Math 152 Lab 8 Use Python to solve each problem 1. Given anne2n Estimate for the Integral Test for N terms, plot the upper bound (function) and the line y-00005 to graphically determine how many terms are needed to sum Σ an to within .00005. n=1 (b) Find the sum of the series to within .00005. (c) Using the Remainder Estimate for the Alternating Series Test for N terms, plot the upper bound (sequence) in the window y [0, .00005] to determine the fewest number of terms needed to sum Σ(-1)n-an to within .00005. n=1 (d) Find the sum of the series to within .00005
Answers
a. Define a function for an. b. Implement a function to approximate the integral using a numerical method, like the trapezoidal rule. c. Plot the upper bound function and the line y = 0.00005 to determine the number of terms needed to reach the desired precision.
2. (b) To find the sum of the series to within 0.00005, you can use the partial sum formula in a loop, stopping when the difference between consecutive sums is less than 0.00005.
3. (c) For the alternating series Σ(-1)^n an, you can use the Remainder Estimate. To do this in Python, you can:
a. Define a function for the alternating series term.
b. Plot the upper bound sequence in the window y [0, 0.00005] to find the fewest number of terms needed to reach the desired precision.
4. (d) To find the sum of the alternating series to within 0.00005, you can again use the partial sum formula in a loop, but this time with the alternating series term, stopping when the difference between consecutive sums is less than 0.00005.
Remember to use appropriate Python libraries, such as NumPy and Matplotlib, for calculations and plotting. Good luck with your Math 152 Lab 8!
To solve this problem using Python, we need to first define the sequence `a_n`. We can do this using a lambda function as follows:
```python
a_n = lambda n: 1 / (n**2 + n)
```
Next, we can use a loop to calculate the partial sums of the series up to `N` terms:
```python
N = 1
s_n = a_n(1)
while abs(s_n - 0.00005) >= 0.00005:
N += 1
s_n += a_n(N)
```
Here, we start with `N = 1` and calculate `s_n` as the sum of the first `N` terms of the series. We then use a while loop to increment `N` and add the `N`-th term to `s_n` until the difference between `s_n` and the target value of `0.00005` is less than `0.00005`.
To plot the upper bound of the Integral Test, we can use the `matplotlib` library as follows:
```python
import matplotlib.pyplot as plt
upper_bound = lambda n: 1 / (n**1.5)
x = range(1, N+1)
y = [upper_bound(n) for n in x]
plt.plot(x, y)
plt.plot(x, [0.00005]*len(x))
plt.show()
```
To find the sum of the series to within `0.00005`, we can simply use the `s_n` value that we calculated earlier.
To plot the upper bound of the Remainder Estimate for the Alternating Series Test, we can use a similar approach as before:
```python
upper_bound = lambda n: 1 / (n**2 + n)
x = range(1, N+1)
y = [upper_bound(n) for n in x]
plt.plot(x, y)
plt.plot(x, [-0.00005]*len(x))
plt.ylim(-0.00005, 0.00005)
plt.show()
```
Here, we define the upper bound function `upper_bound` as `1 / (n**2 + n)` (which is the upper bound for `(-1)**n * a_n`). We then create a range of `x` values from 1 to `N` and use a list comprehension to calculate the corresponding `y` values using `upper_bound`.
To find the sum of the series to within `0.00005`, we can use the formula for the sum of an alternating series:
```python
sum = s_n - a_n(N+1)
```
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Related Questions
Susie leaves to go shopping driving 45 miles per hour toward the Happy Shopper Grocery Store.
Susie is originally 20 miles due west of the store. Sammie leaves for the Happy Shopper Grocery
Store at the same time driving 50 miles per hour on the same road but she is 25 miles due East
Who reaches the store first? By how much time (in hours)? Round to the nearest hundredth if
needed.
Answers
Answer:
Susie reaches the store first being ahead by 0.06 hours.
Step-by-step explanation:
20 miles going 45 miles/hour.
20 miles / (45 miles / hour) = 20 miles hours / 45 miles =
= 20 hours / 45 = 4/9 hours = 0.44 hours
25 miles going 50 miles/hour.
25 miles / (50 miles / hour) = 25 miles hours / 50 miles =
= 25 hours / 50 = 1/2 hours = 0.5 hours
So Susie needs less time (= arrives first).
the difference is 0.5 - 0.44 = 0.50-0.44 = 0.06 hours
as additional practice :
0.06 hours is 60 × 0.06 minutes.
60 × 0.06 = 60 × 6 / 100 = 360 / 100 = 3.6 minutes.
The table below shows Zoey's earnings on the job
How much does she make in 18.2518.25 hours?
Answers
Answer:
she is going to make $408.90 in 18.2518.25 hours
Find the length of the hypotenuse. Simplify your answer.
P(0,q)
0(0,0)
Q(3q,0)
please help and i will give you brainliest
Answers
The length of the hypotenuse is \(\sqrt{10}q\) units.
To find the length of the hypotenuse, we can use the distance formula, which is derived from the Pythagorean theorem. The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Given:
Point P: (0, q)
Point O: (0, 0)
Point Q: (3q, 0)
To find the length of the hypotenuse, we need to calculate the distance between points P and Q.
\(Distance = \sqrt{(3q - 0)^2 + (0 - q)^2}\\ = \sqrt{9q^2 + q^2}\\ = \sqrt{10q^2}\\ = \sqrt{10} * q\)
Therefore, the length of the hypotenuse is \(\sqrt{10}\ q\ units\).
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The slope of the line is 0. It passes through the point (-3,4). Identify two other points on the line. Justify you answer
Answers
Answer:
Two other points: (2, 4) (6, 4)
Step-by-step explanation:
A line with a slope = 0 is a horizontal line [with a y-intercept of (0, b)], given by the linear equation, y = 4. This means that the y-coordinate will always equal to 4, regardless of its corresponding x-coordinate. Basically, we could choose any x-coordinate to pair with the y-coordinate of 4.
I chose the ordered pairs, (2, 4) and (6, 4).
Attached is a screenshot of the graphed linear equation, y = 4.
what would you have to know about the solution set of a homogeneous system of 18 linear equations in 20 variables in order to know that every associated nonhomogeneous equation has a solution
Answers
The solution set of a homogeneous system of 18 linear equations in 20 variables lies in the null space of the coefficient matrix.
To know that every associated nonhomogeneous equation has a solution, we need to ensure that the homogeneous system has a nontrivial solution.
This means that we need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, i.e., whether there exist free variables.
If the rank is less than the number of variables, then there are infinitely many solutions to the homogeneous system, and thus every associated nonhomogeneous equation has a solution.
However,
We also need to ensure that the particular solution to the nonhomogeneous equation does not lie in the null space of the coefficient matrix.
This is equivalent to checking whether the null space of the coefficient matrix is orthogonal to the vector on the right-hand side of the nonhomogeneous equation.
If it is, then the nonhomogeneous equation has a solution.
So, in summary, to know that every associated nonhomogeneous equation has a solution.
We need to know whether the rank of the coefficient matrix of the homogeneous system is less than the number of variables, and we need to check whether the particular solution lies in the null space of the coefficient matrix.
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a certain dj takes requests for songs at a party. assume that there are 120 people at the party, each of whom makes exactly one request for a song. all of their requests are made independently. assume that each person asks for a pop song with probability 0.37, a rock song with probability 0.2, or a rap song with probability 0.43. what is the probability that 50 or more requests are made for pop songs?
Answers
the probability that 50 or more requests are made for pop songs is 0.0967, or about 9.67%.
Define binomial distributionThe binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
We can use the binomial distribution to model this situation, where the number of trials is 120 (the number of people at the party), and the probability of success (making a request for a pop song) is 0.37. Let X be the number of requests for pop songs. Then:
The mean of X is μ = np = 120 x 0.37 = 44.4
The standard deviation of X is σ = sqrt(np(1-p)) = sqrt(120 x 0.37 x 0.63) = 4.32
To find the probability that 50 or more requests are made for pop songs, we can use the normal approximation to the binomial distribution, which applies when np >= 10 and n(1-p) >= 10.
Let Z be a standard normal random variable, then:
P(X >= 50) = P((X - μ)/σ >= (50 - μ)/σ)
= P(Z >= (50 - 44.4)/4.32)
= P(Z >= 1.2963)
= 1 - P(Z < 1.2963)
= 1 - 0.9033
= 0.0967
Therefore, the probability that 50 or more requests are made for pop songs is approximately 0.0967, or about 9.67%.
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Choose the correct answer. Find the unknown, k, by solving the following proportion: (k)/(1.2)=(4)/(3) 1.7 1.6 1.4 1.3
Answers
The correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.
To find the unknown value, k, in the proportion (k)/(1.2) = (4)/(3), we can cross-multiply and solve for k.
cross-multiplying the proportion, we have:
3k = 4 * 1.2
Multiplying the numbers:
3k = 4.8
To isolate k, we divide both sides of the equation by 3:
k = 4.8 / 3
Evaluating the division, we find:
k ≈ 1.6
Therefore, the correct answer is 1.6. By solving the proportion, we determined that the value of k that satisfies the given equation is approximately 1.6.
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5+7-2+5=? Please help me out
Answers
5+7= 12
12-2= 10
10+5= 15
Hope this helps
The answer of 5+7-2+5=15
PLZ HELP ASAP LIKE IM FAILING MY MATH
Answers
Answer:
15 is a
Step-by-step explanation:
PLEASE HELP
The Central Islip community has 9,649 homes in it. Smart Boards cost the school district $5,200 each. The HS needs 175, the Reed School needs 150 and the Mulligan school needs 50 new boards. Network Outsource the schools tech company has 12 workers for the HS, 8 for the Reed School and 4 for Mulligan. They all work 8 hours a day. They work 5 days a week, Monday thru Friday. They earn $58 per hour. It will take 45 weeks to finish the job. Find: a) Total Product Cost b) Total Labor Cost c) Total Cost d) Cost per Home e) Cost per Week
Answers
Using proportions, the costs are given as follows:
a) Total Labor Cost: $2,505,600.
b) Total Product Cost: $1,950,000.
c) Total Cost = $4,455,600.
d) Cost per home = $461.77.
e) Cost per week = $99,013.33.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
For item a, the labor cost is found using the earnings of the workers, as follows:
45 weeks x 5 days x 8 hours x 58 per hour x (12 + 8 + 4 workers)
Hence:
Total Labor Cost = 45 x 5 x 8 x 58 x 24 = $2,505,600.
For item b, the product cost is the cost of the boards, hence:
(175 + 150 + 50 boards) x 5,200
Total Product Cost = 375 x 5,200 = $1,950,000.
For item c, the total cost is the sum of the product cost and the labor cost, hence:
Total Cost = 2,505,600 + 1,950,000 = $4,455,600.
For item d, the cost per home is found dividing the total cost by the 9,649 homes, hence:
Cost per home = 4455600/9649 = $461.77.
For item e, the cost per week is found dividing the total cost by the 45 weeks, hence:
Cost per week = 4455600/45 = $99,013.33.
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writing equations of lines parallel and perpendicular to a given line through a point
Answers
To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.
To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:
1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.
2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.
3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.
Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.
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Exponential from Two Points (Level 1)
Write an exponential function in the form y = ab* that goes through points (0, 13)
and (2, 325).
Answers
a = 13. b^0 = 1, y=a(1), 13 = a 325 = 13(b)^2 b^2 = 325/13 = 25
b = sqr25 = 5 y=13(5)^x is the exponential equation going through the two given points
What is Exponential function?An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.The graphs of all exponential functions have these characteristics. They all contain the point (0, 1), because a0 = 1. The x-axis is always an asymptote. They are decreasing if 0 < a < 1, and increasing if 1 < a. If your function can be written in the form y = a b x , where and are constants, a ≠ 0 , b > 0 , and b ≠ 1 , then it must be exponential. In quadratic equations, your functions were always to the 2nd power. In exponential functions, the exponent is a variableTo learn more about Exponential function refers to:
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Find the sum or difference.
(- 2h + 1) + 2(3h - 4) SHOW YOU WORK FOR POINTS AND BRAINIEST
Answers
Answer: (- 2h + 1) + 2(3h - 4) = 4h -7
Step-by-step explanation:
First, remove unnecessary parentheses
- 2h + 1 + 2(3h - 4)
then distribute 2 through the parentheses
- 2h + 1 + 2(3h - 4) = -2h + 1 + 6h -8
Combine like terms
-2h + 1 + 6h -8 = 4h + 1 - 8
1-8= 7
So the answer is
4h - 7
will mark brainliest for correct answer
Answers
Answer:
Y
Step-by-step explanation:
Look at Y and look at the input and output it shows which one is it and how to find it you welcome :)
I need help with a word problem! I need to find the probability.A gambler places a bet on a horse race. To win, he must pick the top three finishers in order. Seven horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that gambler will win his bet?
Answers
ANSWER
1/35
EXPLANATION
First we have to find how many ways you can pick 3 horses out of 7. For the first place you have 7 horses that can be there. For the second place, you have 6 horses (you already placed one horse) and for the third place you have 5 horses. The number of ways to pick 3 horses - in order - from 7 horses is:
\(7\times6\times5=210\)Now we want to know the permutations for 3 horses. Once you have picked one combination out of the 210 combinations of 3 horses, there are many ways to arrange them. This is:
\(3!=3\times2\times1=6\)Let 'A' be the event where the gambler wins his bet:
\(P(A)=\frac{6}{210}\)We can simplify this fraction:
\(P(A)=\frac{1}{35}\)at what rate is the angle θ, between the ladder and the ground changing then?
Answers
To determine the rate at which the angle θ, between the ladder and the ground is changing, we need to establish a relationship between the angle θ and the given variables.
Let's assume the ladder is leaning against a wall, forming a right triangle with the ground. The ladder acts as the hypotenuse, and the angle θ is the angle opposite to the height of the wall.
Given that the length of the ladder is decreasing at a constant rate of 2 ft/s, we can express this as dh/dt = -2 ft/s, where h represents the height of the wall.
Using trigonometry, we know that sin θ = h/l, where l represents the length of the ladder. Taking the derivative of this equation with respect to time t, we get:
d/dt(sin θ) = d/dt(h/l)
Differentiating both sides using the chain rule, we have:
cos θ * dθ/dt = (dl/dt * h - dh/dt * l) / l²
Since dl/dt is given as -2 ft/s and dh/dt is given as -2 ft/s, we can substitute these values into the equation:
cos θ * dθ/dt = (-2 * h - (-2) * l) / l²
Simplifying further:
cos θ * dθ/dt = (-2h + 2l) / l²
Now, to find the rate at which the angle θ is changing (dθ/dt), we need to know the values of h and l at a specific point in time. Without additional information or specific values for h and l, we cannot determine the exact rate at which θ is changing.
In summary, the rate at which the angle θ is changing (dθ/dt) depends on the specific values of h and l at a given time.
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23.96448 to the nearest tenths
Answers
Answer:
24
Step-by-step explanation:
NEED HELP ASAP ON TIMER 30 MINUTES LEFT
find the least common multiple (lcm) of:
25y^5 and 5xy and 2x^3y
Answers
Answer:
50 x^3 y^2
Step-by-step explanation:
25y^5 = 5*5 * y*y
5xy = 5*x*y
2x^3y = 2*x*x*x*y
The least common multiply is found by taking the least number of times each appears
5 appears 2 times
2 appears 1 time
x appears 3 times
y appears 2 times
5*5*2 * x*x*x * y*y
50 x^3 y^2
Answer:
50 x^3 y^2
Step-by-step explanation:
25y^5 = 5*5 * y*y
5xy = 5*x*y
2x^3y = 2*x*x*x*y
The least common multiply is found by taking the least number of times each appears
5 appears 2 times
2 appears 1 time
x appears 3 times
y appears 2 times
5*5*2 * x*x*x * y*y
50 x^3 y^2
Solve 3(2-1)
This is math
Answers
Answer:3
Step-by-step explanation:
you have to multipy 3 by each of th numbers in the ( ) and then sove by subtracting
3 x 2= 6 and 3 x -1 = -3 so 6-3= 3
Answer:
\(3(2 - 1) = 3\)
Step-by-step explanation:
Use PEMDAS.
===================================
\(3(2-1)\\\rule{150}{0.5}\\\rightarrow 2 - 1 = 1\\\\3(1)\\\\3 \times 1\\\\\boxed{3}\)
===================================
You can also distribute 3 into the parentheses and evaluate form there.
\(3(2-1)\\\rule{150}{0.5}\\\rightarrow 3 * 2 = 6\\\rightarrow 3 * -1 = -3\\\\3(2-1) \rightarrow \boxed{6 - 3}\\\\\boxed{3}\)
===================================
Hope this helps!
I need help with this problem. Please I don’t want any links for “answers”.
Answers
Answer:
why does it say the answer is 165 on top?
PLEASE HELP LOOK AT THE PHOTO BELOW
Answers
Mr. Quesada took out a loan for $12,000. To pay it back, he will make 24 monthly payments of $629. How much will he pay in interest?
Answers
Answer:
$3,096
Step-by-step explanation:
To find the total interest Mr. Quesada will pay, we need to first calculate the total amount he will pay back, and then subtract the original amount borrowed.
The total amount Mr. Quesada will pay back over 24 months is:
$629 x 24 = $15,096
Subtracting the original loan amount, we get:
$15,096 - $12,000 = $3,096
So Mr. Quesada will pay a total of $3,096 in interest over the course of the loan.
Identify the GCF of 6x2y2 − 8xy2 + 10xy3.
6x2y2
2x2y
2xy2
6xy2
Answers
Answer:
B is correct
Step-by-step explanation:
same thing
plz help
Answers
Tide: 12.16•64 = 778.24
Gain: 21•100 = 2,100
Purex: 12.24•72 = 881.28
The answer would be the last bubble: Purex. The value is the greatest for the given amount of laundry.
what is 10 x/10 = 30/10
Answers
Answer: The answer to this math question about solving for x with the given 2 basic fractions is \(x = 3.\)
Step-by-step explanation: Mmmm, that was super extremely easy, so anyway, here are 2 basic steps in order to solve for x with the given 2 basic fractions:
Step 1. First, let's cancel the terms that are in both the numerator and denominator that looks in the equation form like this: \(\frac{10x}{10} = \frac{30}{10}, x = \frac{30}{10}.\)
Step 2. Last but not least is after we cancel the terms that are in both the numerator and denominator, finally, let's divide the numbers that looks in the equation form like this: \(x = \frac{30}{10}, x = 3.\)
I hope that my full given answer with my full given step-by-step explanation is very helpful to your own math question about solving for x with the given 2 basic fractions, please mark me as Brainliest, take care, always be safe, and have a great rest of the day and good night! :D
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Jason Ta,
The Ambitious of The Brainly And The Role of The TDSB And WHCI Student of The High School.
Which of the following is most likely the next step in the series?
Answers
Answer B
\( \huge \cal \colorbox{pink}{❥hope \: it \: helps}\)
How many liters of a 35 percent salt solution must be mixed with 20 liters of a 70 percent salt solution to obtain a solution that is 45 percent salt
Answers
86 liters of 35% salt solution should be added to 20 liters of an 70% salt solution so that the resulting solution contains 45% salt solution .
For given question,
Let x be the quantity ( in liters ) of 35 percent salt solution added to 20 liters of an 70 percent salt solution so that the resulting solution contains 45 percent salt,
Thus,
Quantity of salt solution in 20 liters + Quantity of salt solution in x
= Quantity of salt solution in resultant mixture.
⇒ 70% of 20 + 35% of x = 45% of (20 + x )
⇒ 14 + (0.35x) = 0.45 × ( 12 + x )
⇒ 14 + 0.35x = 5.4 + 0.45x
⇒ 14 - 5.4 = 0.45x - 0.35x
⇒ 8.6 = 0.10x
⇒ x = 86 liters
Therefore, 86 liters of 35% salt solution should be added to 20 liters of an 70% salt solution so that the resulting solution contains 45% salt solution .
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a manufacturer must test that his bolts are 1.00cm long when they come off the assembly line. he must recalibrate his machines if the bolts are too long or too short. after sampling 121 randomly selected bolts off the assembly line, he calculates the sample mean to be 0.94cm. he knows that the population standard deviation is 0.31cm. assuming a level of significance of 0.05, is there sufficient evidence to show that the manufacturer needs to recalibrate the machines?
Answers
There is insufficient evidence to support that bolts are too long or too short.
What is Mean and Standard Deviation?
Mean: Dividing the sum of all values in a data set by the number of values.
Standard Deviation: The standard deviation is a measure that summarizes how far away from the mean each observation is.
Given:
mean: 0.94cm
standard deviation = 0.31cm
Alright, so a manufacturer must test that these bolts are long as they come off the manufacturing line and he must readjust the machines if they're too long or too short. Consequently, sample 121V and sample mean are 0.94 cm. So we want to test whether or not these are actually equal to two, so are no hypothesis is that the mean is too and our alternative hypothesis, because it says that we have to recalibrate if they're too short or too long, is that the mean is not too we could probably go with the left tail test here because the sample mean is under but we'll be safer with a two tail test um just because the standard deviation may sway things.
So what we want to do next is compute the test statistic and that's gonna be a Z score and that's just supplied by X bar minus population mean over standard deviation over squared event. And we're using Z here because we have a high sample size and since we know the population standard deviation.
Hence, There is insufficient evidence to support that bolts are too long or too short.
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I don’t understand this question! Please help me find the answer they are compound shapes
Answers
The area of the shaded region in this problem is given as follows:
995.44 cm².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it's measure is given as follows:
r = 21 cm.
Then the area of the entire circle is given as follows:
A = π x 21²
A = 1385.44 cm².
The right triangle has two sides of length 39 cm and 20 cm, hence it's area is given as follows:
A = 0.5 x 39 x 10
A = 390 cm².
Then the area of the shaded region is given as follows:
1385.44 - 390 = 995.44 cm².
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what is the form of the particular solution for the given differential equation? y''-5y' 4y=8e^x
Answers
The particular solution of the differential equation y''-5y' 4y=8e^x is A*e^x form.
To find the form of the particular solution for the given differential equation, y'' - 5y' + 4y = 8e^x, we will first identify the terms involved and then determine an appropriate trial function for the particular solution.
Given differential equation: y'' - 5y' + 4y = 8e^x
Here, the left side represents a linear differential equation with constant coefficient and the right side is the non-homogeneous term (8e^x).
To find the form of the particular solution, we'll assume a trial function based on the non-homogeneous term. Since the non-homogeneous term is 8e^x, our trial function will have the form:
Trial function: Y_p(x) = A*e^x
Now, we need to find the derivatives of Y_p(x) and substitute them into the differential equation:
First derivative: Y_p'(x) = A*e^x
Second derivative: Y_p''(x) = A*e^x
Substituting these into the differential equation:
(A*e^x) - 5(A*e^x) + 4(A*e^x) = 8e^x
Simplifying the equation:
(A - 5A + 4A)e^x = 8e^x
Now, we compare the coefficients:
A = 8
So, the form of the particular solution for the given differential equation is Y_p(x) = 8e^x
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