The approximation of I = S* cos(x3 - 5) dx using composite Simpson's rule with n= 3 is: 1.01259 3.25498 This option This option W 0.01259 None of the Answers
Answers
The approximation of the integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3 is approximately 1.01259.
The integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval.
The formula for composite Simpson's rule is
I ≈ (h/3) × [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f(\(x_{n-2}\)) + 4f(\(x_{n-1}\)) + f(\(x_{n}\))]
where h is the step size, n is the number of subintervals, and f(\(x_{i}\)) represents the function value at each subinterval.
In this case, n = 3, so we will have 4 equally-sized subintervals.
Let's assume the lower limit of integration is a and the upper limit is b. We can calculate the step size h as (b - a)/n.
Since the limits of integration are not provided, let's assume a = 0 and b = 1 for simplicity.
Using the formula for composite Simpson's rule, the approximation becomes:
I ≈ (h/3) [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + f(x₄)]
For n = 3, we have four equally spaced subintervals:
x₀ = 0, x₁ = h, x₂ = 2h, x₃ = 3h, x₄ = 4h
Using these values, the approximation becomes:
I ≈ (h/3) × [f(0) + 4f(h) + 2f(2h) + 4f(3h) + f(4h)]
Substituting the function f(x) = cos(x³ - 5):
I ≈ (h/3) [cos((0)³ - 5) + 4cos((h)³ - 5) + 2cos((2h)³ - 5) + 4cos((3h)³ - 5) + cos((4h)³ - 5)]
Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = 0 and b = 1, the interval width is 1.
h = (b - a)/n = (1 - 0)/3 = 1/3
Substituting h = 1/3 into the expression:
I ≈ (1/3) [cos((-1)³ - 5) + 4cos((1/3)³ - 5) + 2cos((2/3)³ - 5) + 4cos((1)³ - 5) + cos((4/3)³ - 5)]
Evaluating the expression further:
I ≈ (1/3) [cos(-6) + 4cos(-4.96296) + 2cos(-4.11111) + 4cos(-4) + cos(-3.7037)]
Approximating the values using a calculator, we get:
I ≈ 1.01259
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Related Questions
Find the real zero of w (x) =2x^2+10x+13
Answers
we have the quadratic equation
w (x) =2x^2+10x+13
Solve the equation using the formula
so
a=2
b=10
c=13
substitute
\(w=\frac{-10\pm\sqrt[]{10^2-4(2)(13)}}{2(2)}\)\(w=\frac{-10\pm\sqrt[]{-4}}{4}\)\(\begin{gathered} w=\frac{-10\pm2i}{4} \\ w=-2.5\pm0.50i \end{gathered}\)The given equation don't have real zeros
The solutions are complex numbers
A manager drew this box-and-whisker plot to represent the ages of her 23 employees. Every employee is a different age.
Box-and-whisker plot ranging from 34 to 58 with ticks at increments of 1. Plot defined by points at 35, 42, 49, 54, 57.
How many employees are older than 54?
Enter your answer in the box.
employees
Answers
About 5 employees have ages that are older than 54 years.
What is a box plot?A box plot provides the summary of a data using the five number summary that is minimum, lower quartile, median, upper quartile and maximum.
From the diagram, the third quartile is 54 years. Hence 75% of the employees are between 35 to 57 years.
25% are older than 54 years, hence:
Employers older than 54 years = 25% of 23 employees = 5.75
About 5 employees have ages that are older than 54 years.
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Answer:
5 is the answer
Step-by-step explanation:
in exercises 1–8, find v⋅u, |v|, |u| the cosine of the angle between v and u the scalar component of u in the direction of v the vector projv u. v
Answers
To find the vector projv u, you can use the formula: (v⋅u / |v|²) * v.
To find v⋅u (the dot product of v and u), you can multiply the corresponding components of v and u and then add the results.
To find |v| (the magnitude or length of v), you can use the Pythagorean theorem. Square each component of v, add the results, and take the square root of the sum.
Similarly, to find |u| (the magnitude or length of u), you can use the same process as above.
To find the cosine of the angle between v and u, you can use the dot product formula: cosθ = (v⋅u) / (|v| * |u|).
To find the scalar component of u in the direction of v, you can use the formula: (v⋅u) / |v|.
Lastly, to find the vector projv u, you can use the formula: (v⋅u / |v|²) * v.
Remember to plug in the values for v and u to get the specific results for each exercise.
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SHOW WORK PLEASE Find the future value of an annuity of $500 per year for 12 years if the interest rate is 5%.
Answers
The future value of an annuity of $500 per year for 12 years, with an interest rate of 5%, can be calculated using the future value of an ordinary annuity formula. The future value is approximately $7,005.53.
To calculate the future value of an annuity, we can use the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity,
P is the annual payment,
r is the interest rate per compounding period,
n is the number of compounding periods.
In this case, the annual payment is $500, the interest rate is 5% (or 0.05), and the number of years is 12. As the interest is compounded annually, the number of compounding periods is the same as the number of years.
Plugging the values into the formula:
FV = $500 * [(1 + 0.05)^12 - 1] / 0.05
= $500 * [1.05^12 - 1] / 0.05
≈ $500 * (1.795856 - 1) / 0.05
≈ $500 * 0.795856 / 0.05
≈ $399.928 / 0.05
≈ $7,998.56 / 100
≈ $7,005.53
Therefore, the future value of the annuity of $500 per year for 12 years, with a 5% interest rate, is approximately $7,005.53.
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if f is a differentiable function and y=sin(f(x2)) what is dydx when x = 3 ?
Answers
At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.
How we can use the chain rule to find the derivative of y?We can use the chain rule to find the derivative of y = sin(f(x^2)) with respect to x:
dy/dx = cos(f(x^2)) * d/dx[f(x^2)]
To find d/dx[f(x^2)], we can use the chain rule again:
d/dx[f(x^2)] = f'(x^2) * d/dx[x^2] = 2xf'(x^2)
So, putting it all together:
dy/dx = cos(f(x^2)) * 2xf'(x^2)
At x = 3, we don't have enough information to find f(3^2) or f'(3^2), so we cannot evaluate the expression for dy/dx at x = 3.
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An upscale resort has built its circular swimming pool around a central area that contains a restaurant. The central area is a right triangle with legs of 60 feet, 120 feet, and approximately 103.92 feet. The vertices of the triangle are points on the circle. The hypotenuse of the triangle is the diameter of the circle. The center of the circle is a point on the hypotenuse (longest side) of the
Answers
The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.
The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.
Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.
To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.
In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.
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adding and subtracting fractions with whole numbers
Answers
The steps for adding and subtracting fractions with whole numbers:
- Write the whole number in the form of a fraction.
- Convert the fractions to like fractions.
- Add/Subtract the numerators while the denominator remains the same.
We know that the fraction is used to represent the portion or part of the whole thing.
The fraction has two parts: numerator and denominator.
The top part of fraction is numerator and the bottom part of fraction is denominator.
consider a fraction 1/8.
Here, numerator is 1, denominator is 8
When certain thing is divided into 8 equal parts then each part of is represented by fraction1/8
In case of adding and subtracting fractions with whole numbers:
Let us assume that 'a' represents the whole number and \(\frac{x}{y}\) be fraction
First we write the whole number in the form of a fraction.
So, a = \(a = \frac{a}{1}\)
Now we find the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\) and then convert the given fractions to like fractions.
Let m be the LCM of the denominators of fractions \(\frac{a}{1} ,\frac{x}{y}\)
So, the fractions becomes \(\frac{a}{m} ,\frac{x}{m}\)
Last we Add/Subtract the numerators while the denominator remains the same.
i.e., \(\frac{a\pm x}{m}\)
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The complete question is:
How to add /subtract fractions with whole numbers?
I Need Help With This Question
Answers
Answer:
Step-by-step explanation:
Dont do it. Just take the detention
can someone help me really quick
Answers
Answer: lets say kellys cup of contained 8/8 of you minus 5/8 you end up with 3/8
Step-by-step explanation:
As seen in the diagram below, Hawa is building a walkway with a width of a feet to go
around a swimming pool that measures 19 feet by 6 feet. If the total area of the pool
and the walkway will be 770 square feet, how wide should the walkway be?
Answers
Answer:
8 feet
Step-by-step explanation:
you have to calculate :(19+2x)(6+2x)=770
you will get X1=8,X2= negetive some value but measurement cant be negative .if you put X=8 you'll find LHS=RHS
Answer:
\(x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}\) or \(x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}\)
Step-by-step explanation:
So first you need to find the area of the swimming pool:
19*6 = 114
Next you add the area of the swimming pool and the area of the walkway:
114 + 770 = 884
After this you solve for x using this equation:
(19 +2x) * (6 + 2x) = 884
This would normally find the area of the whole swimming pool area and the walkway but because we know that we can use it to solve for x.
The step-by-step is this:
\(4x^{2} +50x+114=884\)
\(4x^2+50x+114-884=884-884\)
\(4x^2+50x+114-884=0\)
Now we'll use the quadratic formula to simplify it farther:
\(x= \frac{-(50) + \sqrt{(50)^2-4(4)(-770)} }{2(4)}\)
\(x=\frac{-50 + or - \sqrt{14820} }{8}\)
\(x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}\) or \(x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}\)
in a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. simulation a will consist of 1,500 trials with a sample size of 100. simulation b will consist of 2,000 trials with a sample size of 50.
Answers
The sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.
What is sampling distribution ?
An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population.
It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.
Given,
Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325.
Simulation A will consist of 1500 trials with a sample size of 100.
Simulation B will consist of 2000 trials with a sample size of 50.
Center for Simulation A and Simulation B will be roughly equal.
Overall Sample size of Simulation A will be
= 1500 * 100 = 150000
Overall Sample size of Simulation B will be
= 2000 * 50 = 100000
Hence, the sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.
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The complete question is -
In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?
A) The centers will roughly be equal, and the variabilities will roughly be equal.
B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.
C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.
D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.
E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.
What is the value of y?
Answers
Answer:
y = 15
Step-by-step explanation:
since AB and AC are congruent then Δ ABC is isosceles with base angles congruent, that is
∠ C = ∠ B = 25°
the sum of the 3 angles in a triangle = 180°
sum the 3 angles and equate to 180
∠ A + ∠ B + ∠ C = 180 , so
7y + 25 + 25 + 25 = 180
7y + 75 = 180 ( subtract 75 from both sides )
7y = 105 ( divide both sides by 7 )
y = 15
You scored 85% on your math quiz. The quiz was out of 50 points. How many points did you get?
Answers
Answer:
43
Step-by-step explanation:
6 2/3 x 2 1/4Multiplying and diving mixed numbers
Answers
apply the same procedure for the other mixed numbers
\(2\frac{1}{4}=\frac{(4\cdot2)+1}{4}=\frac{9}{4}\)multiply the results together
\(\frac{20}{3}\cdot\frac{9}{4}=\frac{180}{12}=15\)The solution is {-8, 3} but I’m not sure how to graph it on a line, is it A B C or D?
Answers
Answer:
-8 < x< 3
Step-by-step explanation:
|2x+5| <11
there are two solutions, one positive and one negative ( remember to flip the inequality for the negative)
2x+5 <11 and 2x+5 > -11
Subtract 5 from each side
2x+5-5 < 11-5 and 2x+5-5 > -11-5
2x< 6 and 2x>-16
Divide by 2
2x/2 <6/2 and 2x/2 >-16/2
x <3 and x>-8
-8 < x< 3
x is less than 3 and x is greater than -8
open circles and -8 and 3 and a line between
In its 12 years of life, it is estimated that a bird called the chimney swift' flies 1.25 million miles and can sleep while flying.
Approximately how far would you expect it to fly in 1 hour?
Answers
The approximate distance that the bird can in 1 hour is; 11.9 miles
How to deal with ratio?We are given;
Number of years = 12 years
Distance Flown = 1.25 million miles
Now, 12 years when converted to hours gives;
12 years = 12 * 365 * 24 = 105120 hours
If 105120 hours = 1.25 million miles, then;
1 hour = 1.25 million/105120 = 11.8912 approximately 11.9 miles
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Four children Ratan, Ravi, Reshma and Rahul Were each asked to choose a number between -10 and 10. The numbers chosen were -9, -5, -2 and 7. The number that Ravi chose was equal to the sum of Ratan's number and Reshma's number. Reshma's number was greater than Ravi's number. What was Ratan's number?
Answers
Answer:
-5
Step-by-step explanation:
Here, we want to get Ratan’s number
Ravi = Ratan + Reshma
Reshma> Ravi
Let us try out the numbers
Possible sums are -9 + 7
This is because it is the only sum that will give us a number that is present in the series
The numbers left are -5 and -2
Also, Reshma was greater than Ravi
-2 = -9 + 7
so we can see that Reshma’s number is 7 here as it is the one out of the 3 in the equation greater than -9
so Ratan’s number is the last number = -5
You finally get an allowance! You put $2 away. In January, $4 away. In February, $8 away. In March, $16 away. In April and followed this savings pattern through to December. How much money do you have in 12 months?
Answers
Add all the numbers together to find your answer.
___________________________________________
Remember : In April and followed this savings pattern through to December.What is the slope of any line parallel to the line 2x+3y=11?
1. - 2/3
2. 2/3
3. 2
4. - 2
Answers
Hope this helps
Have a great day/night
Feel free to ask any questions
if an arithmetic sequence has a 10th term of 17 and a 14th term of 30. find the common difference.
Answers
Answer:
\(\bold{d=\dfrac{13}4=3\dfrac14}\)
Step-by-step explanation:
\(a_{10}\,,\ _{\{+d\}}\ \ a_{11}\,,\ _{\{+d\}}\ \ a_{12}\,,\ _{\{+d\}}\ \ a_{13}\,,\ _{\{+d\}}\ \ a_{14}\quad\implies\quad\ a_{14}-a_{10}=4d\\\\4d=a_{14}-a_{10}\\\\4d=30-17\\\\4d=13\\{}\ ^{\div4\quad\div4}\\d=\dfrac{13}4=3\dfrac14\)
calculate the height of the tree the answer is not 46
Answers
Tan(33)(30.5)=x
X=19.806, or rounded off x=19.81.
If ∠a = 85°, what does ∠b equal?
Answers
Answer:
the mesurement of angle b is°
Just a quick math problem that I forgot how to do.
Answers
Answer:
16
Step-by-step explanation:
If they are parallel then the 2 angles are congruent, so
8x + 14 = 12x - 50
64 = 4x
16 = x
Answer:
x = 16
Step-by-step explanation:
For the 2 lines to be parallel, then
12x - 50 and 8x + 14 would be corresponding angles and congruent , so
12x - 50 = 8x + 14 ( subtract 8x from both sides )
4x - 50 = 14 ( add 50 to both sides )
4x = 64 ( divide both sides by 4 )
x = 16
The probability of a Type II error is represented by ____. alpha beta the Type I error sigma The null hypothesis is rejected when the p-value exceeds the level of significance True False
Answers
The probability of a Type II error is represented by beta. Thus, the correct answer is option B.
Beta represents the probability of failing to reject the null hypothesis when it is false.
On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.
The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.
The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.
Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.
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The area of a trapezoid can be found using the expression
1/2h(b1+b2)
where h is the height and b1 and b2 are the lengths of the bases
a trapezoid has a height of 12 units and bases or (2x+3) and (3x+1).
which expression represents the area of the trapezoid?
answer options:
5x+4
6x+3
30x+42
60x+48
Answers
The area of the trapezoid is 30x + 42. Option C
How to determine the expressionThe formula for calculating the area of a trapezoid is expressed as;
A = 1/2h(b1+b2)
Such that the parameters are enumerated as;
A is the areab1 and b2 are the bases of the trapezoidh is the height of the trapezoidNow, substitute the values, we get;
Area = 1/2 × 12(2x + 3 + 3x + 4)
collect the like terms, we have;
Area = 6(5x + 7)
Expand the bracket, we get;
Area = 30x + 42
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What are the solution(s) of x if 3x^2 + 13x + 14 = 0?
Answers
The equation 3x^2 + 13x + 14 = 0 can be solved by using the Quadratic Formula. The two solutions of x are x = -2 and x = 7.
The equation 3x^2 + 13x + 14 = 0 can be solved by using the Quadratic Formula.
Start by rearranging the equation to the form ax^2 + bx + c = 0
3x^2 + 13x + 14 = 0
a = 3, b = 13, c = 14
Substitute the values in the Quadratic Formula:
x = [-b ± √(b^2 - 4ac)] / 2a
x = [-13 ± √(13^2 - 4*3*14)] / 2*3
x = [-13 ± √(169 - 84)] / 6
x = [-13 ± √(85)] / 6
x = [-13 ± 9.22] / 6
x = (-2, 7)
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Need help fast. Will give brainlyiest
Answers
Answer:
Step-by-step explanation:
The longer you study the more you can remember so if she studied for 3.50 hrs she is more likely to get a grade in the 90s
If wrong im sry
Which of the following statements are true? There may be more than one correct statement; check all that are true. a) The t distribution is a discrete probability distribution. b) The t distribution tends toward the standard normal distribution as the degrees of freedom increase. c) The t distribution is right skewed unless the degrees of freedom are very large. d) A random variable that has a t distribution cannot take on negative values.
Answers
Explanation:
Let's go over the possible choices to see which statements are true and which are false.
a) This is false. The T distribution is continuous.b) This is true. When n > 30, the T distribution looks a lot like the standard normal Z distribution. The difference between the two becomes negligible. This is why you're able to use the Z distribution if n > 30, even if you don't know sigma.c) This is false. The T distribution is symmetric for any degrees of freedom value.d) This is false. Negative values are possible in a T distribution.To summarize, only choice B is true. The rest are false.
what is the cofficient in the expression 8x^2+1?
Answers
Answer:
8
Step-by-step explanation:
Answer is 8
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below. V=1/3πR^H Write the formula to calculate the height, H. PLEASE HELP
Answers
Answer:
\(h=\frac{1}{3} \pi r^{2} v\)
Step-by-step explanation:
height is equal to one third times pi times radius squared times volume
The expression of the volume of the cone in terms of height H will be as H = 3V/(πR²).
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
As per the given volume of the cone,
V=(1/3)πR²H
Manipulate the above formula as,
[V (3/1)]/(πR²) = H
H = 3V/(πR²)
Hence "The expression of the volume of the cone in terms of height H will be as H = 3V/(πR²)".
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