(1 point) Suppose that you are told that the Taylor series of /(x) = xo? about x = 0) is *++*+ + + + 2! 3! 4! Find each of the following: 0 مرا (مام) 0
Answers
Therefore, the Taylor series for xsin(πx/2) at x = 0 is (π/2) * Σ (-1)ⁿ * (x(2n+1))/((2n+1)!). where Σ denotes the sum from n = 0 to infinity.
What is the vice Taylor series?We must calculate the derivatives of sin(x) in order to use Taylor's method to determine the power series expansion of sin x: Sin(x) = Cos(x), Sin(x) = Sin(x), Sin(4)(x) = Sin, Sin(x) = Sin(x),(x). Sin(4)(x) = Sin(x), so this trend will keep happening.
For sin x at x = 0, the Taylor series is given by:
sin x = x - (x³)/3! + (x⁵)/5! - (x⁷)/7! + ...
Using this result, we can find the Taylor series for xsin(πx/2) at x = 0
x sin(πx/2) = x * (πx/2 - (πx/2)³/3! + (πx/2)⁵/5! - (πx/2)⁷/7! + ...)
= (π/2) * (x₂ - (x⁴)/3! + (x⁶)/5! - (x⁸)/7! + ...)
Therefore, the Taylor series for xsin(πx/2) at x = 0 is:
x sin(πx/2) = (π/2) * Σ (-1)ⁿ * (x(2n+1))/((2n+1)!)
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Question:
Use power series operations to find the Taylor series at x = 0 for the following function. xsin(Злх/2). The Taylor series for sin x is a commonly known series. What is the Taylor series at x = 0 for sin x? Use power series operations and the Taylor series at x = 0 for sin x to find the Taylor series at x = 0 for the given function.
Related Questions
tan40=x/62
Plz help. I will give brainliest
Answers
Answer:
52.0 in degrees
Step-by-step explanation:
x=62tan40
Please help me with question
Answers
Answer:
Yes, you are right.
Step-by-step explanation:
RS = 20
UT = 20
UT also = x + 10
x = 20 - 10
x = 10
So, yes, you are right.
Hope that helps!
find the slope of the line that passes through the given points (9, -3) and (9, 4)
Answers
Answer: No slope.
Step-by-step explanation:
No slope, the x values are the same yet they have different Y values so there isn't a slope and this isn't a function.
bivariate data is the type of data that a scatterplot is used to analyze?
True
or
False
Answers
PLEASE ANSWER ASAP!!!!!!!!!!!!!
Answers
Hey there! :)
Answer:
m∠LOM = 44°
Step-by-step explanation:
OL ⊥ ON, therefore:
m∠LOM + m∠MON = 90°.
Solve:
3x + 38 + 9x + 28 = 90°
Combine like terms:
12x + 66 = 90°
Subtract both sides by 66:
12x = 24°
x = 2°
Plug in x into the equation for m∠LOM:
m∠LOM = 3(2) + 38
m∠LOM = 6 + 38
m∠LOM = 44°
Answer:
44
Step-by-step explanation:
Angle MON + angles LOM = 90
So, 3x + 38 + 9x + 28 = 90
12x + 66 = 90
12x = 24
x = 12
So, LOM = 3x + 38(substitute) = 44
Hope this helps
The cost to rent a car is $25 plus an additional $0.15 for each mile the car is driven. How many miles was a car driven if it had a bill of $71.80? 479 645 454 312
Answers
Answer:
The answer is 312.
Step-by-step explanation:
Because you would start with 71.80 minus 25 to get 46.8 then do 46.8 divided by 0.15 to get 312.
Answer:
312
Step-by-step explanation:
Rashaad leans a 22-foot ladder against a wall so that it forms an angle of 65° with the ground. How high up the wall does the ladder reach? Round vour answer to the nearest hundredth of a foot if necessary.
Answers
The ladder reaches 19.938 foot high from the ground on the wall.
What is a Right Angled Triangle ?A right angled triangle is a triangle that has one of its angle measure as 90 degree.
It is given that
Ladder Length = 22 foot
The angle between the ladder and the ground is 65 degree.
When the ladder leans on a wall , the wall makes 90 degree with the ground and the ladder is the hypotenuse of the right angled triangle formed.
The figure is attached with the answer.
sin 65 = Height of the wall / Hypotenuse
0.9063 = Height of the wall / 22
Height of the wall = 19.938 foot
Therefore the ladder reaches 19.938 foot high from the ground on the wall.
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Answer:
19.94
Step-by-step explanation:
b) If the joint probability distribution of three discrete random variables X, Y, and Z is given by, f(x, y, z)=. (x+y)z 63 for x = 1,2; y=1,2,3; z = 1,2 find P(X=2, Y + Z ≤3).
Answers
The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.
To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.
Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:
X=2, Y=1, Z=1
X=2, Y=1, Z=2
X=2, Y=2, Z=1
Step 2: Calculate the joint probability for each combination:
For X=2, Y=1, Z=1:
f(2, 1, 1) = (2+1) * 1 = 3
For X=2, Y=1, Z=2:
f(2, 1, 2) = (2+1) * 2 = 6
For X=2, Y=2, Z=1:
f(2, 2, 1) = (2+2) * 1 = 4
Step 3: Sum up the joint probabilities:
P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13
They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.
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HElp K 12 test! Will give brainiest PLS HELP!!!!
1. Which product is negative?
a. −6⋅(−7)⋅(−8)⋅0
b. −2⋅(−7)⋅12⋅(4)
c. −3⋅(−2)⋅(−4)⋅(−7)
d. 4⋅(−9)⋅(−3)⋅(−1)
2. Multiply.
−3⋅7
a. −21
b. −11
c. 11
d. 21
3.Multiply.
(−17)⋅(−6)
a. −102
b. −23
c. 23
d. 102
4. What is the product?
−5⋅(−3)⋅(−8)
a. −120
b. −16
c. 16
d. 120
5. What is the product?
4⋅(−9)⋅(−3)⋅(−1)
a. −108
b. −81
c. 81
d. 108
Answers
Answer:
1. d 2. a 3. d 4. a 5. a
Step-by-step explanation:
For 1, d is negative because, if there an even number of negatives, the answer will be positive. a. would have been correct, but you multiply that one by 0. 0 is not negative, so the answer has to be d.
2. is -21. You can multiply 3 times seven then make it negative, or simply add -7 together 3 times.
3. is d because the two negatives cancel each other out. Even numbers of negatives cancel each other out. therefore, 17 times 6 is 102.
4. -120 is the answer because there are 3 negatives. That is an odd number, so we know our answer is negative. -5 times -3 is 15, and 15 times -8 is -120.
5. is a because -1 times 4 is -4, then -4 times -9 is 36. 36 times -3 is then -108.
A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed. 'Number of times per week' is what type of data
Answers
Number of times per week is quantitative data. Quantitative data is a numerical measurement that expresses a magnitude, amount, quantity, or degree of something, while qualitative data is non-numerical information. The number of times per week data is quantitative because it involves counting the number of times people visit the park, and this data can be analyzed mathematically.
Therefore, it involves numbers and is measurable in the form of a count, which makes it quantitative data. In the study to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose, frequency data is being collected by researchers. Frequency data consists of counts and statistics that summarize the number of times a particular event occurs in a particular dataset.
Therefore, in this study, the number of times per week is frequency data. In conclusion, the number of times per week data collected in the study is a type of quantitative data Data can be categorized into two main types: qualitative data and quantitative data. Quantitative data can be expressed in numbers, and it is measurable and objective. On the other hand, qualitative data is non-numerical information and descriptive and subjective. The study aimed to determine the age, number of times per week, and duration of resident use of a local park in San Jose. The number of times per week data collected in the study is quantitative data since it involves counting the number of times people visit the park. This data can be analyzed mathematically, and it is measurable in the form of a count. In research studies, frequency data are collected, and it consists of counts and statistics that summarize the number of times a particular event occurs in a particular dataset.
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A creative writing competition accepts only
poems and stories.
In one year, the competition received 1000
entries.
750 of the entries were poems.
24% of the poems and 65 of the stories were
shortlisted for a prize.
a) Draw a frequency tree to show the
information above.
b) An entry is picked at random. What is the
probability that it is a poem that has not been
shortlisted?
Give your answer as a decimal.
c) A story is picked at random. What is the
probability that it has not been shortlisted?
Give your answer as a decimal.
Answers
Answer:
b) 0.57
c) 0.74
Step-by-step explanation:
part a:
frequency graph is attached with this answer (in png format).
part b:
let A be the event an entry is picked at random and the entry is a poem that has not been shortlisted.
P(A) = \(\dfrac{\text{number of poems not shortlisted}}{\text{total number of entries}}\)
P(A) = \(\dfrac{570}{1000}\) (see the frequency graph)
P(A) = 0.57
part c:
let B be the event a story is picked at random and the story has not been shortlisted.
P(B) = \(\dfrac{\text{number of stories not shortlisted}}{\text{total number of stories}}\)
P(B) = \(\dfrac{185}{250}\) (see the frequency graph)
P(B) = 0.74
Hopefully this answer helped you!!
How many cans of paint are needed to cover an area of 2000?
Answers
The number of cans required to paint an area of 2000 square units is equal to 5 cans.
As given in the question,
Total area to be painted is equal to 2000 square units.
Area covered by one can of paint is equal to 400 square units
400 square units = 1 can of paint
⇒ 1 square units = ( 1 / 400 ) cans of paint
⇒ 2000 square units = ( 2000 / 400 ) cans of paint
⇒ 2000 square units = 5 cans of paint
Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.
The above question is incomplete, the complete question is:
How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?
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Rearrange the equation so q is the independent variable.
9q-43r-6
R =
Answers
Answer:q = 6+43r/9
Step-by-step explanation:
Assuming R=9q-43r-6 is what you meant
R+6 = 9q - 43r
R + 6 + 43r = 9q
q = 6+43r/9
What’s sampling method is being used A factor worker checks every 150 toy for defects
Answers
The sampling method being used in this scenario is systematic sampling.
Systematic sampling involves selecting every kth element from a population to create a sample. In this case, the factory worker is checking every 150th toy for defects. This suggests that the worker is following a systematic approach by examining a specific toy at regular intervals.
By systematically checking every 150th toy, the worker aims to assess the quality of the entire population of toys. This method provides a structured and organized approach to sampling, ensuring that each item has an equal chance of being included in the sample.
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can you answer this pls?
Answers
The value of the slopes must be:
m1 = -1/m2
Equivalently,
m1 • m2 = -1.
Please mark my answers as the Brainliest, if you find this helpful :)
Probability trees. Can someone tell me how im meant to set this one out, and I can work the rest out from there
Answers
Answer:
Step-by-step explanation:
Answer:
.8 = P (laura)
Step-by-step explanation:
Sally passes is .7
both passing is .56
P(sally and laura passing) = P(sally) * P(laura)
.56 = .7 * P(laura)
Divide each side by .7
.56/.7 = .7 * P(laura)/ .7
.8 = P (laura)
Plz help me...What is 46% of 180?
Answers
Answer:
82.8
Step-by-step explanation:
(!)46 % of 180 is. (!)
82.8
"FYI: This type of question could be answered from g0ogle".
(could you mark this question brainliest?)
The current world population is about 7.6 billion, with an
annual growth in population of 1.2%. At this rate, in how many
years will the world's population reach 10 billion?
Answers
The annual growth rate in population of 1.2% means that the population is increasing by 1.2% of the current population each year. To find the time it will take for the population to reach 10 billion, we need to use the following formula:P(t) = P0 × (1 + r)^twhere P0 is the initial population, r is the annual growth rate, t is the time (in years), and P(t) is the population after t years.
We can use this formula to solve the problem as follows: Let \(P0 = 7.6 billion, r = 0.012 (since 1.2% = 0.012)\), and P(t) = 10 billion. Plugging these values into the formula, we get: 10 billion = 7.6 billion × (1 + 0.012)^t Simplifying the right side of the equation, we get:10 billion = 7.6 billion × 1.012^tDividing both sides by 7.6 billion, we get:1.3158 = 1.012^tTaking the natural logarithm of both sides,
we get:ln\((1.3158) = ln(1.012^t)\) Using the property of logarithms that ln \((a^b) = b ln(a)\), we can simplify the right side of the equation as follows:ln(1.3158) = t ln(1.012)Dividing both sides by ln(1.012), we get:t = ln(1.3158) / ln(1.012)Using a calculator to evaluate the right side of the equation, we get:t ≈ 36.8Therefore, it will take about 36.8 years for the world's population to reach 10 billion at an annual growth rate of 1.2%.
In conclusion, It will take approximately 36.8 years for the world's population to reach 10 billion at an annual growth rate of 1.2%. The calculation was done using the formula P(t) = P0 × (1 + r)^t, where P0 is the initial population, r is the annual growth rate, t is the time (in years), and P(t) is the population after t years.
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Which one blue, light blue , yellow or red
Answers
Step-by-step explanation:
light blue.
our function needs to calculate r out of h.
P does not recognize h (hours after midnight) as parameter. P needs c as input.
T needs h as input and delivers c as output.
therefore (P ○ T)(h) = r is correct.
first the "inner" T function is calculated with h as parameter and then P is calculated using the result from T (c) as input and delivers r.
Here is a polygon. Decompose this polygon so that it’s area can be calculated. All measurements are in centimeters. Calculate its area. Organize your work so that it can be followed by others.
Answers
Answer:
88 cm^2
Step-by-step explanation:
Break up the figure as shown in the picture below.
There are two congruent trapezoids above and two congruent trapezoids below.
For each trapezoid, the are is
A = (1/2)(B + b)h
Top left and top right trapezoids:
Large base: 6; small base: 2; height: 2
A = (1/2)(6 + 2)(2) = 8
Bottom left and bottom right:
Large base: 9; small base: 3; height: 6
A = (1/2)(9 + 3)(6) = 36
total area = 8 + 8 + 36 + 36
total area = 88
I need help finding the area to the trapezoid for geometry class :)
Answers
Answer:
313.5 feet cubed
Step-by-step explanation:
A = a+b /2 (h)
14+24/2(16.5)
38/2 (16.5)
= 313.5
Shona bought 5 bags of cement and 4 bags of gravel. The total weight of her bags was 200 kilograms.
Write down an equation to illustrate this information.
Answers
Hope this helps
The equation illustrates the given information is 5x+4y=200
Cement= a bag x kg
Gravel =a bag of y kg
What is the equation?
An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
and the total is 200kg
Therefore we get the equation is
5x+4y=200
Therefore the equation illustrates the given information is 5x+4y=200.
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Kiley had a piece of bamboo skewer that measured 14Three-fifths inches long. She wanted to cut it into toothpicks that were each 3One-fifth inches long. How many toothpicks can she make? 4 toothpicks 5 toothpicks 46 toothpicks 47 toothpicks
Answers
Answer:
Answer is (4 )
9/16 (i turned 14 3/5 into decimal form, as well as 3 1/5 then i simply divided it and turned it back into a fraction!
Step-by-step explanation:
Answer:
its 4 ( I checked and everything
Step-by-step explanation:
It’s question 2
Help
Answers
Answer:
The answer to this one could be 8.2 for x
Step-by-step explanation:
Hope this Helped
137=5x+2
Subtract 2 from both sides
135=5x
135/5=27
. Elena and Marcus jog after school each day. One
day, Elena and Marcus jogged a total of 15 miles.
Elena jogged 1 mile more than Marcus. Use a graph
to find the number of miles each person jogged.
Answers
We conclude that Marcus jogged 7 miles while Elena jogged 8 miles.
This is the concept of algebra, let the number of miles jogged by Marcus be x, the number of miles jogged by Elena is (x+1) miles:
Total number of miles jogged by the two individuals will be:
x+(x+1)=15
2x+1=15
putting like terms together we get:
2x=15-1
2x=14
hence
x=14/2 =7miles
therefore we conclude that Marcus jogged 7 miles while Elena jogged 8 miles.
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
The product of 9 and the difference of a number and 2.
Answers
Answer:
9 · (x - 2)
Step-by-step explanation:
Since the problem tells us to let "a number" be the letter x, let's rewrite the sentence to include x instead of the term "a number". Doing so gives us the sentence "The product of 9 and the difference of x and 2."
Step 1: Multiplication
Now, let's work from left to right. The first word we see is "product", which refers to the operation of multiplication, as this term is used to describe the resultant quantity from multiplying 2 numbers. From the sentence, we see that the two terms we are multiplying are "9" and "the difference of x and 2". Note that we include the difference in one of our terms because of the structure of the sentence - we usually describe a product as being a product of [one term] and [another term] as it is here.
To denote multiplication, we can use the symbol "×", but to avoid confusion between this symbol and the letter x, let's use the symbol "·". Now, we have the expression 9 · (the difference of x and 2).
Step 2: Subtraction
We still aren't done, however, because we still have some words left to "translate" into algebra. The use of the word "difference" tells us that the operation to be used is subtraction, as this term is used to describe the resultant quantity from subtracting 2 numbers. Again, the sentence tells us that the terms we are subtracting are x and 2, but which order do they go in? (This is important to consider because unlike multiplication, subtraction is not a commutative property - in other words, a - b does not necessarily equal b - a, but a · b always equals b · a.)
To answer this question, we refer again to the sentence. When dealing with a non-commutative operation, we write out the terms in the order they appear in. Therefore, "the difference of x and 2" can be represented as x - 2 (note that we use the "-" symbol as we are subtracting quantities).
Step 3: Combine the 2 Operations
Putting all of this information together, we get the algebraic expression of 9 · (x - 2). Remember to put x - 2 in parentheses, otherwise it looks like we are multiplying 9 and x and then subtracting 2 from that quantity, which is not what our original sentence was.
EMERGENCY
Rectangular prism with base of 4 cm by 3 cm and a height of 5 cm. Square pyramid with a base of 4 cm by 3 cm and a height of 5 cm.
What is the volume of the prism?
What is the volume of the pyramid?
Answers
Answer: A = 15cm squared
Step-by-step explanation:
I think :)
Given that the base of the prism is 4 cm by 3 cm and the height is 5 cm, the volume can be calculated as:
The volume of the prism = (length x width x height)
By applying the given values:
Volume of prism = 4 cm x 3 cm x 5 cm
The volume of the prism = 60 cubic cm
That implies the volume of the rectangular prism is 60 cubic cm.
We know that the pyramid's base measures 4 by 3 cm and its height is 5 cm, the base's area may be calculated as follows:
Area of base = length x width
Area of base = 4 cm x 3 cm
Area of base = 12 square cm
The volume of the pyramid can now be calculated as:
Volume of pyramid = (area of base x height) / 3
Volume of pyramid = (12 square cm x 5 cm) / 3
The volume of the pyramid = 20 cubic cm
Therefore, the volume of the square pyramid is 20 cubic cm.
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WILL GIVE BRAINLIEST:
2). Mr. Joe ordered a total of 12 drinks from Peets. She ordered twice as many coffees (x) as chai tea drinks (y). How many of each drink did she order?
Answers
Answer:
She ordered 8 coffees and 4 chai tea drinks.
Step-by-step explanation:
AB has endpoints A(4, ‐3) and B(3, 7). Line d is the perpendicular bisector of AB .
Which of the following is NOT an equation of line d?
Answers
Answer:
B
Step-by-step explanation:
We know that AB has endpoints at A(4, -3) and B(3, 7).
To find Line D, which is the perpendicular bisector of AB, we first need to find the slope of AB and its midpoint.
So, let's find the slope of AB using the slope formula:
\(\displaystyle m=\frac{y_2 - y_1}{x_2 - x_1}\)
Let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the slope formula:
\(\displaystyle m=\frac{7-(-3)}{3-4}=\frac{10}{-1}=-10\)
So, the slope of AB is -10.
Remember that the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, the slope of our Line D is the negative reciprocal of -10. Which is -10 flipped and multiplied by a negative.
So, Line D has a slope of 1/10.
Now, since Line D is also the perpendicular bisector of AB, we need to find the midpoint of AB since Line D must pass through this point.
To find the midpoint, we can use the midpoint formula:
\(\displaystyle M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\)
We can again let (4, -3) be (x₁, y₁) and let (3, 7) be (x₂, y₂). Substitute them into the midpoint formula to obtain:
\(\displaystyle M=\left(\frac{4+3}{2},\frac{-3+7}{2}\right)\)
Evaluate. So, the midpoint is:
\(\displaystyle M=\left(\frac{7}{2},2\right)=(3.5,2)\)
Now, we can find the equation of our Line D. We know that its slope is 1/10, and that it must pass through (3.5, 2). So, we can use the point-slope form:
\(y-y_1=m(x-x_1)\)
Where m is the slope. Let's let (3.5, 2) be (x₁, y₁) and substitute 1/10 for m. This yields:
\(\displaystyle y-2=\frac{1}{10}(x-3.5)\)
This is the same as choice C. So, choice C is indeed an equation of Line D.
We can distribute the right to obtain:
\(\displaystyle y-2=\frac{1}{10}x-0.35\)
Add 2 to both sides to acquire:
\(\displaystyle y=\frac{1}{10}x+1.65\)
This is the same as choice D. So, choice D is indeed an equation of Line D.
Moreover, we can put this into standard form by multiply everything by 10, which gives:
\(10y=x+16.5\)
Subtracting x from both sides yields:
\(-x+10y=16.5\)
This is the same as A. So, choice A is also an equation of Line D.
There is no way to acquire choice B. So, B is not an equation of Line D.
Therefore, our answer is B.
And we're done!
Answer:
a, c and d are not equation lines of d
Step-by-step explanation:
your answer is b i wanna type the whole explanation like i did in my
note book but my hand hurts...hope this helped
Solve each system of linear equations by elimination.
X-6y=7
-x+6y= -7 -
Answers
Answer:
Infinitely many solutions.
Step-by-step explanation:
x-6y=7
-x+6y=-7
--------------
0=0
infinitely many solutions.