use linear approximations to estimate the following quantity. choose a value of a that produces a small error. tan-5
Answers
Our estimate for arctan(0.1) using a linear approximation at x = 0 is approximately 0.1.
To estimate the value of tan^(-1)(x), also known as arctan(x), using a linear approximation, we can utilize the fact that the derivative of arctan(x) is 1/(1+x^2).
First, let's choose a value of a that produces a small error. We can choose a = 0 as it simplifies the calculations and allows us to approximate tan^(-1)(x) around x = 0.
To start, we'll find the linear approximation of arctan(x) at x = a using the tangent line equation:
L(x) = f(a) + f'(a)(x - a)
In this case, f(x) represents arctan(x) and f'(x) represents the derivative of arctan(x), which is 1/(1+x^2).
Using a = 0, the equation becomes:
L(x) = arctan(0) + (1/(1+0^2))(x - 0)
Since arctan(0) is 0, the equation simplifies to:
L(x) = x
Now, we can use this linear approximation to estimate the value of arctan(x) for a given x.
For example, let's say we want to estimate arctan(0.1). Plugging 0.1 into the linear approximation equation, we get:
L(0.1) = 0.1
Therefore, our estimate for arctan(0.1) using a linear approximation at x = 0 is approximately 0.1.
By choosing a value of a that produces a small error, we are able to obtain a reasonably accurate estimation using the linear approximation method.
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Related Questions
What is the standard deviation and its meaning given this population of customer ages? 45, 76, 30, 22, 51, 40, 63, 66, 41
Answers
The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)
SD is the standard deviation
xi is each value from the data set
X is the mean of the data set
N is the number of observations in the data set.
It is given that:
The data set:
45, 76, 30, 22, 51, 40, 63, 66, 41
From the formula:
∑(x(i) - X)² = 2463.55
N = 9
SD = √(2463.55/9)
SD = 16.54
Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.
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A data set has 20 elements. A second data set of 20
ciements is obtained by adding 7 to each element of the
first set. A third data set of 20 elements is obtained by
multiplying each element of the second data set by 3.
The median of the third data set is 63. What is the medi-
an of the first data set?
A.7
B.14
C.21
D.196
E.210
Answers
Answer:
B.14
Step-by-step explanation:
Goodluck guys sa sagot
hello I am having problems doing rounding mixed fractions to whole numbersChange the following mixed numbers to whole numbers:1) 9 5/7, 2) 3 5/6
Answers
To change the following mixed number to a whole number, we can proceed as follows:
\(9\frac{5}{7}=9+\frac{5}{7}\)When we have mixed numbers, we have the sum of an integer and a fraction. Then we need to add both numbers following the rules for adding fractions:
\(\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d+b\cdot c}{b\cdot d}\)Now, we can add both numbers above:
\(\frac{9}{1}+\frac{5}{7}=\frac{9\cdot7+1\cdot5}{1\cdot7}=\frac{63+5_{}}{7}=\frac{68}{7}\)We have an improper fraction that is equivalent to the mixed number. In both cases, if we "transform" both numbers to decimals, we will get:
\(9+\frac{5}{7}=9+0.714285714286=9.71428571429\)And
\(\frac{68}{7}=9.71428571429\)If we see the number
25 = 5 • 3 = 15 True or False
Answers
Answer:
False
Step-by-step explanation:
If f(x) = x + 8 and g(x) = x3, what is (gºf)(-5)?
Answers
Answer:
Step-by-step explanation:
f(-5) = -5 + 8 = 3
g(3) = 3^3 = 27
can anyone help? I’ll give brainlest ❤️
Answers
Answer:
C
Step-by-step explanation:
I inserted 5 for a and c is the correct answer
It would be great if someone could help me with this problem
Answers
Equation of asymptote y=0
Equation of asymptote can also be called horizontal asymptote.
It means the place where the line almost meets but actually not touching the place. The line almost touches y=0 but it actually does not touch it.
Sixty percent, or 12, of the students in Alex's class are going to the movies. 2/3, or 14, of the students in Mary's class are going to the movies. Which class has more students? Justify your answer using equations.
Answers
Answer:
Mary's class.
Step-by-step explanation:
One way to do this is to figure out how many students are in Alex's class and how many students are in Mary's class.
60% of Alex's class is 12 students
\(\frac{12*100}{60}\) = \(\frac{1200}{60}\)= 20 students
\(\frac{2}{3}\) or 66.66% (repeating) of Mary's class is 14 students
\(\frac{14*100}{66.66}\) = \(\frac{1400}{66.66}\) = 21 students
(^^66.66 repeating)
Mary's class has more students than Alex's class.
12-3 ( x-8 ) simplify
Answers
Answer:
-3x + 36
Step-by-step explanation:
The first step is to distribute the -3 to (x - 8), like so:
12 - 3(x - 8)
12 - 3x + 24
Add like terms (12 and 24):
12 + 24 = 36
-3x + 36
F(2)equals 2x squared -3x-4
Answers
Please, send me a picture of your question
solve the problem with simplex method , and verify using graphical method
4) Min Z = -2X1 - 4X2 - 3X3
St. X1 + 3X2 + 2X3 <= 30 X1 + X2 + X3 <= 24
3X1 + 5X2 + 3X3 <= 60
Xi >= 0
Answers
The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.
The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:
Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0
Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |
Identify the entering variable (most negative coefficient in the objective row): X2
Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1
Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |
Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |
The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.
To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.
In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.
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\(24 + 42 - 5\)
whats the answer.
Answers
Answer:
61
Step-by-step explanation:
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Which one of the following is a ratio that is equivalent to 3:5? *
6:12
O
9:15
O 10:16
O 30:60
Answers
Kathy and her friend were making necklaces. They spent $30 on supplies. They sold $150 worth of bracelets in 3 hours. They split their earnings evenly. How much did Kathy make per hour? PLZ WHOEVEr DOES tHIS IN 45 SEC will be marked brainliestttt
Answers
Answer:
Kathy made 25$ per hour
Step-by-step explanation:
You would spit the total of $150 into 3 since it was three hours and that would be $50 but they split the earnings evenly so it would be $25
Answer:
25 dollars per hour
Step-by-step explanation:
it was just the answer I got
Solve: (8x − 4) + (−2x + 3)
Answers
Hey there!
(8x - 4) + (-2x + 3)
= 8x - 4 + (-2x) + 3
= 8x - 4 - 2x + 3
COMBINE the LIKE TERMS
= (8x - 2x) - (4 + 3)
= 8x - 2x - 4 + 3
= 6x - 1
Therefore, your answer is: 6x - 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Hope I helped.
All clearance items are marked an additional 30% off the sale price. A coat that originally costs $100 before any discount is on sale for 20% off. What would your total cost be if the sales tax is 8.5% ?
Answers
The total cost of the coat, including the additional 30% clearance discount and 8.5% sales tax, would be $73.51.
Let's calculate the total cost step by step.
First, we apply the 20% sale discount to the original price of $100:
Sale Price = $100 - (20% of $100) = $100 - $20 = $80
Next, we calculate the additional 30% discount on the sale price:
Discounted Price = $80 - (30% of $80) = $80 - $24 = $56
Now, we need to add the sales tax of 8.5% to the discounted price. Sales tax is calculated as a percentage of the final price:
Sales Tax = 8.5% of $56 = $56 * 0.085 = $4.76. Finally, we add the sales tax to the discounted price to find the total cost:
Total Cost = Discounted Price + Sales Tax = $56 + $4.76 = $60.76 Therefore, the total cost of the coat, including the additional 30% clearance discount and 8.5% sales tax, would be $73.51.
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Help please if you don’t mind!!
Thankyou so much
Answers
Answer:
Step-by-step explanation:
\(F = \frac{9}{5}C+32\)
Subtract 32 from both sides
\(F-32= \frac{9}{5}C\\\)
Multiply both side by 5/9
\(\frac{5}{9}(F-32)=( \frac{5}{9})* \frac{9}{5}C\\\\ \frac{5}{9}(F-32)=C\\\)
F= 41
\(\frac{5(41-32)}{9}=C\\\\ \frac{5*9}{9}=C\\\\ \frac{45}{9}=C\\\\C = 5\\\\\)
41° F = 5° C
Which angle has a negative sine value and a positive cotangent value?
Answers
sin4π/3= sin(π+π/3) = - sinπ/3
cot4π/3=cot(π+π/3)= cotπ/3
OPTION C 4π/3
Express 600g as a ratio of 1kg
please show working.
Answers
3:5
Step-by-step explanation:
change the kilogram into gram and then divide it
Answer:
3 : 5
Step-by-step explanation:
The quantities must have the same units
1 Kg = 1000 g , then
600 : 1000 ( divide both parts by 200 )
= 3 : 5 ← in simplest form
let n be the second smallest positive integer that is divisible by every positive integer less than 7. what is the sum of the digits of n?
Answers
The sum of the digits of n is 3 if n is the second smallest positive integer that is divisible by every positive integer less than 7
What is least common multiple?
The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.
It can be calculated for two or more numbers as well.
For example, LCM of 10, 2 and 7 is 70.
According to the given question:
Now n must be divisible by every positive integer less than 7, or
1, 2, 3, 4, 5, and 6.
Each number that is divisible by each of these is a multiple of their least common multiple.
LCM (1,2,3,4,5,6) = 60
So each number divisible by these is a multiple of 60.
The smallest multiple of 60 is clearly 60, so the second smallest multiple of 60 is 2 x 60 = 120.
Therefore, the sum of the digits of n is 1+2+0 = 3
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a) What type of triangle is triangle ABC? b) Give reasons for your answer. I need the correct answer for B with Reasons Not "ab and ac are the same" any word other than the same
Answers
Answer:
Isosceles triangle
Step-by-step explanation:
Thorough explanation: Through the angles in the triangle ABC.
First, observe that angle ACD = 50 degrees (given)
Since lines AB and DE are parallel to each other,
angle BAC = angle ACD = 50 degrees (by the property of alternate angles)
It is also given that angle ABC = 80 degrees.
Since ABC is a triangle, the sum of the three angles must add up to 180 degrees.
Angle BAC + Angle ABC + Angle ACB = 180 degrees
50 + 80 + Angle ACB = 180
Angle ACB = 180 - 50 - 80
= 50 degrees
Since two of the angles, angles ACB and BAC are the same at 50 degrees, triangle ABC is an isosceles triangle. (With sides AB and BC equal)
HELP PLEASE I NEED IT FAST!!!!!!!!!
1. Use the clues to identify the location of the post office, hospital, mall, nail salon, park, pet store, library, and gas station. (7 points)
- The hospital is at letter c and makes alternate interior angles with the mall.
- The post office and hospital make same side interior angles.
- The mall makes a corresponding angle with the nail salon.
- The pet store and the gas station form alternate exterior angles.
- The pet store forms a vertical angle with the park.
Letter
_____ Gas station
__C__ Hospital
_____ Library
_____ Mall
_____ Nail salon
_____ Park
_____ Pet store
_____ Post Office
Answers
Answer:
can I get ful question........?
Answer:
Here is the full question
Step-by-step explanation:
There were 52 problems on Petunia's last math test. She got 1/4 of them wrong. How many questions did she get correct? Show work in steps!
Answers
Answer:
39
Step-by-step explanation:
1/4 wrong so 3/4 correct;
3/4 of 52 questions: 52×3/4=39
A trapezoid has bases of lengths 14 and 21. Find the trapezoid's height if it's area is 245
Answers
Answer: 8575/2
Step-by-step explanation:
A poster is regularly priced at $19.98 is on sale for 40% off. What is the sale price?
Answers
Answer:
$11.99
Step-by-step explanation:
19.98x.4=7.99
19.98-7.99=11.99
What is the value of x in the equation 2x + 3y = 36, when y = 6?
8
9
27
36
Answers
Answer:
x = 9
Step-by-step explanation:
we can plug in the given value for y into the equation to find x
2x + 3y = 36
2x + 3(6) = 36
2x + 18 = 36
2x = 18
x = 9
Answer:
x = 9
Step-by-step explanation:
2x + 3y = 36
Let y=6
2x+3(6) = 36
2x+18 = 36
Subtract 18 from each side
2x+18-18 =36-18
2x = 18
Divide by 2
2x/2 =18/2
x = 9
Solve each equation. Check your answers. ln 3 x=6
Answers
After solving the equation ln 3x =6, the value of x is equal to \(\frac{e^6}{3}\)
We have been asked to find x in ln 3 x=6
⇒ ln 3 x = 6
⇒ 3x = \(e^6\)
⇒ x = \(\frac{e^6}{3}\)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Sarah borrowed $500 from her mother. She worked for her sister
Allison, who paid her $225 at the end of the week. Her sister Cosima
repaid the $150 that Sarah loaned her. Her sister Helena gave her half
of the $200 they found on the ground while walking together. Sarah
and her brother Felix hosted a party and made $800, $125 of that
amount going to Sarah. Does Sarah have enough money to repay her
mother's loan? Explain your answer in complete sentences.
Answers
Answer:
Yes. She'll have 100 dollars left for her.
Step-by-step explanation:
Sarah borrowed 500. So, first we add 225+150+100+125. That will equal to 600. The 100 is half of 200.
Which table does not represent a
function?
Answers
Answer: G, I think? It’s been awhile
Step-by-step explanation: There is 14 in every box, if i remember correct that means it’s not a function.
Determine if the following statement is true or false. Alex calculated a correlation coefficient of -1.5. He made a mistake in his calculation since the correlation coefficient has to be between - 1 and 1. The statement is
(1) false
(2) true.
Answers
Answer:
(2) The statement is true.
-1 < r < 1