2 :)
I got this by working on the algebraic calculation.
Morris currently makes $325 per week and takes 2 exemptions. How much more will his weekly withholding be if he takes no exemptions?.
Morris would be withholding an additional $12.50 per week if he took no exemptions.
Morris currently earns $325 per week and has two exemptions on his paycheck. If Morris were to take no exemptions, his weekly withholding would increase significantly.
To estimate the additional withholding amount, we can first calculate the amount Morris would have been withholding with two exemptions:
$325 / 52 = $6.25
$6.25 x 2 exemptions = $12.50
If Morris were to take no exemptions, the amount he would be withholding would be:
$325 / 52 = $6.25
$6.25 x 0 exemptions = $0
Therefore, Morris would be withholding an additional $12.50 per week if he took no exemptions.
To learn more about exemptions , click here
https://brainly.com/question/30064512
SPJ4
A recently televised broadcast of a popular television show had a 15 share, meaning that among 5000 monitored households with TV sets in use, 15% of them were tuned to the show. A 0.01 significance level is used to test an advertiser’s claim that among the households with TV sets in use, less than 20% were tuned in to the show. Find the P-value.
1.9998
0.9999
0.0001
0.0002
The p-value of the given hypothesis is; 0.9999
How to find the p-value of the statistics?The formula for the z-score of proportions is;
z = (p^ - p)/√(p(1 - p)/n)
where;
p^ is sample proportion
p is population proportion
n is sample size
We are given;
p^ = 15% = 0.15
p = 20% = 0.2
n = 5000
Thus;
z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)
z = -8.8388
From p-value from z-score calculator, we have;
P(Z < -8.8388) = 1 - 0.0001 = 0.9999
Read more about p-value at; https://brainly.com/question/4621112
#SPJ1
d= ___ meters (photo included)
Answer:
the answer is 4 meters because its equal to the other side
Triangle ABC is reflected across line to create AA'B'C'. C B 3 A A B' What is the area of AA'B'C'? square units
The area of triangle A'B'C' after reflection is: 6 square units.
What is the Area of a Triangle?Area = ½(base)(height).
When triangle ABC is reflected across the line, the image created, triangle A'B'C' is a mirror image of triangle ABC.
They have the same height = 3 units; and the same base = 4 units.
Area of triangle A'B'C'= ½(4)(3)
Area of triangle A'B'C' = 6 square units.
Learn more about the area of a triangle on:
https://brainly.com/question/21735282
#SPJ1