Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x =0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.
|error| <= _________
Answers
Answer:
0.0032
Step-by-step explanation:
We need to compute \(e^{0.4}\) by the help of third-degree Taylor polynomial that is expanded around at x = 0.
Given :
\(e^{0.4}\) < e < 3
Therefore, the Taylor's Error Bound formula is given by :
\($|\text{Error}| \leq \frac{M}{(N+1)!} |x-a|^{N+1}$\) , where \($M=|F^{N+1}(x)|$\)
\($\leq \frac{3}{(3+1)!} |-0.4|^4$\)
\($\leq \frac{3}{24} \times (0.4)^4$\)
\($\leq 0.0032$\)
Therefore, |Error| ≤ 0.0032
Related Questions
In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th.
Answers
Answer:
Solution given:
Y=90°
∠X=73°.
∠ZWY=80°
and XW=80.
ZY=?
We know that
In right angled triangle ∆ XYZ
Tan 73=\( \frac{p}{h} \)
3.27=\( \frac{yz}{xy} \)
3.27×[xy]=yz
xw+wy=\( \frac{yz}{3.27} \)
wy=\( \frac{yz}{3.27} \)-80...........(1)
again
In right angled triangle WYZ
Tan 80=\( \frac{yz}{wy} \)
5.67×wy=yz
wy=\( \frac{yz}{5.67} \)
yz=5.67×wy............................................(2)
Equating equation 1&2
\( \frac{yz}{5.67} \)=\( \frac{yz}{3.27} \)-80
\( \frac{yz}{3.27} \)-\( \frac{yz}{5.67} \)=80
5.67yz-3.27yz=80*5.67*3.27
2.4yz =1483.272
yz=\( \frac{1483.272}{2.4} \)
yz=618.03
:.y=618.03unit.the length of ZY to the nearest 100th is 618.
Help me solve it the answer
Answers
The required top of the ladder from the ground is 7.14 ft.
What is a right angle triangle?A triangle is said to be right-angled if one of its internal angles is 90 degrees, or if any angle is a right angle.
To find the length in right angle triangle, use Pythagoreans theorem,
(hypotenuse)² = (base)² + (height)²
Given that,
The length of the ladder = 10 ft.
The distance of the house from the bottom of the ladder = 7 ft.
Let the length of the top of the ladder from ground is x ft.
To find the height of the ladder from the ground,
Use Pythagoreans theorem,
(hypotenuse)² = (base)² + (height)²
(10)² = (7)² + (x)²
100 = 49 + x²
x² = 100 - 49
x² = 51
x = 7.1414
or x = 7.14 ft
The top of the ladder from the ground is 7.14 ft.
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Need ANSWER ASAP
Consider the following transformed function
y = −2 Sin [2( − 45°)] + 1
a) Graph the five key points of Parent function on the provided grid.
b) State the following for the transformed function
Amplitude=
period=
Horizontal Phase shift =
Equation of axis=
c) Graph at least two cycles of the transformed function by transforming the key points of the parent function. (Don’t forget to label the x-axis and y -axis)
Answers
Answer:
See explanation below.
Step-by-step explanation:
Given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Part (a)The parent function of the given function is: y = sin(x)
The five key points for graphing the parent function are:
3 x-intercepts → (0°, 0) (180°, 0) (360°, 0)maximum point → (90°, 1)minimum point → (270°, -1)(See attachment 1)
Part (b)Standard form of a sine function:
\(\text{f}(x)=\text{A} \sin\left[\text{B}(x+\text{C})\right]+\text{D}\)
where:
A = amplitude (height from the mid-line to the peak)2π/B = period (horizontal distance between consecutive peaks)C = phase shift (horizontal shift - positive is to the left)D = vertical shift (axis of symmetry: y = D)Therefore, for the given transformed function:
\(y=-2 \sin \left[2(x-45^{\circ})\right]+1\)
Amplitude = -2Period = 2π/2 = πPhase shift = 45° to the rightEquation of axis of symmetry: y = 1Part (c)See attachment 2.
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/rHmvQCSFzLuN7xkVIxhNC3hToKfYa2ZX.png)
![Need ANSWER ASAPConsider the following transformed functiony = 2 Sin [2( 45)] + 1a) Graph the five key](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/RTeQ1nKnPwOJZpxZH6e5ecn6PqRfr3g0.png)
Sorry, you think i would get it by now... Which's one not Proportional?
Answers
Answer:
B
Step-by-step explanation:
Graph=is the line curves its not proportional
Table=x/y and a different x/y have to be the same
I want to know the/
X-intercepts
Y-intercepts
Answers
Answer:
x-intercept = .5 y-intercept = 1
Step-by-step explanation:
the x-axis is crossed at .5 and the y-axis is crossed at 1.
Step-by-step explanation:
the x-intercept (crossing the x-axis) is represented by the x value when y = 0.
and the y-intercept by the y value, when x = 0.
so, as we can see in the graphic, the x-intercept is at x = 0.5, and the y- intercept at y = 1.
so, the ordered pairs are
x-intercept (0.5, 0)
y-intercept (0, 1)
a line can have only one of each intercept (never like 2 or 3 y-intercepts). in some cases (parallel to a coordinate axis) it might not have one of these intercepts.
The LCM of 8ab and 12a^2 is
A. 48a³b.
B.) 48a²b.
C. 24a²b.
D. 24ab.
E. 48a².
of 8ab
Answers
Answer:
C. 24a²bStep-by-step explanation:
8ab = 4a × (2b)
12a² = 4a × (3a)
Then
LCM(8ab , 12a²) = 4a × (2b) × (3a)
= (4×2×3) × (a×a×b)
= (24) × (a²×b)
= 24a²b
4(c+3) =4+c+c+c+c+17
Answers
-4c -4c
12 =4+c+17
12=21+c
-21
-9=c
idk if this is what ur looking for?
On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept? (1 point) a −9 b −6 c 6 d 9
Answers
the y-intercept=6.
because y must not be greater than 6
graph the solution to the following equation: x+y= -8
Answers
Select the correct answer. Which graph represents the solution to this system of inequalities? y < -x − 3 y > 2x – 4 A. B. C. D.
Answers
Answer:
I think the answer would be c but I am not to Sure
Answer:
Unknown
Step-by-step explanation:
Neither the graphs or the inequality(ies) were provided in the question, here's some tips to prevent this in the future
- take a screenshot of the problem (or more then 1 screenshot, up to 5 last i seen) and post it with the question, i don't know about mobile or Mac but for windows 10 (on most keyboards0 you can click PrtSc (Print Screen) which will save your screen as a pic in your clipboard which you can then put in a photo editing software by pasting it onto the canvas
- type out a description of the problem to try and convey what it is you need solved, don't forget its ok to ask for a pic for reference ^^
- re-word your question in your own words to ask how to solve said type of problem, then you the info from the answers to help you solve your question
these are just suggestions to help prevent this in the future, take care and stay safe ^^
Given
f(x) = x2 + 5
and
(fg)(x) = 3x(x2 + 5),
what is
g(x)?
g(x) =
Answers
Answer:
We are aware of the equation.
Equation 1 reads (fg)(x) = f(x) * g(x).
Hence, we can resolve it as follows:
Given equation: equation 2 (fg)(x) = 3x (x2 + 5)
Equation 3 is obtained by comparing equations 1 and 2, as follows:
"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5
When we change equation 3 to read f(x) = x2 + 5, we get:
(x2 + 5) * g(x) = 3x (x2 + 5)
See what both equations have in common; it is (x2 + 5)
The result of dividing both sides by x2 + 5 is:
g(x) = 3x
G(x) will therefore have a value of 3x.
From the above equation given in the question , we get that g(x) have a value of 3x.
We are aware of the equation.
Equation 1 reads (fg)(x) = f(x) * g(x).
Hence, we can resolve it as follows:
Given equation: equation 2 (fg)(x) = 3x (x2 + 5)
Equation 3 is obtained by comparing equations 1 and 2, as follows:
"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5
When we change equation 3 to read f(x) = x2 + 5, we get:
(x2 + 5) * g(x) = 3x (x2 + 5)
See what both equations have in common; it is (x2 + 5)
The result of dividing both sides by x2 + 5 is:
g(x) = 3x
G(x) will therefore have a value of 3x.
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mr.Lloyd wants to buy a new television but does not have enough money in his bank account to pay for once which of these is not an option for mr.Lloyd
Answers
Mr. Lloyd could use his credit card to buy the TV. Therefore, option A is the correct answer.
Using a credit card to make a purchase requires that the buyer have a credit limit that is large enough to cover the amount of the purchase. Mr. Lloyd does not have enough money in his bank account to pay for the television, so he would not be able to use a credit card to make the purchase.
Options B, C, and D are all viable options for Mr. Lloyd. He could save up money and pay cash for the television at a later date, or he could use his debit card to make the purchase when he has enough money in his bank account. He could also save money and use his debit card at a later date when he has enough money in his bank account.
Therefore, option A is the correct answer.
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Mr. Lloyd wants to buy a new television, but he does not have enough money in his bank account to pay for one. Which of these is NOT an option for Mr. Lloyd?
A) He can use his credit card to buy the television now.
B) He can save money and pay cash for the television at a later date.
C) He can use his debit card to buy the television now.
D) He can save money and use his debit card to buy the television at a later date.
Lamar wants to attend college that will cost $16,400 for the first year. His uncle gave him a special gift of $2000 to use toward the cost. Lamar plans to attend college in 6 years. How much must Lamar save each month to have enough for the first-year cost?
Answers
Answer:
200
Step-by-step explanation:
16,400-2,000= 14,400
6 years into months 6x12= 72
14,400/72= 200
A train leaves Philadelphia at 3:00 PM. A second train leaves the same city in the same direction at 9:00 PM. The second train travels 120mph faster than the first. If the second train overtakes the first at 11:00 PM, what is the speed of each of the two trains?
Answers
Answer:
Step-by-step explanation:
2nd train DATA:
time = 2 hrs ; rate = x + 120 mph ; distance = 2(x+120) = 2x+240 miles
------
1st train DATA:
time = 8 hrs ; rate ; x mph ; distance = 8x miles
------------------
Equation:
distance = distance
8x = 2x+240
6x = 240
x = 40 mph (speed of the 1st train)
x+120 = 160 mph (speed of the 2nd train)
my regards #3Ss
2(4x-3)-8=4+2x
1) What value for x would make the following equation true ? Solve the equation and CHECK the solution.
2) Explain how you determined your answer by writing all the steps that you used to solve the equation.
3) How many solutions does this equation have ? Explain your reasoning.
Answers
Answer:
x = 3
This equation has only one solution. The only number that will make both sides of the equation equal is 3.
Step-by-step explanation:
2(4x -3) -8 = 4 + 2x Distribute the 2
8x -6 -8 = 4 + 2x Combine like terms
8x -14 = 4 + 2x Subtract 2x from both sides S(Subtraction property of equality)
6x - 14 = 4 Add 14 to both sides (subtraction property of equality)
6x = 18 Divide both sides by 6 (division property of equality)
x = 3
Check:
2[4(3) - 3] - 8 = 4 + 2(3)
2(12 - 3) - 8 = 4 + 6
2(9) - 8 = 10
18 - 8 = 10
10 = 10
Prove that sin^4x + cos^4x= sinxcosx
Answers
Answer:
(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)
Here we have the equation:
\(sin^4(x) + cos^4(x)\)
We can rewrite this as:
\((sin^2(x))^2 + (cos^2(x))^2\)
Now we can add and subtract cos^2(x)*sin^2(x) to get:
\((sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)\)
We can complete squares to get:
\((cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2\)
and we know that:
cos^2(x) + sin^2(x) = 1
then:
\(1 - 2*sin(x)^2*cos(x)^2\)
This is the closest expression to what you wrote.
We also know that:
sin(x)*cos(x) = (1/2)*sin(2*x)
If we replace that, we get:
\(1 - \frac{sin^2(2*x)}{2}\)
Then the simplification is:
\(cos^4(x) + sin^4(x) = 1 - \frac{sin^2(2*x)}{2}\)
0 8. A function f(x) is said to have the jump discontinuity at a point x = a if lim a)x+a+ c) x→a+ f(x) = lim x→a+ f(x) = lim x→a¯ lim X-a f(x). b) lim x→a f(x) = lim x→a¯ _ f(x) f(x) = f(a) d) lim f(x) → +00 x→a+
Answers
The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.
What is jump discontinuity?Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.
According to the given information:
The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.
The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.
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The following table lists the history of 940 orders for features in an entry-level computer product. Extra Memory Yes 68 246 514 Optional high- speed processor Yes 112 Let A be the event that an order requests the optional high- speed processor, and let B be the event that an order requests extra memory. Determine the following probabilities: (a) P(AUB) (b) P(AnB) (e) What is the probability that an order requests an optional high-speed processor given that the order requests extra memory? (f) What is the probability that an order requests extra memory given that the order requests an optional high- speed processor?
Answers
a. P(A'UB) is 0.885106
b. The probability that an order requests an optional high speed processor, given that the order requests extra memory is 0.776397.
c. The probability that an order requests extra memory, given that the order DOES NOT requests an optional high speed processor is 0.123711
What is Probability?
The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
To find the probabilities:
a. A"UB = 510 + 72 + 250 = 832
Total outcomes = 940
The required probability is 832/940 = 0.885106
b. The required probability is 250/250 + 72 = 0.776397
c. The required probability is 72/510 + 72 = 72/582 = 0.123711
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Write an equation of the line that passes through (2,3) and is perpendicular to the line shown. Please help!!
Answers
Answer:
7.0
Step-by-step explanation:
In ΔVWX, the measure of ∠X=90°, the measure of ∠W=9°, and WX = 8.7 feet. Find the length of XV to the nearest tenth of a foot.
find the distance between the following pairs of points (-1,5)and(-7,-3)
Answers
The distance between the points (-1, 5) and (-7, -3) is 10 units.
What is the distance between the given points?The distance formula used in finding the distance between two points is expressed as;
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
Point 1 (-1,5)
x₁ = -1y₁ = 5Point 2 (-7,-3)
x₂ = -7y₂ = -3Plug the given values into the distance formula and simplify.
D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )
D = √[(-7 - (-1))² + (-3 - 5)²]
D = √[(-7 + 1)² + (-3 - 5)²]
D = √[-6² + (-8)²]
D = √[36 + 64]
D = √100
D = 10
Therefore, the distance is 10 units.
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Multiple choice: Select the best answer for Exercises 49 to 52. Most people can roll their tongues, but many can’t. The ability to roll the tongue is genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400 students and find that 317 can roll their tongues. The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (a) 0.008. (b) 0.02. (c) 0.03. (d) 0.04. (e) 0.208.
Answers
The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04
The margin of error is a statistic that describes how much random sampling error there is in survey results.
Given in question,
n = 400
p = 317/400
= 0.7925
Confidence Level = 95%
= 0.95
Formula for margin error, E = \(z\sqrt{\frac{p(1-p)}{n} }\)
Confidence level corresponding to 95 % confidence interval, z = 1.96
Therefore,
Margin Error, E = \(1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }\)
= 0.0397
≈ 0.04
Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.
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Susan bought a 1 kilogram bag of grapes. On the way home, she ate 125 grams of the grapes. How many grams of grapes does Susan have left? use math language and symbols to explain how you used the correct measurement units to solve the problem.
Answers
Susan has 875 grams of grapes left.
1. Susan bought a 1 kilogram bag of grapes, which is equivalent to 1000 grams (since there are 1000 grams in a kilogram).
2. Susan ate 125 grams of the grapes on her way home.
3. To find out how many grams of grapes Susan has left, we need to subtract the amount she ate from the initial weight of the bag. Therefore, we subtract 125 grams from 1000 grams.
1000 grams - 125 grams = 875 grams
4. Thus, Susan has 875 grams of grapes left.
measurement units:
In this problem, we used grams as the measurement unit. Grams are commonly used to measure the weight of small objects like grapes. Since the problem stated that Susan bought a 1 kilogram bag of grapes, it was necessary to convert the kilogram measurement to grams.
This conversion was done by multiplying the kilogram value by 1000 (1 kilogram = 1000 grams). By using the correct measurement units, we were able to accurately calculate the amount of grapes Susan had left after eating a portion.
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) How many arrangements of the 26 different letters of the alphabet (with no repeats) are there in which all the consonants appear before all the vowels (a,e,i,o,u)
Answers
Answer:the answer is 21 with np repeats
Step-by-step explanation:
please help thank you..
Answers
Equation of the volume for a pyramid is
V=l•w•h all divided by 3
the l•w is the base, so multiply 10 and 9
you get 90/3
divide and the answer is 30
Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
Answers
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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Tell whether the ratios form a proportion. 1/3, 7/21
Yes
or
No
(also i give out branislist lol)
Answers
The floor of a dollhouse is shaped like a rectangle with a length of 34 foot and a width of 512 foot. Use this model to determine the floor's area.
What is the floor's area?
Enter your answer as a fraction in simplest form
Answers
Answer:
17408 feet
Step-by-step explanation:
34 * 512 = 17408
Fraction?
Forty percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors. 12. The probability that exactly two are chemistry majors is Type an integer or a decimal. Round to four decimal places as needed.)
Answers
Answer:
0.3110
Step-by-step explanation:
This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.
The general formula for a binomial distribution is:
\(P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}\)
Where n is the sample size and k is the desired number of successes.
The probability of k=2 in a sample of n =6 is:
\(P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110\)
The probability is 0.3110
A box plot is shown. The left-most point on the plot is 20 and the right-most point is 95. The box is labeled 35 on the left edge and 60 on the right edge. A vertical line is drawn inside the rectangle at the point 55.
Part A: List two pieces of information that are provided by the graph and one piece of information that is not provided by the graph. (4 points)
Part B: Calculate the interquartile range of the data, and explain in a sentence or two what it represents. (4 points)
Part C: Explain what affect, if any, there will be if an outlier is present. (2 points)
PLEASE ONLY ANSWER IF YOU KNOW WHAT IT IS!!
Answers
"The box plot tells us about the lower limit, first quartile, median, third quartile, and upper limit.
Step-by-step explanation:
Box plot:
It displays the five-number summary of a set of data. The five-number summary is the lower limit, first quartile, median, third quartile, and upper limit. We draw a box in a box plot from the first quartile to the third quartile. A vertical line goes through the box which represents the median. Anything that lies beyond the upper limit or the lower limit is know as an outlier.
From the information given, we can say that:
The left-most point on the plot is 20 and the right-most point is 95 which means 20 and 95 are the lower and upper limit respectively. The box is labeled 35 on the left edge and 60 on the right edge which means 35 is the first quartile and 60 is the the third quartile. A vertical line is drawn inside the rectangle at the point 55 which means 55 is the median of given data. We cannot know about the mean of data with the given information."
(this is kind of an answer, I hope it's helpful)
The other prson is right, give them brainliest!
divide fra 2. 7/8 x 16 = use a model to solve the problem
Answers
Answer:
2.7/8×16
(2.7×16)/8
43.2/8
5.4