a) Find the power series expansion for cos(x) with center x = 3x/2
Write your answer in ∑ form. Hint: cos3x/2) = 0, sin(3x/2) = -1 b) Find the power series expansion for the function cos(x)/ (x-3x/2) with centers x=3x/2
Write your answer in form.
Answers
a) Power series expansion for cos(x) with center x = 3x/2 is ∑ [(-1)^n * (x - 3x/2)^(2n) / (2n)!]. b) Power series expansion for cos(x) / (x - 3x/2) is obtained by dividing the power series expansions of cos(x) and (x - 3x/2).
a) The power series expansion for cos(x) with center x = 3x/2 is given by:
cos(x) = ∑ [(-1)^n * (x - 3x/2)^(2n) / (2n)!]
where n ranges from 0 to infinity. The hint provided implies that cos(3x/2) = 0, which means that the constant term in the power series expansion is zero. Additionally, sin(3x/2) = -1 can be used to determine the sign alternation of the terms in the series.
b) The power series expansion for the function cos(x) / (x - 3x/2) with center x = 3x/2 can be obtained by dividing the power series expansion of cos(x) by the power series expansion of (x - 3x/2). This can be done by multiplying the numerator by the reciprocal of the denominator's power series expansion, resulting in:
cos(x) / (x - 3x/2) = ∑ [(-1)^n * (x - 3x/2)^(2n) / (2n)!] / (x - 3x/2)
where n ranges from 0 to infinity.
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Related Questions
For the electronics producer problem shown below, how much would we be willing to pay for another assembly hour? X1 = number of PCs to produce X2 - number of Laptops to produce X; - number of PDAs to produce Max Z - $37X, + $35X2 + $45X3 2X1 + 3X2 + 2X3 <= 130 (assembly hours) 4X1 + 3X2 + X3 <- 150 (testing hours) 2X1 + 2X2 + 4X3 <= 90 (packing hours) X4+ X2 + X3 <- 50 (storage, sq. ft.) + X1, X2, X3 >=0
Answers
by solving the linear programming problem and examining the shadow price of the assembly hours constraint, we can determine how much we would be willing to pay for another assembly hour.
To determine how much we would be willing to pay for another assembly hour, we need to solve the linear programming problem and find the maximum value of the objective function while satisfying the given constraints.
Let's define the decision variables:
X1 = number of PCs to produce
X2 = number of Laptops to produce
X3 = number of PDAs to produce
The objective function represents the profit:
Max Z = $37X1 + $35X2 + $45X3
Subject to the following constraints:
2X1 + 3X2 + 2X3 <= 130 (assembly hours)
4X1 + 3X2 + X3 <= 150 (testing hours)
2X1 + 2X2 + 4X3 <= 90 (packing hours)
X4 + X2 + X3 <= 50 (storage, sq. ft.)
X1, X2, X3 >= 0
To find the maximum value of the objective function, we can use linear programming software or techniques such as the simplex method. The optimal solution will provide the values of X1, X2, and X3 that maximize the profit.
Once we have the optimal solution, we can determine the shadow price of the assembly hours constraint. The shadow price represents how much the objective function value would increase with each additional unit of the constraint.
If the shadow price for the assembly hours constraint is positive, it means we would be willing to pay that amount for an additional assembly hour. If it is zero, it means the constraint is not binding, and additional assembly hours would not affect the objective function value. If the shadow price is negative, it means the constraint is binding, and an additional assembly hour would decrease the objective function value.
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sat math scores follow a normal distribution with a mean of 511 and a standard deviation of 110. suppose we choose a student at random. what is the probability that the student scores between 450 and 600?
Answers
The probability that a student scores between 450 and 600 on the SAT math section is approximately 0.4147 or 41.47%.
To find the probability that a student scores between 450 and 600 on the SAT math section, we need to use the properties of the normal distribution. We know that the mean is 511 and the standard deviation is 110.
First, we need to standardize the values of 450 and 600 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For 450:
z = (450 - 511) / 110 = -0.55
For 600:
z = (600 - 511) / 110 = 0.81
Next, we need to find the area under the normal curve between these two standardized values. We can use a table or a calculator to find that the area between z = -0.55 and z = 0.81 is approximately 0.4147.
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write an equation in slope-intercept form of the line shown (1,-9) , (-3,-9)
Answers
Answer:
y = -9
Step-by-step explanation:
y2 - y1 / x2 - x1
-9 - (-9) / -3 - 1
0 / -4
y = 0 + b
-9 = b
Answer:
\(\boxed{\sf{y=-9}}\)Step-by-step explanation:
The slope-intercept form is the only way to solve this problem.
Slope-intercept form:
\(\rightarrow \sf{y=mx+b}\)
The m represents the slope.The b represents the y-intercept.Using the slope is another way to solve.
(1,-9) and (-3,-9)Use a slope formula.
Slope:
\(\sf{\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{rise}{run} }\)
y2= (-9)
y1= (-9)
x2= (-3)
x1= (1)
Rewrite the problem.
\(\sf{\dfrac{(-9)-(-9)}{(-3)-1}=\dfrac{0}{-4}=\boxed{\sf{0} }\)
Therefore, the slope is 0.We're not done yet.
y-intercept= (-9).
The m represents is 0.
The b represents is (-9).
So, the correct answer is y=-9.I hope this helps you! Let me know if my answer is wrong or not.
Suppose that we don't have a formula for g() but we know that (1) - - 2 and 9') +15 for all ar. (a) Use a linear approximation to estimate (0.95) and g(1.05). (Round your answers to two decimal places.) 9(0.95) (1.05) (b) Are your estimates in part(a) too large or too small? Explain The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lle above the curve. Thus, the estimates are too large. The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small. The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large Question Helo Mesas instructor
Answers
Estimates in part (a) are too small because the slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve.
Suppose we don't have a formula for g(), but we know that (1) - - 2 and 9') +15 for all ar. To estimate g(0.95) and g(1.05), we can use linear approximation. Linear approximation is a method to estimate a value of a function using the tangent line at a specific point. In this case, we can use the tangent line at a=1 to estimate g(0.95) and g(1.05).
To find the equation of the tangent line at a=1, we need to find the slope of the curve at that point. Since we don't have a formula for g(), we can use the given information that g'(a)+15 for all a. Therefore, g'(1)+15=-2+15=13. The slope of the tangent line at a=1 is 13.
Using the equation of the tangent line, y=13(x-1)+g(1), we can estimate g(0.95) and g(1.05).
For g(0.95), we substitute x=0.95 into the equation of the tangent line and get y=13(0.95-1)+g(1)=g(1)-0.65. For g(1.05), we substitute x=1.05 into the equation of the tangent line and get y=13(1.05-1)+g(1)=g(1)+0.65. Therefore, our estimates for g(0.95) and g(1.05) are g(1)-0.65 and g(1)+0.65, respectively.
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is (, ) = 3 − 32 an harmonic function? if yes, then find a corresponding analytic function ()
Answers
No, f(x, y) = 3x - 3y^2 is not a harmonic function.
A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
∂²f/∂x² + ∂²f/∂y² = 0.
Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0
Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.
As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.
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What is the inverse of:
f (x) = 9x - 4
O f'(x) = *
Of-'(x) = 4
Of(x) = x + 4
of'(x) = 6
Answers
Answer:
6 is the correct answer.
Name the marked angle in 2 different ways.
J, K, I
Answers
Answer: Where is the image?
Step-by-step explanation:
Which triangle is a 30°-60°-90° triangle?
10
O
5,3
15
5
5/5
10
5
10/3
15
10
5./3
Answers
Answer:
the first one
Step-by-step explanation:
Find the 96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25
Answers
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
arithmetic sequence 1, -12, -25, .. .1,−12,−25
an arithmetic sequence can be written as
a , a + d , a + 2d , a + 3d , . . . . . a + (n-1)d
nth tern of an arithmetic sequence is
aₙ= a+ (n-1)d
a= first term of an arithmetic sequence
d = common difference of an arithmetic sequence
n = number of terms in an arithmetic sequence
So in the above arithmetic sequence
a= 1
d= -13
n= 96
a₉₆= 1+ (96-1)(-13)
= 1- (95)13
= 1- 1235
= -1234
96th term of the arithmetic sequence 1, -12, -25, ...1,−12,−25 is -1234
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I need help to find the volume
Answers
Answer:
320
Step-by-step explanation:
To find the volume of a rectangular prism, you simply need to multiply together the width, length, and height. 16*5*4=320 cubic centimeters. Hope this helps!
use the composite below to mark each statement as true or false.justify your choices.
Answers
For the equation shown below, solve for \( y \) as a function of \( x \) and express the result in function notation. Use \( f \) for the name of the function. \[ -12 x+4 y=32 \] The function is
Answers
The function that represents the given equation is:
f(x) = 3x + 8
The equation is -12x + 4y = 32. To solve for y as a function of x, we need to isolate y on one side of the equation.
Adding 12x to both sides, we get 4y = 12x + 32.
To solve for y, we divide both sides of the equation by 4. This gives us y = 3x + 8.
Hence, the function that expresses y as a function of x is:
f(x) = 3x + 8.
Using this function, we can determine the value of y corresponding to any given x value. For example, if we substitute x = 5 into the function, we have f(5) = 3(5) + 8 = 15 + 8 = 23. Therefore, when x is 5, y is 23 according to the function f(x) = 3x + 8.
In summary, the function f(x) = 3x + 8 represents the relationship between x and y in the given equation, allowing us to calculate the corresponding y value for any given x value.
Therefore, the function that represents the given equation is:
f(x) = 3x + 8
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An investor invested a total of $3,000 in two mutual funds. One fund earned a 7% profit while the other earned a 3% profit. If the investor's total profit was $142, how much was invested in each mutual fund?
Answers
Answer:
Step-by-step explanation:
x= fund that got 7%
y= fund that got 3%
x+y=3000
.07x+.03y=142
y=3000-x
.07x+.03(3000-x)=142
.07x+90-.03x=142
.04x=52
x= 1300
x+y=3000
1300+y=3000
y=1700
1300 in the fund that earned 7%
1700 in the fund that earned 3%
Find the gradient of the line segment between the points (4,-3) and (5,-6).
Answers
Solve for the value of m.
(8m+7)°
(5m+5)°
Answers
Step-by-step explanation:
The two angles added together = a right angle = 90 degrees
so 8m+7 + 5m+5 = 90
13m + 12 = 90
13m = 78
m = 78/13 = 6
Which of the functions below could have created this graph?
A. F(x)=x-2x
B. F(x)=x²+5
C. F(x)=-1¹-x²+x+2
D. F(x)=x³+x²+x+1
Answers
Answer:
Answer is C. x=-1/2x^4-x^2+x+2
Step-by-step explanation:
A state representative took several random surveys of adults to find which palce they visited most frequently. The average of all of the surveys is shown in this table.
Answers
Answer:
On average, 2 out of 10 adults visited the museum most frequently
Step-by-step explanation:
Place the steps in Order to solve each equation. Plz sb help ITS NOT MUCH!!!!!
Answers
for the one on the left:
distribute: -18x + 27 - 10x = -1
combine like terms: -28x + 27 = -1
subtract 27 from both sides: -28x = -28
divide -28: x = 1
on the right:
distribute: 10x - 15 + 8 = 9
combine like terms: 10x - 7 = 9
add 7 to both sides: 10x = 16
divide: x = 1.6
Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
Answers
Answer:
Step-by-step explanation:
Based on the information provided, the following three equations are true for the values of x, y, and z:
x + y + z = 360 degrees (Since the sum of the angles in a quadrilateral must equal 360 degrees)
x = 65 degrees (As given, the first angle is 65 degrees)
y + z = 295 degrees (From equation 1, 360 - 65 = 295)
So, the values of x, y, and z can be calculated as 65 degrees, 115 degrees, and 180 degrees respectively.
138×14÷28+209
A)278
B)288
C)298
D)388
Answers
Answer: A
Step-by-step explanation:
First you multiply 138 x 14 =1932 then divide 28 then you have 69 then add 209 then you have 278.
sorry if its wrong.
Answer:
A) 278
Step-by-step explanation:
Use PEMDAS for order of operations:
Start with anything in parentheses, and then operations are performed on any exponents (also called powers). Next, perform operations on multiplication or division from left to right. Finally, operations on addition or subtraction are performed from left to right.
Anatoliy has a combination of 104 nickels and quarters totaling $22. which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, anatoliy has?
Answers
The system of linear equation which can be used to find the number of nickles n, and quarters q Anatoily has are n + q = 104 and 1/20(104 - q) + (1/4)q = 22there are total 20 nickels and 84 quarters Anatoily has.
According to the given question.
Total number of nickles and quarters Anatoily have is 104.
'n' represents the total numbers of nickles and 'q' represents total number of quarters. So, the linear equation which represents the given condition
⇒ n + q = 104
Since, 20nickles = 1 dollar
⇒ 1 nickle = 1/20 dollar
And, 4 quarters = 1 dollar
⇒ 1quarter = 1/4 dollar
Here, it is also given that combination of 104 nickels and quarters totaling $22.
So, we have an other linear equation $(1/20)n + $(1/4)q = $22
Form
n + q = 104
We can write
n = 104 - q
Substitute the value of n in $(1/20)n + $(1/4)q = $22
Therefore,
$1/20(104 - q) + $(1/4)q = $22
⇒ 5.2 - q/20 + q/4 = 22
⇒ 5.2 + (-q + 5q)/20 = 22
⇒ 5.2 + 4q/20 = 22
⇒ 5.2 + q/5 = 22
⇒ q/5 = 22 - 5.2
⇒ q/5 = 16.8
⇒ q = 16.8 × 5
⇒ q = 84
Therefore,
n = 104 - 84
⇒ n = 20
Hence, the system of linear equation which can be used to find the number of nickles n, and quarters q Anatoily has are n + q = 104 and 1/20(104 - q) + (1/4)q = 22there are total 20 nickels and 84 quarters Anatoily has.
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WHAT ARE THE ANSWERS PLEASE ITS THE FIRST QUESTION AND I CANT EVEN AND DONT SEND A LINK TO SOME FILE
Answers
Answer:
2 4 6
Step-by-step explanation:
A
5
B
3
4
С
Find tan(B) in the triangle.
Answers
Answer:
Step-by-step explanation:The tangent of an angle is the trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle. Example: In the triangle shown, tan(A)=68 or 34 and tan(B)=86 or 43 .
Given two sides
if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)
if leg b is unknown, then. b = √(c² - a²)
for hypotenuse c missing, the formula is. c = √(a² + b²)
Answer:
it’s 3/4
Step-by-step explanation:
it’s right for khan (trigonometric ratios in right triangles)
Figure ABCD is transformed to obtain figure A′B′C′D′:
A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 1, B prime at 2, negative 1, C prime at 2, negative 4, D prime at 4, negative 2.
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)
Part B: Are the two figures congruent? Explain your answer. (4 points)
Answers
Answer:
Reflected along x axis
Translated 7 units to the right
Step-by-step explanation:
If a point (x, y) is reflected along the x axis, its x coordinate remains the same and the y coordinate is opposite (negated). The new point is at (x, -y)
If a point (x, y) is translated h units to the right, the new coordinate is (x+h, y).The transformation are as follows:
It is reflected along the x axis so that the new coordinates would be at A1 at (- 4, -4), B1 at (- 2, -2), C1 at (- 2, 1), D1 at (- 4, -1)
It is translated 7 units to the right, The new coordinates are A' at (3, -4), B' at (5, -2), C' at (5, 1), D' at (3, -1)
Hope that's better
Someone pls help me asap
Answers
Answer:
2/3
Step-by-step explanation:
If the denominators (bottom numbers) of the fraction are the same, just add the numerators (top numbers) together.
Find all unknown measures in the triangle. Round answers to the nearest tenth.
Answers
The unknown measures in the triangle are:
Side b ≈ 6.9
Side c ≈ 9.2
Angle A ≈ 55 degrees
To find all unknown measures in the triangle, we need to use the properties of triangles and trigonometry. Let's label the angles and sides of the triangle as follows:
Angle A is opposite side a
Angle B is opposite side b
Angle C is opposite side c
Using the Law of Sines, we can find one of the unknown sides, let's say side c:
c/sin(C) = a/sin(A)
Plugging in the given values:
c/sin(65) = 8/sin(55)
Solving for c:
c = 8(sin(65)/sin(55)) ≈ 9.2
Next, we can use the Law of Cosines to find another unknown side, let's say side b:
b² = a² + c² - 2ac*cos(B)
Plugging in the known values:
b² = 8² + 9.2² - 2(8)(9.2)*cos(60)
Solving for b:
b ≈ 6.9
Finally, we can find the remaining angle, angle A, using the fact that the angles in a triangle add up to 180 degrees:
A = 180 - B - C = 180 - 60 - 65 = 55
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I need help on this one
Answers
Answer:need help on what?
Step-by-step explanation:i cant see it
what are the answers i cant see them
Step-by-step explanation:
50 points!! This student made an error in solve the equation. Your job is to
1. Identify the error
2. Explain to the student what they should have done instead.
3. Show work
Answers
Answer:
Mistake was subtracting x rather than adding x in the first step
The true answer is x = - 4
Step-by-step explanation:
Lets first solve the equation so we can compare to identify where the mistake is.
6 - x = 5x + 30
==> add x to both sides
6 = 6x + 30
==> subtract 30 from both sides
-24 = 6x
==> divide both sides by 6
-4 = x is the correct answer.
After comparing our work with their work, the mistake seems to be made in the first step. They subtracted x from both sides rather than adding x to both sides. This is wrong because the inverse of subtraction is addition.
what are outliers and how can the sigmoid function mitigate the problem of outliers in logistic regression?
Answers
Outliers are observations in a dataset that significantly deviate from the majority of the data points. These observations can affect the statistical analysis, as they can skew the results or increase the error in the model.
In logistic regression, outliers can be problematic as they can cause the model to overfit or underfit the data. Overfitting occurs when the model is too complex and captures noise or outliers in the data, while underfitting occurs when the model is too simple and cannot capture the underlying patterns in the data.
The sigmoid function used in logistic regression can mitigate the problem of outliers by compressing extreme values in the data towards the middle of the function. The sigmoid function is a curve that approaches 0 or 1 as the input value becomes very negative or very positive, respectively. This means that extreme values in the data will be transformed to values closer to 0 or 1, which can reduce the influence of outliers on the model.
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Please answer the math problem... I will mark you brainliest
Answers
Answer:
E.
F.
G.
Step-by-step explanation:
I listed the correct ones