find an upper bound on the error that can result if cos(x) is approximated by 1−(x2/2!) (x4/4!) over the interval [−0.7,0.7].
Answers
An upper bound on the error that can result from approximating cos(x) by 1−(x^2/2!) + (x^4/4!) over the interval [-0.7, 0.7] is 0.00567.
The Taylor series expansion for cos(x) is given by cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) + ... . The approximation 1−(x^2/2!) + (x^4/4!) is a truncated version of this series. The error between the actual value of cos(x) and the approximation can be estimated using the Lagrange form of the remainder term, which gives an upper bound on the error.
In this case, the Lagrange remainder term is given by Rn(x) = (f^(n+1)(c)/n+1!) * (x-x0)^(n+1), where f^(n+1)(c) is the (n+1)th derivative of cos(x) evaluated at some point c in the interval [-0.7, 0.7].
The maximum value of Rn(x) over the interval [-0.7, 0.7] occurs when x = ±0.7, and the upper bound on the error is found by evaluating Rn(±0.7).
The resulting upper bound is approximately 0.00567.
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Related Questions
Claim: The mean pulse rate (in beats per minute) of adult males is equal to 69 bpm. For a random sample of 173 adult males, the mean pulse rate is 68.6 bpm and the standard deviation is 10.8 bpm. Find the value of the test statistic.
The value of the test statistic is ___
Answers
the value of the test statistic is -0.4866
To find the value of the test statistic, we can use the formula for a t-test:
t = (x - μ) / (s / √n)
where x is the sample mean, μ is the population mean (69 bpm), s is the sample standard deviation, and n is the sample size (173).
Substituting the given values, we get:
t = (68.6 - 69) / (10.8 / √173)
t = -0.4 / (10.8 / 13.1529)
t = -0.4 / 0.8223
t = -0.4866 (rounded to four decimal places)
Therefore, the value of the test statistic is -0.4866
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A teacher provides 4 sets of cupcakes for the class party. Each set contains 10 cupcakes. If
the class has 24 students and each student eats 1 cupcake, how many are leftover?
Answers
Answer:
16 cupcakes.
Step-by-step explanation:
4 times 10 = 40
40 - 24 = 16
Answer: 16 are left over
Step-by-step explanation:
how to find future value?
Answers
Step-by-step explanation:
FV=$1000×(1+0.1)5
try solving with this it might help you and if it did please make me brainliest plzzzzxx
Quadrilateral JKMN is a rectangle.
If m ∠N J M=2 x-3 and m∠K J M=x+5 , find x .
Answers
The value of x is 8 in this case.
In a rectangle, opposite angles are congruent. Therefore, we can set up an equation to find the value of x by equating the measures of the given angles.
Given:
∠NJM = 2x - 3
∠KJM = x + 5
Since JKMN is a rectangle, ∠NJM and ∠KJM are opposite angles and thus congruent. Therefore, we can write the equation:
2x - 3 = x + 5
Now we can solve this equation to find the value of x.
Subtract x from both sides:
2x - x - 3 = x - x + 5
Simplifying the left side:
x - 3 = 5
Add 3 to both sides:
x - 3 + 3 = 5 + 3
Simplifying the left side:
x = 8
So, x is equal to 8.
Therefore, the value of x is 8 in this case.
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a good way to get a small standard error is to use a ________.
Answers
Answer: A good way to get a small standard error is to use a large sample.
Step-by-step explanation:
In order to find the small standard error, there is always need of a complete set which is called the large sample.
If tried to do a small or repeating sample, you will most likely not get an error and you could get a repetition. If you do a population sample, you wont get accurate results at all.
Therefore, a good way to get a small standard error is to use a large sample. Hope this helps!
-From a 5th Grade Honors Student
A bakery uses 2 ½ pounds of cookies to prepare every 2 packages of cookies. How many pounds of cookies will be used to prepare each package of cookies
Answers
Answer:
6.67lbs
Step-by-step explanation:
let's write cookies as C.
we know dozen means 12 so we multiply 5 by 12 to know how many cookies that the bakery uses 2lbs of butter for.
That would be; 2lbs= 5×12 C
2lbs=60C.
now we can find how much butter is used for a single cookie(C) by dividing both sides by 60;
lbs=C;
C= lbs
since we know what C is, we can use that in finding how much butter will be needed for 200 cookies(C)
200C=200(lbs)
200C= lbs
200C= 6lbs or 6.67lbs
if oil leaks from a tank at a rate of r(t) gallons per minute at time t, what does 120 0 r(t) dt represent?
Answers
the total amount of oil that leaks out over the entire time interval [0, 120].
integral ∫₀¹₂₀ r(t) dt represents the total amount of oil that leaks from the tank in 120 minutes.
To see why, consider the definition of an integral. If we divide the interval [0, 120] into small subintervals of width Δt, then the amount of oil that leaks out during each subinterval is approximately r(t)Δt. Summing up all these small amounts over the entire interval gives:
Σᵢ r(tᵢ) Δt
where tᵢ is the midpoint of the i-th subinterval. As we take the limit as the subinterval width goes to zero, this sum becomes the integral:
∫₀¹₂₀ r(t) dt
which represents the total amount of oil that leaks out over the entire time interval [0, 120].
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The boston marathon is 26.2 miles use the time shown in the table to calculate the miles per hour for joshua cassidy
Answers
Answer:
he finished 20.045 miles in 1 hour
i think this is what the question is asking
Answer:
See Explanation
Step-by-step explanation:
Use the formula rate = distance/time
Rate= 26.2/1.307
Rate= 20.06 Mph
Why the order of a succession is important
Answers
Answer:
Step-by-step explanation:
The order of a succession is a way that the terms (the first, the second, the third, etc.) can be distinguished according to a certain formation law or order criterion.
Example:
a¹/a²/a³/a⁴ And successively
In the order of a sequence you can assign any letter.
Eazy points just answer the question and no I am not a stalker I have a graph to do and theses are the poll question I need 10 people to answer plz.
height
number of siblings
number of times per month they watch a movie
age
hours of sleep they get each night (on average)
job yes or no
favorite color of the three blue, pupple, green
Answers
6'3
4 sibs
7 times
12 5 20 and 7
8 hours
no
purple
:3 good luck!
For each of the following integrals, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition. (To indicate convergence or divergence, enter one of the words converges or diverges in the appropriate answer blanks.) x²+1 x³+5x+3 da: a similar integrand is so we predict the integral x ₁ dæ: a similar integrand is dx so we predict the integral x+4 f₁dx : a similar integrand is so we predict the integral x³+4 x+3 ₁732733 dx : a similar integrand is so we predict the integral x³+2x²+3
Answers
x²+1 / x³+5x+3 -> diverges
x / x+4 -> converges
x³+4 x+3 / x³+2x²+3 -> diverges
A similar integrand to x²+1 / x³+5x+3 is x / x². The integral of x / x² is ln(x), which diverges as x approaches infinity. Therefore, we can predict that the integral of x²+1 / x³+5x+3 will also diverge.
A similar integrand to x / x+4 is x / x². The integral of x / x² is ln(x), which converges as x approaches infinity. Therefore, we can predict that the integral of x / x+4 will also converge.
A similar integrand to x³+4 x+3 / x³+2x²+3 is x³ / x². The integral of x³ / x² is x², which diverges as x approaches infinity. Therefore, we can predict that the integral of x³+4 x+3 / x³+2x²+3 will also diverge.
The comparison test is a method for comparing the convergence or divergence of two integrals. The test states that if the integral of f(x) converges and the integral of g(x) diverges, then the integral of f(x)/g(x) diverges.
In this problem, we are not formally applying the comparison test. We are simply looking at the behavior of the integrands to build intuition about whether they will converge or diverge. The integrands in the first two problems have a higher degree than the integrands in the last two problems. This means that the integrals in the first two problems will diverge, while the integrals in the last two problems will converge.
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Translate figure A8 units to the left to form figure A’.
Then reflect figure A' across the x-axds to form figure A".
Draw figures A' and A". Is figure A congruent to figure A?
How do you know?
Answers
Answer:
A' across the x-axds to form figure A".
Draw figures A' and A". Is figure A congruent to figure A?
How do you know?
what is the sum fo the series pi/e-pi/e^2
Answers
As per the information given, the sum of the series π/e - π/e² is (π * e) / (e - 1).
To calculate the sum of the series π/e - π/e², we can treat it as a geometric series.
The series can be written as:
π/e - π/e² = π/e * (1 - 1/e)
Sum = a / (1 - r)
In this case, a = π/e and r = 1/e.
Substituting the values into the formula, we have:
Sum = (π/e) / (1 - 1/e)
To simplify the above expression, multiply the numerator and denominator by e:
Sum = (π * e) / (e - 1)
Therefore, the sum of the series π/e - π/² is (π * e) / (e - 1).
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Only answer if you know for sure you’re right! :)
Answers
Answer:
14x+14=14(x+1)
Urgent help
Solve the whole right triangle
Answers
Answer:
Angle L= 53 degrees. Side ML = 4.521 and Side NL= 7.513
Step-by-step explanation:
Need help asap please
Answers
Answer: it is B. 39t + 54
Step-by-step explanation:
9(4t + 6) + 3t --- (distribute the 9 to 4t and 6 (9(4t) + 9(6))
36t + 54 + 3t --- (combine like terms, 36t + 3t)
39t + 54
Multiple 9(4t+6)
36t+54+3t
Add all together
39t+54
about how many kilograms does a 12 pound bag of potatoes weigh?
Answers
Answer:
5.5 kg
Step-by-step explanation:
One kilogram is roughly equivalent to 2.2 pounds. So,
\(12\ lb(\frac{1\ kg}{2.2\ lb})=5.5\ kg\)
How do you write 39% as a decimal?
Answers
Answer:
0.39
Step-by-step explanation:
To write 39% as a decimal, divide the percentage by 100.
39% ÷ 100 = 0.39
So 39% as a decimal is 0.39.
Answer:
0.39
Step-by-step explanation:
100% would be 1.00, 99 would be 0.99
Arthur has x pennies. His father gave him 6 dimes, and his mother gave him 4 nickels. Which expression represents the number of coins Arthur has now?
a) x+80
b) x+10
c) 6x+4
d) 4x+6
Answers
The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.
How to calculate for the number of coinsWe shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.
A penny = 1 cent, so
x pennies = x cents
A dime = 10 cents so;
6 dimes = 6 × 10cents
6 dimes = 60 cents
A nickel = 5 cents so;
4 nickels = 4 × 5 cents
4 nickels = 20 cents
Arthur's coins in total = (x + 60 + 40) cents
Arthur's coins in total = (x + 80) cents.
Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.
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Which steps will generate an expression equivalent to 17(x+5)?
MARK BRAINLIEST
Answers
Answer:
multiply 17x5=85,85+5=90 so aswer is 90
Step-by-step explanation:
Answer:
17+85 is the answer that I got
3. for questions 3-5, complete the missing values in each table below using the graph
Answers
The missing values are derived from the graph as follows:
3 ) 7, 14, 21, 28, 35
4) 3, 7, 10, 14, 17
5) 1, 21, 10, 49, 19
What is a graph?In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.
In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:
F(y) = 3.5x
In the first table, where x = 2
y= 3.5 *2
= 7
This iteration goes on and on and is consistent for all the values.
In the second table,
Where F(y) is known, for example 10.5, then x is derived as:
10.5 = 3.5x (divide both sides by 3.5)
x = 3
This iteration goes on and on and is consistent for all the values.
In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.
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A regular hexagon is inscribed in a regular hexagon. The length of each side of the inside hexagon is 8 in. What is the area of the shaded region? Round to the nearest tenth.
Answers
Answer: I need to see the picture of the shaded part to awnser
Step-by-step explanation:
draw the graph of the function y=f(x)
Answers
When Nellie Newton hangs at rest in the middle of a clothesline, tensions will be the same in each side of the rope when:
a. the lengths of each rope are the same
b. the angles for both sides of the rope are equal
c. she is in equilibrium
Answers
The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.
When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.
For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.
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The area of a rectangle is 90 square inches. Find the length and width so that the rectangle has the least perimeter. Assume that the length and width are both whole numbers
Answers
Thus finding the factors of 90: 1, 2,3,5,6,9,10,15,18,30,45,90. So the closest are 9 and 10
There fore 19+19=38
Jan is enlarging the sketch shown on a photocopier. Which could be the dimensions of her enlargement?
3 in.
2 in.
A 4 inches * 5 inches
B 5 inches x 6 inches
7 inches 10.5 inches
D 8 inches x 9 inches
Answers
Let f(x) =4x-1 and g(x)=2^x+3. Find (f-g) (5)
Answers
Answer:
\(-16\)
Step-by-step explanation:
\(f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16\)
Find the missing side. Round to the nearest tenth.
52°
27
Answers
Answer:
x = 16.6
Step-by-step explanation:
Use Cos
Cos 52 = x / 27
Cos of 52 is 0.61566
0.61566 = x / 27
Multiply 27 on both sides
16.622 = x
Round to the nearest tenth
16.622 = 16.6
\(\frac{ \cos(52) }{1} = \frac{x}{27} \)
Cross multiply!
\(x = 27 \cos(52) \)
Determine by using a calculator!
Answer: x is approximately 16.6
Larissa bakes a cake with an area of 3.9 square feet. She cuts off a rectangle with an area of 0.6 square feet and eats it. What fraction of her original cake does she have left?
Answers
it is becase he is just a happy dog
I need help with this- thank you
Will mark brainliest! :)
Answers
Answer: 5x^{2} +3x + 4
Hope this helped! :)
Answer:
(X^2 + 2x + 7) + (4x^2 + x - 3) =
x^2 + 2x + 7 + 4x^2 + x - 3 =
5x^2 + 3x + 4