Integrate the function y=f(x) between x=2.0 to x = 2.8, using the simpson's 1/3 rule with 6 strips. assume a =1.2, b= -0.587, y=a/x+b Sqrt(x)
Answers
the integral of the function y = f(x) between x = 2.0 and x = 2.8, using Simpson's 1/3 rule with 6 strips, is approximately 0.3790.
To integrate the function y = f(x) using Simpson's 1/3 rule, we'll follow these steps:
Step 1: Determine the interval and number of strips.
Step 2: Calculate the width of each strip.
Step 3: Evaluate the function at the interval points.
Step 4: Apply Simpson's 1/3 rule to compute the integral.
Given: y = a/x + b√(x) with a = 1.2 and b = -0.587
Interval: x = 2.0 to x = 2.8
Number of strips: 6
Step 1: Determine the interval and number of strips.
The interval is from x = 2.0 to x = 2.8.
We have 6 strips.
Step 2: Calculate the width of each strip.
The width, h, of each strip is given by:
h = (b - a) / n
= (2.8 - 2.0) / 6
= 0.1333
Step 3: Evaluate the function at the interval points.
We need to evaluate the function f(x) = a/x + b√(x) at the interval points.
Let's calculate the values:
f(2.0) = 1.2/2.0 - 0.587√(2.0)
= 0.6 - 0.587 * 1.414
= 0.6 - 0.8287
= -0.2287
f(2.1333) = 1.2/2.1333 - 0.587√(2.1333)
= 0.5624
f(2.2666) = 1.2/2.2666 - 0.587√(2.2666)
= 0.5332
f(2.3999) = 1.2/2.3999 - 0.587√(2.3999)
= 0.5128
f(2.5332) = 1.2/2.5332 - 0.587√(2.5332)
= 0.4963
f(2.6665) = 1.2/2.6665 - 0.587√(2.6665)
= 0.4826
f(2.8) = 1.2/2.8 - 0.587√(2.8)
= 0.4714
Step 4: Apply Simpson's 1/3 rule to compute the integral.
Now, we'll apply the Simpson's 1/3 rule using the evaluated function values:
Integral = (h/3) * [f(x₀) + 4 * (Σ f(xi)) + 2 * (Σ f(xj)) + f(xₙ)]
Where:
h = width of each strip
f(x⁰) = f(2.0)
Σ f(xi) = f(2.1333) + f(2.3999) + f(2.6665)
Σ f(xj) = f(2.2666) + f(2.5332)
f(xₙ) = f(2.8)
Let's calculate the integral:
Integral = (0.1333/3) * [(-0.2287) + 4 * (0.5624 + 0.5128 + 0.4826) + 2 * (0.5332 + 0.4963) + 0.4714]
= (0.1333/3) * [(-0.2287) + 4 * (1.5578) + 2 * (1.0295) + 0.4714]
= (0.1333/3) * [(-0.2287) + 6.2312 + 2.0590 + 0.4714]
= (0.1333/3) * [8.5329]
= 0.1333 * 2.8443
= 0.3790
Therefore, the integral of the function y = f(x) between x = 2.0 and x = 2.8, using Simpson's 1/3 rule with 6 strips, is approximately 0.3790.
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Related Questions
A typical person begins to lose consciousness if subjected to accelerations greater than about 5 g(49.0 m/s^2) for more than a few seconds. Suppose a 3.00×10^4−kg manned spaceship's engine has an exhaust speed of 2.50×10^3 m/s. What maximum burn rate ∣ΔM/Δt∣ could the engine reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness?
Answers
The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.
Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.
Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.
Let the mass of the spaceship be m and the exhaust speed of the engine be v.
Using the formula for the thrust of a rocket,
T = (mv)e
After substituting the given values into the formula for thrust, we get:
T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N
Therefore, the acceleration produced by the engine, a is given by the formula below:
F = ma
Therefore,
a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²
The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,
x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s
Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.
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A rectangular lawn is yards by 26 yards. It would cost $6.00 per yard to install a fence around the lawn. How much would it cost to put a fence around the lawn?
Answers
solve the following expontential equation. express your answer as both an exact expression and a decimal approxaimation rounded to two deicmal places e^2x-6=58^x 10
Answers
To solve the exponential equation e^(2x-6) = 58^x - 10, we can take the natural logarithm (ln) of both sides to remove the exponential terms:
ln(e^(2x-6)) = ln(58^x - 10)
Using the property ln(e^a) = a, we have:
2x - 6 = ln(58^x - 10)
Now, let's solve for x algebraically.
2x - 6 = ln(58^x - 10)
Adding 6 to both sides:
2x = ln(58^x - 10) + 6
Dividing both sides by 2:
x = (ln(58^x - 10) + 6) / 2
This is the exact expression for the solution. To obtain a decimal approximation, you can substitute the expression into a calculator or computer software.
Using a calculator or computer software, the decimal approximation for x is approximately x ≈ 2.50 (rounded to two decimal places).
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Charlie subtracts two polynomials, 5x^2 – 9x^2, and says that the difference proves that polynomials are not closed under subtraction.Kate argues that the difference does in fact show that polynomials are closed under subtraction. Who is correct? Type only 'Charlie' orKate' as your answer in the box.
Answers
Charlie
Here, we want to check if polynomials is closed under subtraction or not
To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not
We have;
\(\begin{gathered} 5x^2-9x^2=-4x^2 \\ \\ \text{And;} \\ \\ 9x^2-5x^2=4x^2 \end{gathered}\)As we can see, both results are not equal
If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.
Tessa has a coin jar full of dimes and pennies. When she took the coin jar to the bank, she was told that it contained exactly $27.34. Give three different combinations of the number of dimes and pennies that could have been in the coin jar.
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Matt runs the Lee Farm, which produces many different crops, including wheat. The more plots of land that are devoted to growing wheat, the more bushels of wheat the farm will produce.
p = the number of plots of land devoted to growing wheat
w = the number of bushels of wheat produced each year
Which variable is the dependent variable?
Answers
The dependent variable is the number of bushels of wheat produced each year.
The independent variable is the number of plots of land devoted to growing wheat.
It is given that, the more plots of land that are devoted to growing wheat, the more bushels of wheat the farm will produce.
There are two variables. One is called the independent variable and the other is called the dependent variable.
The variable whose value does not depend on the other variable is the independent variable. The variable whose value depends on the other variable is the dependent variable.Start by finding the dependent variable.
Since, the number of bushels of wheat produced each year. So, w is the dependent variable.
Since the number of plots of land devoted to growing wheat. So, p is the independent variable.
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Kelsey is making spaghetti for lunch. The recipe calls for 2 cups of tomato sauce to serve 12 people. If Kelsey serves 48 people, how many cups of tomato sauce does she need?
Answers
Answer: 8 cups
Step-by-step explanation:
Since 2 cups is for 12 people you have to multiply 12 x ? = 48 which ?=4 so then you have to multiply 4 x 2 to find out how many cups for 48 people
the bag of mass is 1.5kg what is the mass of bag in grams
Answers
Answer:
the mass of the bag in grams is 1500
Answer:1500
Step-by-step explanation: Have a good day
The segments shown below could form a triangle.
A
с
B
4
9
B
15
A
A. True
B. False
Answers
Answer: True.
Step-by-step explanation:
do the math and u will see
No, The segments shown below could not form a triangle.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Three line segment with measure 9 , 4 and 15 are shown.
We know that;
The sum of two sides of a triangle are always greater than the third side,
Here, 9 + 4 = 13 < 15
Hence, The segments shown below could not form a triangle.
Thus, The segments shown below could not form a triangle.
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You pick a card at random. 4 5 6 7 What is P(divisor of 24)? Write your answer as a percentage.
Answers
Answer: The percentage is a 2/4
Step-by-step explanation:
Answer:
50%
Step-by-step explanation:
You want to know the probability of drawing a divisor of 24 from the set of cards with numbers {4, 5, 6, 7}.
DivisorThe divisors of 24 in this set are 4 and 6, which comprise half the cards. As a percentage, this is ...
1/2 × 100% = 50%
The probability of picking a divisor of 24 is 50%.
Evaluate the expression y-3+2 when x = 6 and y=8
Answers
Answer:
7
Step-by-step explanation:
Hey there!
In order to answer this question you need to substitute the "y-value"
As you can see, y=8 and we need to put 8 where there is y
8-3+2 is what the equation will look like
Now we can simplify
8-3 is 5 and 5+2 is 7
So your answer is 7
Help me please y=-3x-4 A.(-2,4) B.(-3,5) C. (-2,4)(-3,5) D.Neither
Answers
Answer:
B
Step-by-step explanation:
Which, if any, of the following generalized formulas does not exist for interhalogen compounds? (X and Y represent different halogens.)
XY
XY2
XY3
XY5
All the above can represent stable interhalogen compounds.
Answers
All the above can represent stable interhalogen compounds. Interhalogen compounds are formed when different halogens combine with each other.
The general formula for interhalogen compounds is given by XYn, where X and Y represent different halogens, and n represents the number of Y atoms bonded to the X atom. The interhalogen compounds can have different stoichiometries, resulting in different values of n. Therefore, all the given formulas, XY, XY2, XY3, and XY5, can represent stable interhalogen compounds, depending on the specific combination of halogens and their bonding arrangements.
Hence, none of the given formulas does not exist for interhalogen compounds, as all of them can be valid representations of stable interhalogen compounds.
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Need a quick answer please!
Answers
Answer:
It’s going to be b
Step-by-step explanation:
Because add then then divide then put the x on top and simplify then and then subtract
noah makes 3 statements about the incenter of a triangle. a. to find the incenter of a triangle, you must construct all 3 angle bisectors
b. the incenter is always equisistant from the verticles of the triangle
c. the incenter is always equidistant from each side of the triangle
for each of the following statements, decide whether you agree with noah. explain your reasoning.
Answers
I partially agree with Noah's statements about the incenter of a triangle. Statement (a) is correct, as constructing all three angle bisectors is indeed necessary to find the incenter.
However, statement (b) is incorrect because the incenter is not always equidistant from the vertices of the triangle. Statement (c) is correct; the incenter is always equidistant from each side of the triangle.
Noah's first statement (a) is accurate. The incenter of a triangle is the point where all three angle bisectors intersect. An angle bisector divides an angle into two congruent angles, and constructing all three angle bisectors ensures that the incenter is determined correctly. However, Noah's second statement (b) is incorrect. The incenter is not always equidistant from the vertices of the triangle. It is possible for the incenter to be closer to one vertex than the others. The only case where the incenter is equidistant from the vertices is when the triangle is equilateral. On the other hand, Noah's third statement (c) is correct. The incenter is always equidistant from each side of the triangle. This property is known as the incenter's "equal-distance property." The distance from the incenter to any side of the triangle is equal to the radius of the incircle, which is the circle inscribed inside the triangle.
Constructing all three angle bisectors is necessary to find the incenter (statement a), but the incenter is not always equidistant from the vertices (statement b). However, the incenter is always equidistant from each side of the triangle (statement c).
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A company makes a profit of $60 per software program and $45 per video game. The company must produce both and can produce at most 225 software programs and at most 350 video games per week. Total production cannot exceed 455 items per week.
(a) Write out the set of inequalities you would use to represent the constraints in this situation.
(b) Identify the corner points.
(c) How many items of each kind should be produced per week to maximize profit? Show your work. Be sure
to show the comparison in your work.
Use linear programming to solve.
Answers
Step-by-step explanation:
a)
(a)255+350 <455
ans...605-455
..150
.........profit per week is 60 +45
105.
105 x 150
weekly profit is..$15750
Answer:
See below.
Step-by-step explanation:
Let's first define our variables. Let's let:
x denote the amount of software programs made and
y denote the amount of video games made.
Part A)
Now, let's write our equations and constraints.
The company can produce at most 225 software programs. So:
\(x\leq225\)
And the company can produce at most 350 video games. So:
\(y\leq 350\)
Total product (the sum of software programs and video games) cannot exceed 455 items per week. In other words:
\(x+y\leq455\)
Part B)
Refer to the first graph:
We have four corner points: A, B, C, and D.
The darkest portion represents the feasible portion. Any combination of software programs and video games within this portion can be produced.
Part C)
Refer to the second graph.
To find what to produce to find the maximum profit, let's write an equation. Let P equal to maximum profit. So, it would be the sum of the total profit from the software programs and video games. We can write the following equation:
\(P=60x+45y\)
Let's solve for y in order to graph it. Subtract 60x from both sides:
\(45y=-60x+P\)
Divide both sides by 45:
\(y=-\frac{4}{3}x+\frac{P}{45}\)
In order produce the maximum profit, P must be the greatest while simultaneously touching our corner points.
Note: The P, Q, R, and S are just rough estimates.
I've graphed four versions of our equation using different variables (for P). We can see that the equation with the highest profit P is the one the crosses point C with P equaling approximately $24,000.
Therefore, in order to maximize profits, the company should produce (Remember that C is at (225, 230)) 225 software programs and 230 video games.
And we're done!
Which of the following lists is in order from smallest to largest?
0.05, 0.2, 0.48, 0.6
0.2, 0.05, 0.48, 0.6
0.2, 0.48, 0.05, 0.6
0.05, 0.2, 0.6, 0.48
WHO EVER SAYS IT FIRST GETS 100 POINTS
Answers
Answer:
first option
Step-by-step explanation:
Answer:
A. 0.05, 0.2, 0.48, 0.6.
help me with this pls
Answers
The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is. Find x.
Answers
If the perimeter of the isosceles triangle is 12 cm, then the base of the triangle (x), as well as the length of the triangle leg (x) is 4 cm.
An isosceles triangle is a type of triangle in which two sides have the same length. These two equal sides are referred to as the legs of the triangle, while the remaining side is known as the base.
The perimeter of a triangle is the sum of the lengths of all its sides. In this case, since the triangle is isosceles, the base and one leg have the same length (x), and the other leg also has the same length (x). Therefore, the perimeter of the triangle is 2x + x = 3x. Given that the perimeter of the isosceles triangle is 12 cm, then:
3x = 12
x = 12/3
x = 4
So, the base and legs of the isosceles triangle each have a length of 4 cm.
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Your question seems to be missing the value for the perimeter of the triangle, but I suppose the complete question was:
"The length of the base of an isosceles triangle is x. The length of a leg is x. The perimeter of the triangle is 12 cm. Find x."
Find the length of X
Answers
It’s because it’s an isosceles triangle so both sides are the same length
Btw brainliest pls
x – 2y = -2 3x -6y = 30
Sloved by Elimination
Answers
Answer:
No solutions.
Step-by-step explanation:
When given the following system of equations,
\(\left \{ {x-2y=-2} \atop {3x-6y=30}} \right.\)
Solve by the process of elimination. The process of elimination is when one manipulates one or both of the equations such that one of the variables is the inverse of the other variable in its corresponding equation. When one adds the system, one of the variables will cancel, and one can solve for the other variable, then back solve for the canceled variable.
In this case, one can see that all terms in the second equation have a common factor of (3), to make manipulating the equation easier, divide the entire equation by (3).
\(\left \{ {{x-2y=-2} \atop {3x-6y=30}} \right.\)
\(\left \{ {{x-2y=-2} \atop {x-2y=10}} \right.\)
However, in doing so, one can see that the left sides of the equation are equal, however, the right side is not. Such a statement is not possible, thus there are no solutions to this system of equations.
What would be the coordinates of Point D to complete square ABCD? Ay B 2. A Х -2 o 2. 2. С (2.2) (2, 2) (-2,2 (2-2)
Answers
Answer:
D: which is (2, -2)Step-by-step explanation:
please help i have no clue how to this any tips appreciated:))
Answers
Answer:
\( \displaystyle PW = \underline{ \quad18 \quad}\)
Step-by-step explanation:
by tangent property we acquire:
\( \displaystyle 3x - 6 = x + 10\)
add 6 to both sides:
\( \displaystyle 3x= x + 16\)
cancel x from both sides:
\( \displaystyle 2x= 16\)
divide both sides by 2:
\( \displaystyle x= 8\)
so,
\( \displaystyle PW = 3x - 6\)
plug in the got value of x:
\( \displaystyle PW = 3.8 - 6\)
simplify multiplication:
\( \displaystyle PW = 24- 6\)
simplify Substraction:
\( \displaystyle PW =18\)
hence, The measure of PW is 18 unit
A number is increased by 11 is multiplied by 2 the answer is 26
Answers
Answer:
Number = 2
Step-by-step explanation:
Let the number be x.
According to the question,
Number increased by 11 = x+11Multiplied by 2 is 26 : (x+11)*2 = 26Equation will be,
2(x+11) = 26Solving for x,
2x+22 = 262x = 26-222x = 4x = 4/2x = 2Thus,the number is 2.
#10: A Caterer’s total cost for a party includes a fixed cost, in addition the caterer also charges a certain amount for. Each guest
$300 to serve 25 guests
$420 to serve 40 guests
Find the fixed cost and the cost per guest
Answers
F+40X=420 SUBTRACT.
-----------------
-15X=-120
X=-120/-15
X=$8 PER GUEST.
F+25*8=300
F+200=300
F=300-200
F=$100 IS THE FIXED COST.
PROOF:
100+40*8=420
100+320=420
420=420
the weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a standard deviation of 17 . if 15 fish are randomly selected, what is the probability that the mean weight will be between 16.1 and 22.1 lb? (sorry, there is an error here, for now use z-scores on this)
Answers
The probability that the mean weight will be 0.4923
What is Probability?
A probability is a number that represents the likelihood or chance that a specific event will occur. Probabilities can be expressed as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Given,
µ = 18
Standard Deviation = 17
N = 15
Find: P(16.1 < bar{X} < 22.1)
= P ( \(\frac{16.1 - µ}{σ / \sqrt{N} }\) < \(\frac{X - µ}{σ / \sqrt{N} }\) < \(\frac{22.1 - µ }{σ / \sqrt{N} }\) )
= P ( \(\frac{16.1 - 18}{17 / \sqrt{15} }\) < Z < \(\frac{22.1 - 18}{17 / \sqrt{15} }\) )
= P(-0.4329 < Z < 0.9341)
= P(Z < 0.9341) - P(Z < -0.4329)
= 0.8249 - 0.3326
= 0.4923
The probability that the mean weight will be 0.4923
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what does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to zero?
Answers
The probability of a success gets closer to zero is 15.
What is behavior of the standard deviation ?
The average squared difference between data points and their mean value is called variance, and it is the variance's square root that is used to calculate standard deviation. The symbol for standard deviation can be seen below.
Both the standard deviation and the variance are indicators of dispersion, but the standard deviation is more explicitly the typical distance between a data point and the mean. The majority of the data will be within one standard deviation of the mean. While the variance is not measured in the same units as the actual data, the standard deviation is
If mean deviation is 12, what is its standard deviation?
Lets look the problem .
Given ,
Mean deviation (MD) =12
Here is the inequality to calculate the standard deviation.
6QD=5MD=4SD ,
Where ,QD stands for the Quartile deviation.
SD stands for the standard deviation.
So,
Standard deviation =(5/4)*MD
=(5/4)*12
=15
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the first three common multiples of 2 5 and 10
Answers
:
Multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ………… etc. Multiples of 5 are: 5, 10, 15, 20, 25, ………… etc. Therefore, common multiples of 2 and 5 = 10, 20, ………..etc.
Write two congruence statements for the congruent triangles. i will give out brainly
Answers
Answer:
If two sides in one triangle are congruent to two sides of a second triangle, and also if the included angles are congruent, then the triangles are congruent. ... If in triangles ABC and DEF, AB = DE, AC = DF, and angle A = angle D, then triangle ABC is congruent to triangle DEF.
If you roll a 6-sided die 48 times, what is the best prediction possible for the number of times you will roll a five?
Answers
Answer:
8
Step-by-step explanation:
probability of getting a 5 is 1/6 so you would do 1/6 x 48
48/6 = 8