The approximation of 1 = Lo cos (x2 + 5) dx using simple Simpson's rule is: -0.93669 -0.65314 N This option This option -1.57923 0.54869
Answers
The approximation of the integral ∫cos(x² + 5) dx using simple Simpson's rule is approximately -0.65314.
The integral ∫cos(x² + 5) dx using simple Simpson's rule, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval.
The formula for simple Simpson's rule is:
I ≈ (h/3) × [f(x₀) + 4f(x₁) + f(x₂)]
where h is the step size and f(xi) represents the function value at each subinterval.
Assuming the lower limit of integration is a and the upper limit is b, and n is the number of subintervals, we can calculate the step size h as (b - a)/n.
In this case, the limits of integration are not provided, so let's assume a = -1 and b = 1 for simplicity.
Using the formula for simple Simpson's rule, the approximation becomes:
I ≈ (h/3) × [f(x₀) + 4f(x₁) + f(x₂)]
For simple Simpson's rule, we have three equally spaced subintervals:
x₀ = -1, x₁ = 0, x₂ = 1
Using these values, the approximation becomes:
I ≈ (h/3) × [f(-1) + 4f(0) + f(1)]
Substituting the function f(x) = cos(x² + 5):
I ≈ (h/3) × [cos((-1)² + 5) + 4cos((0)² + 5) + cos((1)² + 5)]
Simplifying further:
I ≈ (h/3) × [cos(6) + 4cos(5) + cos(6)]
Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = -1 and b = 1, the interval width is 2.
h = (b - a)/2 = (1 - (-1))/2 = 2/2 = 1
Substituting h = 1 into the expression:
I ≈ (1/3) × [cos(6) + 4cos(5) + cos(6)]
Evaluating the expression further:
I ≈ (1/3) × [cos(6) + 4cos(5) + cos(6)] ≈ -0.65314
Therefore, the approximation of the integral ∫cos(x² + 5) dx using simple Simpson's rule is approximately -0.65314.
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Related Questions
how many 10-bit strings are there that contain exactly 4 ones?
Answers
By combinations, there are 210 10 bit strings which contains exactly 4 ones.
To find out how many 10-bit strings there are that contain exactly 4 ones, we can use the binomial coefficient formula.
The binomial coefficient formula is given by `C(n, k) = n! / (k! * (n-k)!)`,
where,
n is the total number of items, and k is the number of items
we want to choose from n. In this case, we want to choose 4 ones from 10 bits, so n = 10 and k = 4. Therefore, the number of 10-bit strings that contain exactly 4 ones is:
`C(10, 4) = 10! / (4! * (10-4)!) = 210`.
Hence, there are 210 10-bit strings that contain exactly 4 ones.
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Express the inequality −1.8≤x≤−0.03 using interval notation.
Answers
Answer:
[-1.8,0.03]
Step-by-step explanation:
This is how you use interval notation, square brackets means including the numbers, circular brackets means not including
Answer:
(-1.3,1.8]
Step-by-step explanation:
The inequality −1.3<x≤1.8 means "all numbers between −1.3 and 1.8." In interval notation, we express this as (−1.3,1.8]. Notice that we use a parenthesis to show that the number −1.3 is not included and a bracket to show that the number 1.8 is included.
In 2019, the distribution of golfer Lexi Thompson's driving distance had a mean of 276 yards. Assuming that her distribution of
driving distance is approximately normal with an 80th percentile of 290 yards, calculate its standard deviation.
Answers
The standard deviation is approximately 16.67 yards.
The standard deviation is a measurement of how much a group of values are spread over an area. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the average value) of the collection.
Standard deviation is calculated from the z-score by using the formula
\(z=\frac{x-\mu}{\rho} \\\) where ,
z is the z-score , x is the data value at that z-score , μ denotes the mean of the data set and σ is the standard deviation.
Given the mean is 276 yards , the data value at the 80th percentile is 290 . By using the z-score tables we find the z-score value to be 0.84 .
Therefore using the above formula we can find the standard deviation.
\(0.84=\frac{290-276}{\rho} \\\\or, \rho=\frac{290-276}{0.84}\\\\or,\rho=16.66...\\\\or,\rho\approx16.67\)
Hence the standard deviation is approximately 16.67 yards.
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A metal strip is being installed around a rectangular workbench that is 8 feet long and 4 feet wide. If the stripping costs $4 per foot, find the total cost of the stripping.
Answers
Answer:
$144
Step-by-step explanation:
Length*Width*Price
12*3 = 36
36*4 = 144
$144
A certain type of bacteria is growing at an exponential rate that is modeled by the equation y=aekt, where t represents the number of hours. There are 100 bacteria initially, and 500 bacteria five hours later.
Answers
Answer:
meow meow
Step-by-step explanation:
Vocab in your own words:
How to add two positive integers:
How to add two negative integers:
How to add a positive and a negative integers:
Answers
How to add two positive integers:
You add the numbers like you normally would. There's no trick even though it seems like a trick question.
Example: 3+5 = 8
In that example, you can think of like starting at 3 on the number line. Then you move 5 units to the right to arrive at 8 on the number line.
-----------------------------------------------------
How to add two negative integers:
Treat the negative numbers as their positive version of themselves. Next, you add those positive counterparts like normal. The last thing you do is make the result negative.
For example,
-9 + (-12) = -21
which we can think of like this
9+12 = 21
Then we just make everything negative to get that first equation mentioned.
-----------------------------------------------------
How to add positive and negative integers:
This will depend on which has larger absolute value. In other words, which is further away from 0 on the number line.
In any event, you basically subtract the positive version of each number. Then the one furthest from 0 will determine if the result is positive or negative.
Examples:
-8 + 9 = 1
7 + (-12) = -5
In the first example, we can think of it like 9-8 = 1. I'm subtracting the two numbers 8 and 9, but doing so large - small and only focusing on the positive versions so far. Because 9 is further away from 0 compared to -8, this ultimately means the result is positive (since 9 is positive).
In the second example, we would say 12-7 = 5. Then note how -12 is farther away from 0 compared to 7. This means the negative side wins, so to speak, and the final result is negative.
suppose that the lifetime of a transistor is a gamma random variable x with mean of 24 weeks and standard deviation of 12 weeks. what is the probability that the transistor will last between 12 and 24 weeks?
Answers
The probability that the transistor will last between 12 and 24 weeks is 0.424
X= lifetime of the transistor in weeks E(X)= 24 weeks
O,= 12 weeks
The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.
X~gamma(\(\alpha ,\beta\))
E(X)= \(\alpha \beta\) \(\beta\)= \(12^{2}/24\)=6 weeks
V(x)= \(\alpha \beta ^{2}\) \(\alpha\)=24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X, \(\alpha\), \(\beta\), False)
P(\(12\leq X\leq 24\))
P(\(12/6\leq G\leq 24/6\))
P(\(2\leq G\leq 4\))
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
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Answer:
Step-by-step explanation:
0.424 is the probability that the transistor will last between 12 and 24 weeks.
X= lifetime of the transistor in weeks E(X)= 24 weeks
Standard deviation= 12 weeks
Finding the parameters alpha and beta X~gamma(αβ)
E(X)= αβ β =6 weeks
V(x)=αβ^2 α =24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X,α,β,False)
P(12≤X≤24)
P(12/6≤G≤24/6)
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
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How to do this question plz answer my question plz
Answers
Answer:
The total distance around the running track is 194.3 m
Step-by-step explanation:
Here, we are interested in calculating the distance around the running track.
We have two semi-circles of diameter 30m and two parallel straight lines of length 50m
Firstly let’s add the parallel straight lines, we have 50 + 50 = 100 m
Now these two semicircles when joined together gives a full circle. And since they are of same diameter, by calculating the circumference of the full circle, we can have the length around the two bends
Mathematically, that would be; πd
The circumference is thus; 22/7 * 30 = 94.29 m
Thus, the length of the running track will be 100 + 94.3m = 194.3m
SOLVE EACH EQUATION BY TAKING SQUARE ROOTS. 1.) 3(x-5)^2=48 2.)2x^2-56=42
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
3(x - 5)² = 48 ( divide both sides by 3 )
(x - 5)² = 16 ( take the square root of both sides )
x - 5 = ± \(\sqrt{16}\) = ± 4 ( add 5 to both sides )
x = 5 ± 4
Thus
x = 5 - 4 = 1
x = 5 + 4 = 9
Solutions are x = 1, x = 9
(2)
2x² - 56 = 42 ( add 56 to both sides )
2x² = 98 ( divide both sides by 2 )
x² = 49 ( take the square root of both sides )
x = ± \(\sqrt{49}\) = ± 7
Solutions are x = - 7, x = 7
let f be the function given by f(x)=sin(2x)cos(1 x). what is the average value of fon the closed interval 1≤x≤3 ? 0.739 0.739 0.369 0.369 0.281 0.281 −0.098
Answers
The average value of the function on the closed interval 1≤x≤3 is approximately 0.281.
1. Determine the length of the closed interval. The interval is from x=1 to x=3, so the length is (3-1) = 2.
2. Integrate the function over the closed interval. To do this, you need to find the integral of sin(2x)cos(x) with respect to x from 1 to 3:
∫[1,3] sin(2x)cos(x) dx
3. Divide the result of the integration by the length of the closed interval to find the average value:
(1/2) * ∫[1,3] sin(2x)cos(x) dx
Now, let's calculate the integral:
∫ sin(2x)cos(x) dx = (1/4) * sin^2(x) + C (using integration by parts)
Now, we evaluate the definite integral from 1 to 3:
[(1/4) * sin^2(3)] - [(1/4) * sin^2(1)]
Finally, divide the result by 2 to find the average value:
(1/2) * {[(1/4) * sin^2(3)] - [(1/4) * sin^2(1)]}
After calculating the values, the average value of the function on the closed interval 1≤x≤3 is approximately 0.281.
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Hailey took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.60 plus $0.75 per mile. The total fare was $8.35, not including the tip. Write and solve an equation which can be used to determine xx, the number of miles in the taxi ride.
Answers
Answer:
1.60+0.75x=8.35
x=9
Step-by-step explanation:
1.60+0.75x=8.35 will be the equation to determine the number of miles x.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given that,
Pickup charge (fixed charge) = $4.60
Charge per mile = $0.75 /mile
Total charge = $8.35
So,
Total charge = pick up charge + Charge per mile × number of mile(x)
8.3.5 = 1.60 + 0.75x
1.60+0.75x=8.35
Hence "1.60+0.75x=8.35 will be the equation to determine the number of miles x".
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ILL GIVE 100 POINTS PLS ANSWER QUICK
Simplify negative two thirds times m times quantity negative four sevenths times m minus one fifth end quantity.
negative 8 over 21 times m squared minus 2 over 15 times m
8 over 21 times m squared plus 2 over 15 times m
negative 8 over 21 times m squared plus 2 over 15 times m
8 over 21 times m squared plus one fifth
Answers
Answer:
\(\dfrac{8}{21}m^2+\dfrac{2}{15}m\)
Step-by-step explanation:
Given expression:
\(-\dfrac{2}{3}m\left(-\dfrac{4}{7}m-\dfrac{1}{5}\right)\)
Apply the distributive law a(b - c) = ab - ac :
\(\implies \left(-\dfrac{2}{3}m\right)\cdot \left(-\dfrac{4}{7}m\right)-\left(-\dfrac{2}{3}m\right)\cdot \left(\dfrac{1}{5}\right)\)
Apply the rule -(-a) = a :
\(\implies \dfrac{2}{3}m\cdot\dfrac{4}{7}m+\dfrac{2}{3}m\cdot \dfrac{1}{5}\)
\(\implies \dfrac{2}{3}\cdot\dfrac{4}{7} \cdot m \cdot m+\dfrac{2}{3}\cdot \dfrac{1}{5}\cdot m\)
\(\textsf{Apply the fraction rule} \quad \dfrac{a}{c}\cdot\dfrac{b}{d}=\dfrac{ab}{cd}:\)
\(\implies \dfrac{2\cdot 4}{3\cdot 7} \cdot m \cdot m+\dfrac{2\cdot 1}{3\cdot 5} \cdot m\)
Simplify:
\(\implies \dfrac{8}{21}m^2+\dfrac{2}{15}m\)
Solve 2(1 - x) > 2x.
a.) O x < 0.5
b.) Ox> 2
c.) Ox<2
d.) O x > 0.5
Answers
Answer:
a) Ox<0.5 wjsjdhdjdjdj
Answer:
a.)x < 0.5
Step-by-step explanation:
2(1 - x) > 2x
2 - 2x > 2x
+2x +2x
2 > 4x
/4 /4
0.5 > x
find a square root of 340 modulo 437
Answers
One possible square root of 340 modulo 437 is 281.
To find a square root of a number modulo another number, we can use the Tonelli-Shanks algorithm. First, we check that 340 is a quadratic residue modulo 437 by calculating 340^((437-1)/2) mod 437, which gives 1. Then we can choose a starting value for the square root, such as 281, and use the Tonelli-Shanks algorithm to iteratively improve our estimate. After a few iterations, we should arrive at a more precise square root. Note that there may be multiple square roots, and this is just one example.
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Show your work and write an expression using the following criteria:
Divide 4,200 by a multiple of 10
The quotient is also a multiple of 10
Answers
Answer:
420
Step-by-step explanation:
edge
d=√C8-7)° +65--0 OSI='ZN=p
Answers
Answer:
3r57i99097654322 that is the answer
solve for x -2x = -4
Answers
given that:
\(-2x=-4\)Solve for x:
\(\begin{gathered} -2x=-4 \\ 2x=4 \\ x=\frac{4}{2} \\ x=2 \end{gathered}\)Find the midpoint of A (-8,-1) and B (4,3)?
Answers
Hi, your midpoint is (-2, 1). Hope this helps, have a great day and please mark me brainliest:)
Clare used 25% less butter this month than last month when baking holiday treats. If she used 240 tablespoons of butter last month, how many tablespoons did she use this month?
Answers
Answer:
180 tablespoons
Step-by-step explanation:
240×.25=60
240-60=180
Answer:
180
Step-by-step explanation:
Use the vertical line test to determine if the graph represents a function. Type in yes or no for your answer. Please answer as soon as possible ASAPP!!
Answers
Answer:
Step-by-step explanation:
this graph does not pass the vertical line test as it has many y values for the on x value. the answer is no, it is not a function
Explica qué significan las variables "m" y "b" en la ecuación y = mx +b*
Answers
Answer:
La M representa la pendiente de la recta y la b representa la intersección con el eje y
Step-by-step explanation:
Que tengas un excelente verano :)
Respuesta: En la ecuación y= mx + b, “m” representa la pendiente y “b” representa el y-intercept.
Espero que esto ayude, buena suerte! :D
just some simple math fro points reward brainliest
Answers
Answer: first one is function second is not a function
Step-by-step explanation:
help asap check picture
Answers
The answer will be option D {(R,1),(R,2)(R,3)(R,4(R,5)(R,6),(B,1)(B,2)(B,3)(B,4)(B,5)(B,6).
What is probability?
The probability is defined as the chances of happening of any random event. or the possibility of happening of any event is called as the probability.
It is given in the question that there are two colours in the spinner and the dice have 6 faces from {1 to 6} numbers on it.
The sample outcomes with the spinner and the dice will be as follows:-
S= {(R,1),(R,2)(R,3)(R,4(R,5)(R,6),(B,1)(B,2)(B,3)(B,4)(B,5)(B,6).
Hence answer will be {(R,1),(R,2)(R,3)(R,4(R,5)(R,6),(B,1)(B,2)(B,3)(B,4)(B,5)(B,6).
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helppppp pleaseeeeeeeeeeer
Answers
By using the property of congruency of triangles,
\(\angle\)PSR = \(\angle\)PSQ has been proved
What is congruency of triangles?
Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.
There are different axioms of congruency. They are
SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom
PS bisects \(\angle\)QPR [Given]
PQ \(\cong\) PR [Given]
\(\angle\)QPS \(\cong \angle\)RPS [PS bisects \(\angle\)QPR]
PS \(\cong\) PS [Reflexive property of congruence]
\(\Delta\) PQS \(\cong \Delta\) PRS [SAS axiom]
\(\angle\)PSR = \(\angle\)PSQ [Corrosponding parts of congruent triangles are congruent]
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Use the work shown below to write the equation for a line that has a slope of Negative two-fifths and passes through (15, –2).
y = mx + b
1. Substitute the known values: negative 2 = negative two-fifths (15) + b. 2. Solve for b: negative 2 = negative 6 + b. b = 4.
What is the equation of the line in slope-intercept form?
Negative 2 = negative two-fifths x + 4
y = negative two-fifths (15) + 4
y = negative two-fifths x minus 4
y = negative two-fifths x + 4
Answers
Answer:
y=negative two fifths x plus 4
Step-by-step explanation:
DNA tbh ishrb jd ge kem is j.g cr. ks i.v rgjs gusnrie84b isbsuosb sojdl
Answer:
its A
Step-by-step explanation:
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pls and ty
<3 anmol
A textbook store sold a combined total of 240 chemistry and history textbooks in a week. The number of chemistry textbooks sold
was two times the number of history textbooks sold. How many textbooks of each type were sold?
Answers
Answer:
160 chemistry books and 80 history books
Step-by-step explanation:
C=chemistry books sold, H=history books sold
C=2H
C+H=240, 3H=240, H=80, C=160
Marisol went to a hair salon for a haircut. The hair stylist cut off 3 inches of her hair. The length of her hair is now 11 inches. Let b represent the length of her hair before she went to the salon. Which of the following represents an equality between two different ways of expressing the length of Marisol's hair now?
A.b-3=11 B.b=11 C.b+3=11 D. 11b=3
Answers
Answer:
C
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation: took it on times4learning math assignment
HELP FAST LOL HAHAHAH
Answers
Answer:
184
Step-by-step explanation:
First, note that the sides that are opposite to each other are congruent (this will come into play in a second). We can find the area of each triangle by doing 0.5(b)(h) (aka half * base* height). Since we've established tha opposite sides are congruent and the triangles are opposite to each other, they must be congruent. That means that the area is going to be the exact same for both triangles. So, we get the expression (0.5)(6)(4)(2), which comes out to 6*4 = 24. Then, to find the area of the 2 rectangles that are the sides, just do 5*10*2 = 100 square meters for both rectangles combines. Lastly, we need to find the area of the floor. The dimensions of the floor are 6 and 10, so we just do 6*10 = 60. Now, add all those numbers together. We get 100+60+24 = 184. Hope this helps! Let me know if anything is still confusing.
You need a 10% alcohol solution. On hand, you have a 120 mL of a 85% alcohol mixture. How much pure water will you need to add to obtain the desired solution?A) Write an equation using the information as it is given above that can be used to solve this problem. Use x as your variable to represent the amount of pure water you need to use.Equation: ________ You will need ____mL of pure waterto obtain ____mL of the desired 10% solution.
Answers
Here the mixture (or solution) contains alcohol and water.
Given that you have 85% alcohol mixture. It means that each 1 mL of the mixture will contain 0.85 mL of alcohol, and the remaining 0.15 mL of pure water.
So the amount of alcohol in 120 mL of mixture is calculated as,
\(\begin{gathered} =120\times0.85 \\ =102 \end{gathered}\)When 'x' mL of pure water is added to the solution, the total amount of water in the mixture becomes,
\(\begin{gathered} =x+(120\times0.15) \\ =x+18 \end{gathered}\)Since no alcohol is added, the amount of alcohol in the final mixture will remain same, that is, 102 mL.
Now, it is given that the concentration of the final mixture is 10%, So the amount of alcohol in the solution should be 10% of the total mixture,
\(\begin{gathered} 0.10\times(x+18+102)=102 \\ x+120=\frac{102}{0.10} \\ x+120=1020 \\ x=1020-120 \\ x=900 \end{gathered}\)Thus, you need to add 900 mL of pure water in order to have 10% alcohol solution.
And the equation used to solve this problem is,
\(0.10\times(x+18)=102\)13 PONITS! PLEASE ANWSER!
A rug is 8 3/4 feet long the area of a rug is 36 1/4 square feet what is the width of the rug
Answers
Answer:
36.25 = 8.75*x
36.25/8.75 = x
x = 4.1428571429 feet in length