Use the remainder term to find the minimum order of the Taylor polynomial, centered at 0, that is required to approximate the following quantity with an absolute error no greater than 10^-2.
√1.06.
n>= __________
Answers
Answer:
n ≥ 3
Step-by-step explanation:
Applying the remainder term in evaluating the minimum order of the Taylor polynomial
absolute error ≤ 10^-2
[tex]\sqrt{1.06}[/tex]
∴ n ≥ ?
The remainder term is the leftover term after computation ( dividing one polynomial with another )
attached below is the detailed solution
The minimum order of the Taylor polynomial, n≥3
What is Taylor polynomial?Taylor polynomial is a series of functions that has an infinite sum of terms that are expressed in terms of the function's derivatives.
[tex]\rm f(a)+\frac{f'(a)}{1!} (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +....,[/tex]
Applying the Taylor series polynomial, the minimum order of the Taylor polynomial, centered at 0
[tex]\rm f(0)+\frac{f'(0)}{1!} (x-0)+\frac{f''(0)}{2!} (x-0)^{2} +....,[/tex]
f(x) = [tex]\sqrt{x+1}[/tex]
[tex]f'(x)=\frac{1}{2}[/tex]
[tex]f''(x)=3/8[/tex]
substituting in the Taylors series
T(x) = [tex]1+\frac{x}{2} -\frac{x^{2} }{8} +\frac{x^{3} }{16}[/tex]......
T(0.06) = [tex]1+\frac{0.06}{2} -\frac{0.06^{2} }{8} +\frac{0.06^{3} }{16}...[/tex]
T(0.06) =1.03
f(0.06) =
[tex]\sqrt{0.06+1}\\= 1.03[/tex]
Therefore, the minimum order of the Taylor polynomial, n≥3
Learn more about Taylor polynomial;
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Related Questions
If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?
Answers
Answer:
The cube root parent function:
f(x) = [tex]\sqrt[3]{x}[/tex]Horizontally stretched by a factor of 4:
g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]Translated 5 units right:
h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]Translated 3 units up:
k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]The number of basic trigonometric ratios is....
A.3
B.4
C.5
D.6
Answers
Answer:
There are three basic trigonometric ratios: sine , cosine , and tangent .
Step-by-step explanation:
b Draw a picture to show 3:5= 6:10. Explain how your picture show equivalerit ratios.
Answers
Answer:
3:5 = 6:10
3x2 : 5x2
= 6:10
Answer:
Step-by-step explanation:
Draw 3:5 balls shaded, and draw 6:10 balls shaded. Then, divide the 10 balls into two, with three shaded balls and 5 total balls on one side.
6. The perimeter of a square room is 48 m, how much square metre carpet required it cover it ?
Answers
Answer:
144
Step-by-step explanation:
Answer:
first you have to now each side length ,since it is square so all sides are equal so 48/4=12 i.e perimeter =4 so our qoustion is area so the area of square is side square
Step-by-step explanation:
so side =12 , 12square is 144 that set.
Will mark brainliest
Plz solve on a paper or draw on the picture thx in advance
Answers
9514 1404 393
Answer:
the red angle has no specific value
Step-by-step explanation:
There is sufficient information here to specify all of the angles except the two unknown angles in the 70° (dark blue) triangle. Those two angles must total 110°, but that measure cannot be allocated between them based on the information in the diagram.
The attachments show that all of the given angle constraints can be met while the red angle may vary considerably. It can range through the interval (0°, 110°), but cannot be either of those end values.
Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?
(2pts)
Select Men had significantly less distress from nausea. as your answer
Men had significantly less distress from nausea.
Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answer
Men had half as much distress from nausea as woman but we can not determine if this is a significant difference.
Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answer
Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Select There is a positive correlation between distress from nausea and gender. as your answer
There is a positive correlation between distress from nausea and gender.
Answers
Answer:
A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Step-by-step explanation:
Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.
What is the volume of the following rectangular prism?
Answers
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
Write a quadratic equation with integer coefficients having the given numbers as solutions.
Answers
9514 1404 393
Answer:
x² -22 = 0
Step-by-step explanation:
The roots are opposites, so the equation is pretty simple.
x = ±√22
x² = 22 . . . . . square both sides
x² -22 = 0 . . . . your quadratic equation in standard form
OMG!! I’m stuck on 4a) b) c)
Help please
Answers
Answer:
a) 750 cmb) 288 cmc) 2112 cmStep-by-step explanation:
Formula for getting the surface area of a rectangular prism: SA = 2 (WL + HL + HW)a) SA = 2 (WL + HL + HW) = 2(75) + 2(225) + 2(75) = 150 + 450 + 150 = 750 cm^2b) SA = 2 (WL + HL + HW)= 2(48) + 2(72) + 2(24)= 96 + 144 + 48=288 cm^2c) SA = 2 (WL + HL + HW)= 2(400) + 2(400) + 2(256)= 800 + 800 + 512= 2112 cm^2[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
(a) The surface area consists of the sum of the area of 3 sets of 2 congruent rectangles. The 2 rectangles are on opposite sides of the solid.
= 2(15*15) + 2(5*15) + 2(5&15)
= 450 + 150 + 150
= 750 unit^2.
(b). Similarly to the above:
Surface area = 2(12*6) + 2(4*12) + 2(4*6)
= 144 + 96 + 48
= 288 unit^2.
(c) Again:
Surface area = 2(25*16) + 2(25*16) + 2(16*16)
= 400 + 400 + 256
= 1056 unit^2.
Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°
Answers
9514 1404 393
Answer:
67.0 square units
Step-by-step explanation:
The formula for the area is ...
Area = 1/2ab·sin(C)
Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units
The area of the triangle is about 67.0 square units.
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.4 inches, and standard deviation of 4.1 inches.
A) What is the probability that a randomly chosen child has a height of less than 61.25 inches?
Answer= (Round your answer to 4 decimal places.)
B) What is the probability that a randomly chosen child has a height of more than 46.5 inches?
Answer= (Round your answer to 4 decimal places.)
Answers
(A)
P(X < 61.25) = P((X - 55.4)/4.1 < (61.25 - 55.4)/4.1)
… ≈ P(Z ≤ 0.1427)
… ≈ 0.5567
(B)
P(X > 46.5) = P((X - 55.4)/4.1 > (46.5 - 55.4)/4.1)
… ≈ P(Z > -2.1707)
… ≈ 1 - P(Z ≤ -2.1707)
… ≈ 0.9850
A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.
Which of the following statements is not true, according to the graph?
The left-handed group has a higher percentage of people who prefer baseball.
The right-handed group has a lower percentage of people who prefer basketball.
The percentage of people who prefer soccer has a lower percentage in the left-handed group.
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Answers
Answer:
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.
Step-by-step explanation:
The bar for the right-handed group representing soccer is between 10% and 20% (below 20%) while the bar for the left-handed group representing soccer is at 20%.
Percentage of left-handed group of people who prefer soccer is higher than the right-handed group who prefer soccer. Therefore, they don't have the same percentage.
Answer:
D
Step-by-step explanation:
;)
Let a=⟨1,−4,2⟩ and b=⟨−5,−5,−2⟩. Compute:
a+b=⟨ ,, ⟩
a−b=⟨ ,,⟩
2a=⟨ ,,⟩
3a+4b=⟨ ,, ⟩
|a|=
Answers
Answer:
a + b = ⟨-4, -9, 0⟩
a - b = ⟨6, 1, 4⟩
2a = ⟨2, -8, 4⟩
3a + 4b = ⟨-17, -32, -2⟩
|a| = √21
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightPre-Calculus
Vectors
OperationsScalars[Magnitude] ||v|| = √(x² + y² + z²)Step-by-step explanation:
Adding and subtracting vectors are follow the similar pattern of normal order of operations:
a + b = ⟨1 - 5, -4 - 5, 2 - 2⟩ = ⟨-4, -9, 0⟩
a - b = ⟨1 + 5, -4 + 5, 2 + 2⟩ = ⟨6, 1, 4⟩
Scalar multiplication multiplies each component:
2a = ⟨2(1), 2(-4), 2(2)⟩ = ⟨2, -8, 4⟩
Remember to multiply in the scalar before doing basic operations:
3a + 4b = ⟨3(1), 3(-4), 3(2)⟩ + ⟨4(-5), 4(-5), 4(-2)⟩ = ⟨3, -12, 6⟩ + ⟨-20, -20, -8⟩ = ⟨-17, -32, -2⟩
Absolute values surrounding a vector signifies magnitude of a vector. Follow the formula:
|a| = √[1² + (-4)² + 2²] = √21
Can someone help me find the answer?
Answers
Answer: B. This function has no intercept. I think B is the correct answer.
Find the length of the missing side
Answers
9514 1404 393
Answer:
short leg: x; long leg: 12; hypotenuse: yStep-by-step explanation:
The sides of the triangle can be read from the figure:
short leg: xlong leg: 12hypotenuse: yThe ratios tell you ...
long leg = x√3 = 12
x = 12/√3 = 4√3 . . . . . divide by √3. (same as multiply by (√3)/3)
2x = 2·4√3 = 8√3
Then the missing sides are ...
short leg: 4√3long leg: 12hypotenuse: 8√3Question 4 of 16
If the probability of rain today is 35%, what is the probability that it will not rain
today?
A. 100%
B. 65%
C. 35%
D. 50%
Answers
Answer:
I think the answer is B. 65%
The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false.(i)∀x ∃y(x+y≥0)
Answers
The domain of a set is the possible input values the set can take.
It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers
Given that: ∀x ∃y(x+y≥0)
Considering x+y ≥ 0, it means that the values of x + y are at least 0.
Make y the subject in x+y ≥ 0
So, we have:
[tex]\mathbf{y \le -x}[/tex]
There is no restriction as to the possible values of x.
This means that x can take any real number.
Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.
Read more about domain at:
https://brainly.com/question/15110684
I need to know the answer ASAP
Answers
Answer:
Step-by-step explanation:
The true length of recovery for patients with knee surgery is normally distributed with a mean of 123 days and a standard deviation of 1 day. What proportion of the patients will recover between 121 and 124 days?
Answers
Answer:
0.81859
Step-by-step explanation:
Given that the length of recovery days for patients with knee surgery is normally distributed with :
Mean, μ = 123 days
Standard deviation, σ = 1 day
The proportion of patients that will recover with 121 and 124 days :
We obtain the Probability of Z score :
Z = (x - μ) / σ
P(Z < (x - μ) / σ) < Z < P(Z < (x - μ) / σ)
P(Z < (121 - 123) / 1) < Z < P(Z < (124 - 123) / 1)
P(Z < - 2) < Z < P(Z < 1)
Using the normal distribution table :
P(Z < 1) - P(Z < - 2)
0.84134 - 0.02275
= 0.81859
An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the proportion of scanners that can be expected to fail within plus or minus 6 months of the mean. (Enter your answer as a percentage without the percent sign; keep 2 decimal places)
Answers
Answer:
The answer is "36.14%"
Step-by-step explanation:
The complete question is given in the attached file please find it.
[tex]\mu =41\\\\\sigma= 4\\\\P(42<\bar{x}<48)= p(\bar{x}<48)-p(\bar{x}<42)\\\\Z =\frac{(42-41)}{4} = \frac{1}{4} =0.25\\\\Z =\frac{(48-41)}{4} = \frac{7}{4} = 1.75\\\\[/tex]
Using z-table to find the value.
[tex]\to P(41<\bar{x}<48) = 0.9599- 0.5987 = 0.3614\times 100= 36.14\%[/tex]
This means that between 42 and 48 months, 36.14 % of scanners could be predicted will break down.
Find the measure of the incanted angle to the nearest degree
Answers
Answer:
34⁰
Step-by-step explanation:
let unknown angle be x
cos x=19/23
cos x=0.826
x=cos inverse of 0.826
x=34.3⁰
what is the answer for this question?
1. Dayne has three investment portfolios: A, B and C. Portfolios A, B and C together are worth a total of $175000, portfolios A and B together are worth a total of $143000, while portfolios A and C together are worth a total of $139000.
Use Cramer’s Rule to find the value of each portfolio.
Answers
Answer:
The correct answer is:
Portfolio A = $107,000
Portfolio B = $36,000
Portfolio C = $32,000
Step-by-step explanation:
According to the question,
[tex]A+B+C=175000[/tex]...(1)
[tex]A+B = 143000[/tex]...(2)
[tex]A+C=139000[/tex]...(3)
Now,
From (1) and (2), we get
⇒ [tex]Portfolio \ C = (1)-(2)[/tex]
[tex]=175000-143000[/tex]
[tex]=32000[/tex]...(4)
From (1) and (3), we get
⇒ [tex]Portfolio \ B =(1)-(3)[/tex]
[tex]=175000-139000[/tex]
[tex]=36000[/tex]...(5)
From (1), (4) and (5), we get
⇒ [tex]Portfolio \ A = (1)-(4+5)[/tex]
[tex]=175000-(36000+32000)[/tex]
[tex]=175000-68000[/tex]
[tex]=107000[/tex]
Thus the above is the correct answer.
Twelve different video games showing drug use were observed. The duration times of drug use were recorded, with the times (seconds) listed below. Assume that these sample data are used with a 0.05 significance level in a test of the claim that the population mean is greater than 85 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for a confidence interval? If the confidence interval is found to be −1.8 sec<μ<213.5 sec, what should we conclude about the claim? The given confidence interval ▼ does not contain contains the value of 85 sec, so there ▼ is is not sufficient evidence to support the claim that the mean is greater than 85 sec
Answers
Answer:
95% confidence level should be used for a confidence interval.
The given confidence interval contains the value of 85 sec, so there is not sufficient evidence to support the claim that the mean is greater than 85 sec.
Step-by-step explanation:
0.05 significance level
1 - 0.05 = 0.95
0.95*100% = 95%
This means that a 95% confidence level should be used for a confidence interval.
Confidence interval is found to be −1.8 sec<μ<213.5 sec, what should we conclude about the claim?
Contains the value of 85 sec, thus there is not sufficient evidence to support the claim that the mean is greater than 85 sec.
Please help! I will give you a lot of points if you do and the brainiest!
Answers
Answer:
First truth table:
~q p V ~q ~(p V ~q)
F T F
T T F
F F T
T T F
Second truth table:
~q p V ~q ~(p V ~q)
F T F
Step-by-step explanation:
The ~ operator is a negator (or NOT), such that it is the opposite of the sign.
The first column wants the negation of [tex]q[/tex], and the values of q are
T, F, T, F, for the columns starting from the top. The negation for the columns are F, T, F, T.
For the second column, The 'V' operator is the OR operator, so a single True, or T will result in a True.
For the first row, not q is F, and T OR F will result in T.
For the second row, not q is T, and T OR T will result in T.
For the third row, not q is F, and F OR F will result in F.
For the fourth row, not q is T, and F OR T will result in T.
In the last column, we must figure out not p OR not q, which we did in the last column, so all we must do is figure out the NOT of values of the last column.
The values of the last column are T, T, F, T, respectively, so the not of the columns will be F, F, T, F.
In the bottom truth table, not q, will be F because the value of q is T. The second column wants p OR not q, and we already know that not q is F, and the value of p is T. T OR F is equal to T. In the last column, the question wants the not of p OR not q, which we did in the last column, so we must figure out the not value of the last column, which is T. The not of T is F.
if 12 +2 =2 orderly what is 6 +3 orderly
Answers
Answer:
3
Step-by-step explanation:
Please Mark me brainliest
Answer:
aren't one of the numbers in the equations supposed to be negative?
The sume of the reciprocals of two consecutive integers is 3/2. Find the two integers
Answers
Answer:
1 and 2
Step-by-step explanation:
Let's say our first number is x. Our second number is the number after that, or x+1. A reciprocal of a number is 1/that number. Therefore, the reciprocal of x is 1/x and the reciprocal of x+1 is 1/(x+1). The question states the sum of the reciprocals of the two numbers is equal to 3/2. Therefore,
1/x + 1/(x+1) = 3/2
multiply both sides by 2 to remove a denominator
2/x + 2/(x+1) = 3
multiply both sides by x to remove a denominator
2 + (2*x)/(x+1) = 3x
multiply both sides by (x+1) to remove the other denominator
2*(x+1) + 2*x = 3x*(x+1)
expand
2*x+2 + 2*x = 3x²+3
combine like terms
4x + 2 = 3x²+3
subtract (4x+2) from both sides to make everything equal to 0 and to form a quadratic
3x² - 4x + 1 = 0
To factor this, we need to find two numbers that add up to b and multiply to a*c in an equation of form ax²+bx + c. Here, a=3, c=1, and b = -4
Two numbers that add to -4 and multiply to 3*1=3 are -3 and -1. We can thus factor this out to get
3x²-3x-x+1 = 0
3x(x-1) -1 ( x-1) = 0
(3x-1)(x-1) = 0
Therefore, solving for 0, we get
3x-1=0
x = 1/3
x-1 = 0
x=1
The only integer solution possible is x=1
To confirm, 1/1 + 1/(1+1) = 3/2, so x=1 is correct, with 1+1=2 being the second integer
7. Solve for x: x/6 - y/3 = 1
Please give steps!
Answers
<=> x/6 = 1+ y/3
<=> x/6 = (3+y)/3
<=> x = (3+y)/3 x 6
<=> x = 2(3+y)
So the answer is x = 2(3+y)
Can someone help me out
Answers
Answer:
π×64×4=804.25
Step-by-step explanation:
Formula of cylinder is π×square of radius×height
Answer:
803.8
Step-by-step explanation:
it's 3.14×8×8×4 which would give you 803.84 and then you round which would give you 803.8
32% adults favor the use of unmanned drones by police agencies. Twelve u.s. adults are randomly selected. Find the probability that the number of u.s. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight
Answers
Answer:
C
Step-by-step explanation:
32% of 12 =
32/100 x 12
= 3.84
So, C would be the correct choice
I wasn't sure about my answer so used the Gauthmath App
(ii). nth term of: 10+4-2...
Answers
9514 1404 393
Answer:
an = 10 -6(n -1)
Step-by-step explanation:
The series is an arithmetic series with a first term of 10, and a common difference of 4-10 = -6. The n-th term of an arithmetic series is given by ...
an = a1 +d(n -1) . . . . . for first term a1 and common difference d
__
For the parameters this series has, the n-th term is ...
an = 10 -6(n -1)
