The Maclaurin series for f(x) is [tex]f(x) = 3cos(x^2) = 3 - (3x^4)/2! + (3x^8)/4! - (3x^{12})/6! + ...[/tex]
What is the Maclaurin series expansion for [tex]f(x) = 3cos(x^2)[/tex]?A Maclaurin series is a special case of a Taylor series expansion, which is a representation of a function as an infinite sum of terms. The Maclaurin series specifically is centered around the point x = 0.
To obtain the Maclaurin series for the given function [tex]f(x) = 3cos(x^2)[/tex], we can start by finding the Maclaurin series for the cosine function and then substitute [tex]x^2[/tex] for x in the resulting series.
The Maclaurin series for cos(x) is given by:
[tex]cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...[/tex]
Now, let's substitute x^2 for x in the above series:
[tex]cos(x^2) = 1 - ((x^2)^2)/2! + ((x^2)^4)/4! - ((x^2)^6)/6! + ...[/tex]
Simplifying this expression, we have:
[tex]cos(x^2) = 1 - (x^4)/2! + (x^8)/4! - (x^{12})/6! + ...[/tex]
Finally, multiplying the entire series by 3 to account for the coefficient of 3 in the original function, we get:
[tex]f(x) = 3cos(x^2) = 3 - (3x^4)/2! + (3x^8)/4! - (3x^{12])/6! + ...[/tex]
This is the Maclaurin series for the function f[tex](x) = 3cos(x^2).[/tex]
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The number of fish in a lake decreased by 53% between last year and this year last year there where 245 fish in the lake what is the population this year?
The number of fish remaining in the lake this year will be 115.
What does a population mean?A population mean any group that shares at least one characteristic. Populations are more than just individuals. People, animals, businesses, buildings, motor vehicles, farms, objects, or events are examples of populations.
Data
The decrement in number of fish = 53%.
Number of fish previous year = 245
Remaining number of fish will be 47%.
The population of fish this year will be:
= 47% * 245 fish
= 115 fish.
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A jacket costs $75, and it is on sale for 60% off. What is the discounted price of the jacket?
Explain what you did.
Answer:$30
Step-by-step explanation:
$75 jacket is 60% off
Step 1: Plug in numbers
Use is/of=%/100 method
is/75=60/100=45
Step 2: Find the Price of Discounted Jacket
75-45=$30
Answer:
The discounted price of the jacket is $30-----------------------------------
Initial cost is $75 and the discount is 60%.
Subtract 60% to find the discounted amount:
75 - 60% = 75 - 75*60/100 = 75 - 45 = 30write an expression for “the quoitient of 9 and c
The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The quotient of the number 9 and the letter 'c' is written as,
⇒ 9 / c
The expression that the quotient of the number 9 and the letter 'c' will be 9 / c.
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BRAINLIEST Please and Thank you
Lucas has 36 pages of a book left to read. If he reads 6 pages a day, how many days will it take Lucas to finish the book?
Answer:
6
Step-by-step explanation:
36/6
equals 6
Answer:
6 days.
Step-by-step explanation:
36 total pages
6 page a day
Then:
36/6 = 6
You earn $28.50 per hour. Worked 34 hours last week. What was your gross pay?
Your answer
Answer:$969
Step-by-step explanation:
dose anyone know how to do this attached below
The area of the shaded section is approximately equal to 219.711 square meters.
How to determine the area of the shaded section
In this problem we find the case of a shaded section, whose area must be determined. This can be realized by finding the area of rhombus OPQR and subtract the circular section OPR from it. All missing lengths of the triangles from the rhombus can be found by trigonometric functions.
The formula to determine the area of the shaded area is:
A = 2 · 0.5 · OR · RQ - (140 /360) · π · OR²
RQ = OR · tan 70°
If we know that OR = 12 m, then the area of the shaded section is:
RQ = 12 · tan 70°
RQ = 32.970
A = 2 · 0.5 · OR · RQ - (140 /360) · π · OR²
A = OR · RQ - (7π / 18) · OR²
A = 12 · 32.970 - (7π / 18) · 12²
A ≈ 219.711 m²
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find the probablility that the sum of two randomly chosen numbers from the set{0,1,2,3,4,5,6,7,8,9} is no grreater than 10
Answer:
1 /5
Step-by-step explanation:
formulae -
possible outcomes / total chances
2/10
1/5
Sarah needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4. 25 hours and charged her $54 for parts. The total was $585. 25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The labour cost per hour charged by the technician for the laptop is $124.91
Here we see that it cost Sarah $54 dollars for the parts. Now, the technician charged her $585.25.
Since nothing else is mentioned, we will assume that the technician charged Sarah only for the parts and their labour hours.
Hence after deducting the charge for the computer parts, we can get the cost for the labour. We know the labour hours to be 4.25 hours. We don't know the labour cost, which is to be found.
Let the cost of labour per hour be $x
Hence the labour cost will be $4.25x
Adding the cost of parts will give us the charged amount. Hence we get
4.25x + 54 = 585
or, 4.25x = 531
or, x = 531/4.25
or, x = 124.941
Hence the cost per hour is $124.941
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What is the image point of ( 6 , 5 ) after the transformation D 5 ∘ 0 ∘T 0,0 ?
The image point of P(x,y) = ( 6 , 5 ) after applying a horizontal reflection is P'(x,y) = (1, 5).
How to determine the image after transformation?In geometry, a rigid transformation is a transformation applied onto a geometric object such that Euclidean distance in every point of it is conserved. Translations are examples of rigid transformations and are defined by this formula:
P'(x,y) = P(x,y) + T(x,y) (1)
Where:
P(x,y) - Original point
T(x,y) - Translation vector
P'(x,y) - Image point
If we know that P(x,y) = (6, 5) and T(x,y) = (5, 0), then the image point is:
P'(x,y) = (6, 5) + (5, 0)
P'(x,y) = (1, -6)
The image point of P(x,y) = (6, 5) after applying a horizontal reflection is P'(x,y) = (1, 5).
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Correct form of the question
What is the image point of (x, y) = (6, 5) after the transformation of translating horizontally the point 5 units to the y-axis?
What is the secant segment theorem?
The secant segment theorem states that If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.
A secant is a line on the circle that connects exactly two distinct points on the curve. Secant is not a chord but a chord is part of a secant. Two different secants can intersect each other internally or externally.
Further, the secant segment theorem defines two more theorems or properties and they are:-
The angle formed by two internally intersecting secants in a circle is half the sum of the intercepted arcs.The angle formed by two externally intersecting secants in a circle is half the difference between the intercepted arcs.Arcs are line segment that is part of the circumference of a circle. It is like a smooth curve that joins two points. If an arc is of exactly the half-length of circumference then it is called a semicircular arc.
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Ryan deliver flower to two cotumer. He drive 12 minute at an average peed of 40 mile per hour to reach the firt cotumer. He drive for 15 minute at an average peed of 50 mile per hour to reach hi econd cutomer. During the 27 of driving time how many mile doe Ryan drive?
The total distance Ryan drives during the 27 minutes of driving time is 20.5 miles.
Ryan delivers flowers to two customers and drives 12 minutes at an average speed of 40 miles per hour to reach the first customer and 15 minutes at an average speed of 50 miles per hour to reach the second customer.
To find the total distance that Ryan drives during the 27 minutes of driving time, we can use the formula: distance = speed x time
We know that Ryan drives 12 minutes at 40 miles per hour and 15 minutes at 50 miles per hour. So we can use the formula to find the distance for each part of the trip and then add them together:
distance = 40 miles/hour x (12 minutes / 60 minutes/hour) = 8 miles
distance = 50 miles/hour x (15 minutes / 60 minutes/hour) = 12.5 miles
The total distance Ryan drives during the 27 minutes of driving time is 8 miles + 12.5 miles = 20.5 miles
Therefore, The total distance Ryan drives during the 27 minutes of driving time is 20.5 miles.
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what is 7/10+1/2+38 and type the anserw for me betterly
Answer: 39 1/5
Step-by-step explanation:
7/10 + 1/2 + 38
= 7/10 + 5/10 + 38
= 12/10 + 38
= 38 12/10
= 39 2/10
= 39 1/5
If the 38 was supposed to be 3/8, heres the answer :
7/10 + 1/2 + 3/8
= 28/40 + 20/40 + 15/40
= 63/40
= 1 23/40
I'm not sure how to solve it
Answer: x = 3; y = -2
Step-by-step explanation:
Simultaneous Equations:
3^(2x) x 3^(3y) = 3^0
2x + 3y = 0
2^(2x) x 2^(-0.5y) = 2^7
2x - 0.5y = 7
2x = -3y
-3y - 0.5 y = 7
y = -2
x = 3
Answer:
x=3 y=-2
Step-by-step explanation:
its at the bottom of the page ♂️♂️
What is the formula for a 45 degree triangle?
Using the formula of Pythagorean Theorem we can find a 45 degree triangle.
The degrees of the triangle's three inner angles give rise to its name, 45, 45, and 90. The triangle formed by the angles 45, 45, and 90 is said to be isosceles since two of the angles are less than the third.
Due to the fact that this triangle has one angle that is precisely 90 degrees, it is also regarded as a right triangle.
The following guidelines apply to the 45-45-90 triangle's characteristics:
1. There must always be a right angle in one angle.
2. The second pair of angles must always be 45-degree angles.
3. A triangle has two equal-length sides, but the third side is always longer.
Using the Pythagorean Theorem - Since a 45-45-90 triangle has a right angle, the length of its sides may be calculated using the Pythagorean Theorem.
Recall the formula for the Pythagorean Theorem:
a^2 + b^2 = c^2.
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What is y 3x 10 in function notation?
The equation y = 3x + 10 can be written in function notation as f(x) = 3x + 10.
In this notation, x is the input variable, and f(x) is the output or dependent variable.
Function notation is used to express the relationship between two variables, where one variable is a function of the other. In this case, the equation y = 3x + 10 tells us that y is a function of x, with a slope of 3 and a y-intercept of 10.
So, in function notation, this equation can be written as:
f(x)=3x+10
In conclusion, the equation y = 3x + 10 can be written in function notation as f(x) = 3x + 10. This notation expresses the relationship between the two variables x and y, where y is a function of x, represented by f(x) with a slope of 3 and a y-intercept of 10.
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What is y = 3x + 10 in function notation?
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What are the two types of inequality?
There are many different types of inequality, but generally, they can be grouped into two main categories economic inequality and social inequality.
Economic inequality: This refers to the unequal distribution of wealth, income, and resources among individuals or groups within a society. Economic inequality can manifest in various forms, such as income inequality, wealth inequality, and poverty.
Social inequality: This refers to the unequal distribution of social status, power, and privilege among individuals or groups within a society. Social inequality can manifest in various forms, such as discrimination, prejudice, and bias, which can limit opportunities and access to resources for certain groups.
It's important to note that these two types of inequality are often interconnected and can have a significant impact on individuals and groups, leading to reduced opportunities, access to resources, and lower quality of life.
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Marty is making a layaway purchase of a $2,050 sofa at Frank's Furniture Store. He will be paying $173.19 every 2 weeks for 32 weeks on a layaway plan. What is
the layaway fee for this purchase?
$721.07
$721.06
$721.04
$721.05
Answer:
Step-by-step explanation:
The layaway fee for this purchase should be considered as the $60 when the purchase should be done.
Marty is making a layaway purchase of a $1,500 couch at Frank’s Furniture Store. He will be paying $156 every 2 weeks for 20 weeks
So, it can be like
= $1,560 - $1500
= $60
The layaway fee for this purchase should be considered as the $60 when the purchase should be done.
What are the 5 steps in solving rational inequality?
The following are the 5 steps in solving a rational inequality: simplifying the inequality, factoring the numerator and denominator of the inequality, set the numerator and denominator equal to zero.
Solving a rational inequality involves isolating the variable and determining the range of values that make the inequality true.
Simplify the inequality by clearing any fractions: This can be done by multiplying both sides of the inequality by the least common multiple (LCM) of the denominators of the fractions.
Factor the numerator and denominator of the inequality: This can be done to cancel out any common factors between the numerator and denominator.
Set the numerator and denominator equal to zero and solve for the zeros: This can be done to find the values of the variable that make the numerator and denominator equal to zero.
Test the zeros and any critical values: This can be done by substituting the zeros and critical values back into the inequality and determining if they make the inequality true or false.
Plot the solution on the number line: This can be done by plotting the zeros and critical values on a number line and shading the region that makes the inequality true.
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HELP ME PLEASE!!!!!! Q and R are independent events. if P(Q)=1/8 and P(R)=2/5 find P(Q and R). 19/40,21/40,1/20
Answer:
Step-by-step explanation:do 1/8 *2/5*=
Can you PLSS help me answer these question?
AND PLS GIVE A EASY + DETAILED STEP BY STEP ON HOW U GOT THE ANSWER BC IM SLOW LOL
1. 3x - 2y = 11
x + 2y=9
2. 3x + y= 9
2x+ y = 5
3. -x - 2y=4
3x + 2y=4
4. x + 3y= (-2)
3x + 4y= (-1)
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
[tex]\displaystyle \left \{ {{3x-2y=11} \atop {x+2y=9}} \right.\\\\(3x-2y)+(x+2y)=11+9\\3x+x-2y+2y=20\\4x=20\\x=5\\\\x+2y=9\\5+2y=9\\2y=4\\y=2\\\\(5,2)[/tex]
Problem 2
[tex]\displaystyle \left \{ {{3x+y=9} \atop {2x+y=5}} \right.\\\\(3x+y)-(2x+y)=9-5\\3x-2x+y-y=4\\x=4\\\\2x+y=5\\2(4)+y=5\\8+y=5\\y=-3\\\\(4,-3)[/tex]
Problem 3
[tex]\displaystyle \left \{ {{-x-2y=4} \atop {3x+2y=4}} \right.\\\\(-x-2y)+(3x+2y)=4+4\\3x-x-2y+2y=8\\2x=8\\x=4\\\\-x-2y=4\\-4-2y=4\\-2y=8\\y=-4\\\\(4,-4)[/tex]
Problem 4
[tex]\displaystyle \left \{ {{x+3y=-2} \atop {3x+4y=-1}} \right.\\ \\\\\left \{ {{3x+9y=-6} \atop {3x+4y=-1}} \right.\\\\(3x+9y)-(3x+4y)=-6-(-1)\\3x-3x+9y-4y=-6+1\\5y=-5\\y=-1\\\\x+3y=-2\\x+3(-1)=-2\\x-3=-2\\x=1\\\\(1,-1)[/tex]
Basically, the goal is to eliminate one variable from a system of equations to solve for the other variable. In the case of problem 4, we had to multiply an equation by a constant in order to eliminate that variable.
How do you determine if three points are in a straight line in 3D?
To determine if three points are in a straight line in 3D, you can calculate the vector between the first two points and then check if the third point is in the same direction as the vector.
What is straight line?Straight line is a line that extends infinitely in two opposite directions and has no curves or bends. It is the shortest distance between two points and is the basic form of geometry. A straight line is composed of two end points and all the points in between that make up the line. Straight lines are used to create shapes and constructions in mathematics, science and engineering.
If the dot product of the vector and the point is 0, then the three points are in a straight line. Alternatively, you can calculate the area of the triangle formed by the three points and if it is 0, then the points are in a straight line. Another option is to calculate the determinant of the matrix formed by the three points and if it is 0, then the points are in a straight line. Finally, you can calculate the angle between the two vectors formed by the three points and if it is 0, then the points are in a straight line.
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hi i dont know can u may answer???????
Answer:
B) 2 5/8 - 1 4/8
Step-by-step explanation:
I'm bad at explaining but I hope this helps!! ₍^ >ヮ<^₎
The following bar graph summarizes the weather conditions in Crayonton for each day this month so far.
The reasonable estimate of the probability that it is sunny tomorrow is 25%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Probability of an event is calculated by dividing the number of desirable outcomes by the total number of events possible.
From the graph, we have,
Number of days weather is sunny = 3
Total number of days = Days weather is sunny + Days weather is cloudy + Days weather is rainy + Days weather is snowy
Total number of days = 3 + 5 + 2 + 2 = 12
Probability that weather is sunny = 3 / 12 = 1/4 = 0.25 = 25%
Hence there is a 25% probability that weather is sunny.
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The complete question is as follows :
The following bar graph summarizes the weather conditions in Crayonton for each day this month so far. Based on this data, what is a reasonable estimate of the probability that it is sunny tomorrow? Choose the best answer.
write the slope intercept form of the equation of a line with a slope of -5/8 that passes through the point (-14, 6)
Answer:
Step-by-step explanation:
Slope intercept for y=mx+b
point it passes (-14, 6) wherein b (0, b) is b=6
slope m = -5/8
substitute: y = mx+b
y= (-5/8)x+6
can you use the angel bisector theorem to solve for m∠TVW?
So, on solving the provided question we can say that in this quadrilateral we know that sum of all angles is 360, so other will be 90 each too.
what is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
here in this quadrilateral
we know that sum of all angles is 360
two of the are 90 each
so other will be 90 each too.
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Plot a point on the coordinate plane to represent each of the ratio values in the table.
The points on the coordinate plane which represent the ratio values given in the table are given attached, where Distance is on the Y-Axis and Time is on the X-Axis.
Ratio data is a type of numerical (quantitative) data. It computes the distance between neighboring numbers on a continuous scale.
While it shares these characteristics with interval data (another form of quantitative data), ratio data is distinguished by the presence of a 'real zero.' In other words, a ratio scale measure of zero is absolute: ratio data can never be negative.
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What is equivalent to 3/4 equal 6/?
The equivalent to 3/4 equal 6/ is 8
What is equivalent fraction?
Equivalent fractions are the fractions that have different numerators and denominators but are equal to the same value. For example, 2/4 and 3/6 are equivalent
from the question,
3/4 equal 6/?
Let x represent the unknown value
= 3/4=6/x
We can simplify this by cross multiplying
3x=24
Divide both sides of the equation by 3
3x/3 = 24/3
x=8
Hence the equivalent to 3/4 equal 6/? is 8
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A traveler is walking on a moving walkway in an airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 1 ft/s against the walkway and 5 ft/s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?
Answer:
this is it
Step-by-step explanation:
Can someone please help me with problem 6 of this assignment?I included the measurements of the triangle so that you are able to solve it accurately.
Geometry Topic: 6.1 - 6.4 Constructing Parts and Centers
Problem 6 Directions: Remember! Triangle centers may be outside the triangle. Locate the orthocenter of each triangle by finding the intersection of the altitudes.
Answer:
see drawing
Step-by-step explanation: