The approximation of the integral I = ∫s⋅cos(x² + 5) dx using simple Simpson's rule is: -1.57923.
Simpson's rule is a numerical method used to approximate definite integrals. It divides the interval of integration into several subintervals and approximates the integral using quadratic polynomials. In simple Simpson's rule, the number of subintervals is even.
The formula for simple Simpson's rule is:
I ≈ h/3 [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + 2f(x₄) + ... + 2f(xₙ₋₂) + 4f(xₙ₋₁) + f(xₙ)],
where h is the step size and n is the number of subintervals.
In this case, the function to be integrated is f(x) = s⋅cos(x² + 5), and we have the values of x and f(x) at each subinterval. By applying the formula of simple Simpson's rule and substituting the given values, we can calculate the approximation.
Based on the provided information, it appears that the approximation obtained using simple Simpson's rule is -1.57923. However, it is important to note that without additional context or information about the specific subintervals and step size, it is not possible to verify or provide a more detailed explanation of the calculation.
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Box 1 has a volume of 210 cubic meters. Box 2 has a volume of 130 cubic meters. What is the total volume?
Answer:
340
Step-by-step explanation: 210 plus 130 equals 340 please give me brainlyist
7. Find the corresponding angle.
(look at the picture)
Answer:
angle SXV
Step-by-step explanation:
The angle measurements in the diagram are represented by the following expressions. A=5x-5 B=3x+13
Answer:
Step-by-step explanation: 5x-5=3x+13---> 5x-3x=13+5---> 2x=13+5---- 2x=18----> x=9 hope it helps
Answer:
Step-by-step explanation: 40
(-8, 4), (4, -4)
Write in standard form
Answer written in standard form:
2x + 3y = -4
9514 1404 393
Answer:
2x +3y = -4
Step-by-step explanation:
The slope of the line is given by the slope formula:
m = (y2 -y1)/(x2 -x1
m = (-4 -4)/(4 -(-8)) = -8/12 = -2/3
This can be used in the point-slope formula to find an equation of the line:
y -y1 = m(x -x1)
y -4 = -2/3(x -(-8)) . . . . substituting for (x1, y1) and m
Multiplying by 3 eliminated fractions:
3(y -4) = -2(x +8)
3y -12 = -2x -16
Adding 2x+12 to both sides gives the standard form equation:
2x +3y = -4
(HELP)
JK⎯⎯⎯⎯⎯ is tangent to ⊙G at point K , m∠JKG=(52x+1314)° , and m∠KGJ=(54x+998)° . What is m∠KGJ ?
m∠JGK= -----°
Answer:
41°
Step-by-step explanation:
The tangent line of circle is perpendicular to the radius of a circle
m∠JKG = (5/2 x + 131/4)° = 90°
x = 22.90
m∠JGK = (5/4 x + 99/8)° = ((5/4 * 22.90) + 99/8)° = 41°
The price for 2 kilograms of ham is $36.00. What is the unit price of ham per 100 grams?
Answer: $1.8
Step-by-step explanation:
From the question, we are informed that the price for 2 kilograms of ham is $36.00. We should remember that 1000 gram = 1 kilogram; therefore, 2 kilograms = 2000 grams.
The cost of a gram of ham will then be:
= $36.00/2000
= $0.018
The unit price of ham per 100 grams will be:
= 100 × 0.018
= $1.8
Help me pless!!!!!!!!!
Answer:
p = 7
Step-by-step explanation:
2p = 14
p = 14/2
p = 7
Octavian became the emperor of Rome in 27 B.C. He ruled until his death in A.D. 14. How long did he rule as emperor?
The computation shows that the number of years ruled is 41 years.
How to compute the value?From the information, Octavian became the emperor of Rome in 27 B.C and he ruled until his death in A.D. 14.
Therefore, the number of years that he rules will be:
= 14 - (-27)
= 14 + 27
= 41
Therefore, the number of years will be 41.
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consider the dihedral point group constructed from two generators express a 3d matrix representation for the two generators of the group in the hexagonal basis
the groups generated by two elements of order 2 are K4 and dihedral group.
We are given that G be a finite group with x, y belong to G have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that Zn is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to Zn
But we are given that two elements of order 2 in given group
Therefore, group G can be K4 or dihedral group
Because the groups generated by two elements of order 2 are K4 and dihedral group.
We know that is abelian group of order 4 and every element of K4 is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to K4 or D2.
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Find the value of x so that the ratios are equivalent. 9:x and 54:8
I keep trying 48 its never right
Answer:
Maybe it is right, but you need to phrase it a different way
Step-by-step explanation:
like x= 48
or 48
or 9:48
you know
The value of x so that the ratios are equivalent is 48.
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b"
Then their ratio will be formed as
\(\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}\)
where is a common factor (not 1)
Which shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly cancelled from both the numerator and the denominator.
Thus, a = px, b = qx
Therefore, the value of x so that the ratios are equivalent.
9:x and 54:8
x= 48
or 9:48
Hence, the value of x so that the ratios are equivalent is 48.
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a person with tuberculosis is given a chest x-ray. four tuberculosis x-ray specialists examine each x-ray independently. if each specialist can detect tuberculosis % of the time when it is present, what is the probability that at least 1 of the specialists will detect tuberculosis in this person?
The probability that at least one of the specialists will detect tuberculosis in this person is 0.9999 or 99.99%.
To calculate the probability that at least one of the specialists will detect tuberculosis in this person, we can use the concept of the complement rule.Let's denote the probability that a specialist will detect tuberculosis as p. The probability that a specialist will not detect tuberculosis is then (1 - p).Since each specialist examines the x-ray independently, the probability that none of the specialists will detect tuberculosis is (1 - p) raised to the power of the number of specialists.Let's assume there are four specialists. The probability that none of them will detect tuberculosis is (1 - p)⁴.
Therefore, the probability that at least one of the specialists will detect tuberculosis is 1 minus the probability that none of them will detect tuberculosis.
Probability(at least one specialist detects tuberculosis) = 1 - Probability(none of the specialists detect tuberculosis)
= 1 - (1 - p)⁴
Substituting the given information that each specialist can detect tuberculosis % of the time when it is present (which means p = %/100), we can calculate the probability.
Probability(at least one specialist detects tuberculosis) = 1 - (1 - p)⁴
= 1 - (1 - %/100)⁴
For example, if each specialist has a 90% detection rate (% = 90), the probability would be:
Probability(at least one specialist detects tuberculosis) = 1 - (1 - 90/100)⁴= 1 - (1 - 0.9)⁴
= 1 - (0.1)⁴
= 1 - 0.0001
= 0.9999
Therefore, the probability that at least one of the specialists will detect tuberculosis in this person is 0.9999 or 99.99%.
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Can you please answer the question???
The volume of given triangular prism is 24,000 cubic yards.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Here, the dimensions of base are 30 yards and 20 yards.
Here, area = 1/2×30×20
= 300 yd²
Volume of a triangular prism = Area of base triangle × Length of the prism.
= 300×80
= 24,000 yd³
Therefore, the volume is 24,000 yd³.
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Solve for w.
4 = 2w − 4
w =
Helppppp please!!!!!!!
Which pairs of rational numbers are equivalent? Select all that apply.
-0.5 and Negative one-half
0.ModifyingAbove 7 with barand StartFraction 7 over 10 EndFraction
StartFraction 11 over 20 EndFractionand 0.55
StartFraction negative 1 over 50 EndFractionand -0.02
0.15 and 0.1ModifyingAbove 5 with bar
Answer:
A C D
Step-by-step explanation:
Answer:
A C D
Step-by-step explanation:
Graph the equation then find the solution
By graphing the system of equations, we can see that the solution is (4, -2)
How to solve the system of equations?Here we want to solve the system of equations:
y = (-3/2)*x + 4
y = (1/2)*x - 4
To solve this graphically, we just need to graph both equations on the same coordinate axis and find the point where the lines intersect.
The graph can be seen on the image at the end.
We can see that the solution is (4, -2)
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Four times Theo’s number added 20 is 10. what is theo’s number ?
Answer:
ur mom
Step-by-step explanation:
genehrrddjdhxxhdhdi hope this didnt help
Help me out and show me the full solution on how you solved it, please!
The value of each trigonometric identity is:
3/2
5/6
14/3
We have,
We will use the trigonometric formula and substitute the given values.
So,
Cosec θ
This can be written as,
= 1/ sin θ
= 1/(2/3)
= 3/2
And,
Sin θ
This can be written as,
= 1/ cosec θ
= 1/(6/5)
= 5/6
And,
Sec θ
This can be written as,
= 1/cosθ
= 1/(3/14)
= 14/3
Thus,
The value of each trigonometric identity is:
3/2
5/6
14/3
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I need help asap 20 points
Answer:
Step-by-step explanation:
Input Output
1 12
2 2*12 = 24
3 3*12 = 36
4 4*12 = 48
Function:
y = 12x
I WILL GIVE BRAINLIEST!!!
Answer:
Just watch the video
Step-by-step explanation:
1. Consider
dt
dy
=f(t,y),y(0)=y
0
. where f(t,y)=
2
1
(y+1)(3−y)t,y
0
=1 (a) (2 pts) Solve this initial value problem and write its exact solution y(t). (b) (5 pts) Use Euler's method with h=0.1 to obtain a numerical solution u(t) at t=3 and plot the numerical solution u(t) (solid line) along with the exact solution y(t) (dashed line) for 0≤t≤3. (c) (3 pts) Compute the error e
1
defined by e
1
=max∣u(t)−y(t)∣(0≤t≤3) for h=0.1, 0.05, and 0.025, and make a table showing the variation of e
1
with h. What do you observe? 2. Consider the second-order Runge-Kutta method (or improved Euler's Method), which is given by v
n+1
=v
n
+
2
h
(k
1
+k
2
), where k
1
=f(t
n
,v
n
),k
2
=f(t
n
+h,v
n
+hk
1
). (a) (7 pts) For the initial value problem considered in Problem 1, find a numerical solution v(t) at t=3 with h=0.1 and plot the numerical solution v(t) (solid line) along with the exact solution y(t) (dashed line) for 0≤t≤3. (b) (3pts) Compute the error e
2
defined by e
2
=max∣v(t)−y(t)∣(0≤t≤3) for h=0.1, 0.05, and 0.025, and make a table showing the variation of e
2
with h. What is the difference between the two numerical methods?
In problem 1, an initial value problem is given with a first-order differential equation. The exact solution, y(t), is obtained, and Euler's method is used with different step sizes to obtain numerical solutions, u(t), at t=3.In problem 2, the second-order Runge-Kutta method (improved Euler's method) is applied to the same initial value problem. The numerical solution, v(t), is obtained at t=3 with h=0.1.
In problem 1, the initial value problem is solved analytically to obtain the exact solution, y(t). Euler's method is then applied with different step sizes (h) to approximate the solution numerically at t=3. The numerical solution, u(t), is plotted alongside the exact solution, y(t), to visualize their comparison. The error, e1, is calculated as the maximum absolute difference between u(t) and y(t) over the interval [0, 3]. By varying the step size and computing e1, the effect of the step size on the accuracy of the numerical solution can be observed.
In problem 2, the second-order Runge-Kutta method is employed to approximate the solution numerically. The numerical solution, v(t), is computed at t=3 with h=0.1 and compared to the exact solution, y(t), through a plot. The error, e2, is calculated as the maximum absolute difference between v(t) and y(t) over the interval [0, 3]. By computing e2 for different step sizes and comparing it to e1 from problem 1, the difference between the two numerical methods can be observed in terms of accuracy and convergence.
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15% of $30=
A $0.45
B $2.00
C $ 0.50
D $4.50
E None
15% of $30 is $4.50 because of the concept of percentage which is a chapter from mathematics.
Given: 15% of $30
Find: You need to find the 15% rate of $30.
Solution: A percentage can be defined as a number or ratio expressed as a fraction of 100. It is often denoted by the percent sign (%), but the abbreviation percent, percent, and in some cases percent is also used. Percentages are dimensionless numbers (pure). There are no units of measurement.
Example: If 25% of the total number of students in a class are male, 25 out of 100 are male. He has 500 students, 125 of whom are male.
So 15% of $30 = (15/100) x $30 = 0.15 x $30 = $4.50.
So using the percentage gives the answer as $4.50.
Therefore, percentages are very useful in our daily life.
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Histograms based on data on _________ ______ and ________ typically are skewed to the right.
By organizing countless data points into comprehensible ranges or bins, the histogram, which resembles a bar graph in appearance, condenses a data series into an understandable visual. So Histograms based on data on housing, prices and salaries typically are skewed to the right.
A histogram in statistics is a graphic depiction of the data distribution. The histogram is shown as a collection of rectangles that are next to one another, where each bar represents a different type of data.
A branch of mathematics called statistics is used in many different fields. Frequency is the term for how often numbers appear in statistical data; it can be shown as a table and is known as a frequency distribution.
A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. The numerical count or percentage of occurrences for each column in the data are shown on the vertical y-axis.
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Elia rode her bicycle from her house to the beach at a constant speed of 181818 kilometers per hour, and then rode from the beach to the park at a constant speed of 151515 kilometers per hour. The total duration of the rides was 111 hour and the distances she rode in each direction are equal.
Let bbb be the number of hours it took Elia to ride from her house to the beach, and ppp the number of hours it took her to ride from the beach to the park.
The number of hours it took from her house to the beach is 50.5 hour while The number of hours it took from her beach to the park is 60.5 hour.
What is the number of hours it took Elia from her house?
Given: speed from house to the beach (Sb) = 181818 km/h, speed from the beach to park (Sp) = 151515 km/h and total duration(T) = 111 h.
Also, we are told the distances are the same. Let's represent that with the letter D
We are instructed to represent the number of hours it took Elia to ride from her house to the beach with bbb and the number of hours it took her to ride from the beach to the park with ppp.
From the information we can say:
bbb + ppp = T
bbb + ppp = 111
Also: ppp = 111 - bbb
Using the formula for speed:
Speed = distance / time
Sp = D/ppp
151515 = D/ ppp
D = 151515 x ppp
Also:
Sb = D/ppp
181818 = D/ bbb
D = 181818 x bbb
Since the distances (D) are the same. We can equate the two distances:
181818 x bbb = 151515 x ppp
Put ppp = 111 - bbb:
181818 x bbb = 151515 x (111 - bbb)
181818bbb = 16818165 - 151515bbb
181818bbb + 151515bbb = 16818165
333333bbb = 16818165
bbb = 16818165/333333 = 555/11 hour = 50.5 hour
Put bbb = 555 into ppp = 111 - bbb:
ppp = 111 - 555/11 = 666/11 hour = 60.5 hour
Therefore, the number of hours it took her to ride from her house to the beach and the number of hours it took her to ride from the beach to the park are 50.5 hour and 60.5 hour respectively.
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Evaluate this expression. 32 + (−72.1) please answer
Answer:
-40.1
Sorry if it's wrong but Hope it Helps!~
The cost of an
8
-ounce box of cereal is
$
1.68
. At this rate, what is the cost per ounce of the cereal, in dollars and cents?
Answer:
.21 cents
Step-by-step explanation:
To get .21 do 1.68 divided by 8
1.68 ÷ 8 = .21
Hope this helps ya!!
What is the Systematic Approach algorithm?
The Systematic Approach algorithm is a problem-solving methodology that is widely used in many different fields, such as engineering, business, and science.
It is a structured and systematic process that involves identifying a problem, analyzing it, generating possible solutions, evaluating these solutions, and selecting the best one. The algorithm is also known as the "systems engineering process" or "systems analysis and design."
The algorithm is typically divided into several phases, including:
Problem identification: This involves defining the problem, its boundaries, and its scope. This step also involves identifying the objectives and constraints of the problem. Analysis: This step involves gathering data and information related to the problem, and identifying the root cause of the problem. This may involve conducting surveys, interviews, or experiments. Design: In this step, potential solutions are generated, and a conceptual design is created. The design should be flexible enough to allow for the incorporation of new information and changes. Evaluation: The potential solutions are evaluated based on predetermined criteria, and the best solution is selected. Implementation: The selected solution is implemented and monitored to ensure it is working effectively. Any necessary modifications or adjustments are made during this phase.
The Systematic Approach algorithm is a powerful tool for problem-solving as it provides a structured, step-by-step approach to analyzing and solving complex problems. It also allows for a thorough understanding of the problem and its potential solutions, as well as the ability to evaluate and select the best solution based on predefined criteria.
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Verizon charges $76.00 for 500 minutes and Sprint charges $54.00 for 450 minutes. Who has the better deal? *
Answer:
i think it would be sprint cause it is lest money and the mintues is 450 but the other is just 50 more mintues and you have to pay 22 more dollor for verizion so i pick sprint have a nice day
Step-by-step explanation:
Find the seasonalized forecast for Q2 of 2017.The sales trend
has been modeled as: Sales = 181.00+ 2 * t , where t= time in
quarters, beginning in Q1 2014. Seasonality for the four quarterly
periods i
The sales trend Sales = 181.00 + 2t where t= time in quarters, beginning in Q1 2014The seasonal factors for the four quarters are i.e: {0.9, 1.1, 1.2, 0.8}
To find the seasonalized forecast for Q2 of 2017, the following steps must be followed:
Step 1: Calculate trend for the Q2 of 2017 t = 3.25
Step 2: Determine seasonal factor for Q2 which is 1.1 since it's the second quarter
Step 3: Multiply trend and seasonal factors to get seasonalized trend for Q2 = (181 + 2(3.25)) * 1.1 = 198.95
Step 4: Therefore, the seasonalized forecast for Q2 of 2017 is 198.95.
Therefore, we have Sales = 181.00 + 2t where t is the time in quarters, starting from Q1 2014. In other words, t = 1 for Q1 2014, t = 2 for Q2 2014, and so on.
In addition, we have seasonal factors for each quarter, i.e, {0.9, 1.1, 1.2, 0.8}.
To calculate the seasonalized forecast for Q2 of 2017, we need to follow the following steps:
Step 1: Calculate trend for the Q2 of 2017t = 3.25 [since there are 13 quarters between Q1 2014 and Q2 2017.
The 13th quarter corresponds to Q2 2017. So, t = 13. Therefore, t = 2 + 4(13 - 1) = 3.25]
Step 2: Determine the seasonal factor for Q2 of 2017
The seasonal factor for Q2 of 2017 = seasonal factor for the second quarter = 1.1
Step 3: Multiply trend and seasonal factors to get seasonalized trend for Q2
Therefore, seasonalized trend for Q2 of 2017 = (181 + 2(3.25)) * 1.1 = 198.95Step 4:
Therefore, the seasonalized forecast for Q2 of 2017 is 198.95.
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how to solve and algebraic riccati equation using matlab
You can solve an algebraic Riccati equation using MATLAB.
How to solve and algebraic riccati equation using matlab:
Here's a step-by-step guide:
STEP 1: To solve an algebraic Riccati equation using MATLAB, you will need to use the built-in function `care`.
This function is part of the Control System Toolbox, so ensure you have that installed.
STEP 2: Define the matrices A, B, Q, and R in your equation.
The algebraic Riccati equation is of the form:
A'*X + X*A - X*B*R^(-1)*B'*X + Q = 0
Here's an example of how you might define these matrices in MATLAB:
```MATLAB
A = [1 2; 3 4];
B = [5; 6];
Q = [1 0; 0 1];
R = 1;
```
STEP 3: Use the `care` function to solve the algebraic Riccati equation.
The syntax is:
```MATLAB
X = care(A, B, Q, R);
```
STEP 4: After running the above code, the variable `X` will store the solution to the algebraic Riccati equation.
You can display the result by typing `X` in the command window.
Remember to replace the example matrices A, B, Q, and R with the ones specific to your problem.
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