A power series representation for the function is:
x^8 tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^(6n + 11)/2n + 1)
In this question we need to find a power series representation for the function.
f(x) = x^8 tan^-1(x^3)
We know that the Maclaurin series:
1/(1 - x) = ∑[n = 0 to ∞] x^n
Replacing x with -x^2 we get,
1/(1 + x^2) = ∑[n = 0 to ∞] (-x^2)^n
= ∑[n = 0 to ∞] (-1)^n x^2n
Integrating above equation we get,
tan^-1(x) = ∑[n = 0 to ∞] (-1)^n (x^(2n + 1)/2n + 1) + c
For x = 0 we get c = 0
so, tan^-1(x) = ∑[n = 0 to ∞] (-1)^n (x^(2n + 1)/2n + 1)
Now we replace x by x^3, we get,
tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^3(2n + 1)/2n + 1)
Therefore, the required power series would be,
x^8 tan^-1(x^3) = ∑[n = 0 to ∞] (-1)^n (x^(6n + 11)/2n + 1)
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When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. How tall wa the buh after the two week
When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is [tex]\\26 \frac{2}{5}[/tex].
What is improper fractions?
An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.
12 times 120% + 12
12*120%+12
[tex]$$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$[/tex]
Follow the PEMDAS order of operations
Multiply and divide (left to right) [tex]$12 \times \frac{6}{5}: \frac{72}{5}$[/tex]
[tex]=\frac{72}{5}+12$$[/tex]
Add and subtract (left to right) [tex]$\frac{72}{5}+12: \frac{132}{5}$[/tex]
[tex]=\frac{132}{5}$$[/tex]
Convert improper fractions to mixed numbers: [tex]$\frac{132}{5}=26 \frac{2}{5}$[/tex]
[tex]=26 \frac{2}{5}$$[/tex]
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Please help read text on image.
Answer: -4 < n [tex]\leq[/tex] 5
Step-by-step explanation:
PLEASE HELP BRO I NEED IT !!!!
The value of x = 25
The measure of the angle ∠R = 101°
What is a Parallelogram?
A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the parallelogram be TPRS
Now , the measure of ∠T = ( 4x + 1 )°
The measure of ∠S = ( 3x + 4 )°
Now , from the properties of a parallelogram ,
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
So ,
The value of ∠T = ∠R
And , value of ∠T + ∠S = 180°
Substituting the values in the equation , we get
∠T + ∠S = 180°
( 4x + 1 ) + ( 3x + 4 ) = 180
On simplifying the equation , we get
7x + 5 = 180
Subtracting 5 on both sides of the equation , we get
7x = 175
Divide by 7 on both sides , we get
x = 25
So , the value of x = 25
Now , the measure of ∠T = ( 4x + 1 )° = ∠R
So , the measure of ∠R = ( 4 x 25 + 1 )°
The measure of ∠R = 101°
Hence , The value of x = 25
The measure of the angle ∠R = 101°
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a coin is tossed and a die is rolled. find the probability of getting a head and a number greater than 5
The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.
A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)
We have, Let us assume two independent events be ,
A : A coin is tossed and the head is thrown.
B : A die is rolled, and a number greater than 5 occurs.
Total possible outcomes when a coin tossed = 2 ={ H ,T }
Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .
We have to determine probability of getting a head and a number greater
than 5.
Probability of getting the head on toss a coin, P(A) = 1/2
Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6
So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)
=(1/2)× 1/6 = 1/12=0.0833
Hence, required probability is 0.0833.
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Solve each equation by completing the square
z-5=z^2-25
after completing the equation, the equation is __ and the solution is ____
WHOEVER ANSWERS CORRECTLY AND FIRST WILL BE MARKED AS BRAINLIEST
The equation becomes z + 5 = 1 and the value of the z in the given equation by completing the square is z = -4.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
As per the given equation,
z - 5 = z² - 25
z - 5 = z² - 5²
By property that A² - B² = (A + B)(A - B)
z - 5 = (z - 5)(z + 5)
z + 5 = 1
z = - 1 / 5 = - 4
Hence "By completing the square, the equation is changed to z + 5 = 1, and the value of z in the given equation is changed to z = -4".
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Answer:
The equation after completing the square is (z - 1/2)² = (9/2)²;The solution is z = {-4; 5}-----------------------------------------------------------
Given equation:
z - 5 = z² - 25Solve it as follows:
z - 5 = z² - 25 Givenz² - 25 - z + 5 = 0 Bring all terms to one sidez² - z - 20 = 0 Simplifyz² - 2*z*1/2 + (1/2)² = 20 + (1/2)² Complete the square on left(z - 1/2)² = 20 1/4 (z - 1/2)² = 81/4 Square on the right(z - 1/2)² = (9/2)² Square root both sidesz - 1/2 = 9/2 and z - 1/2 = - 9/2z = 1/2 + 9/2 and z = 1/2 - 9/2z = 10/2 and z = - 8/2z = 5 and z = - 4 AnswerRecall that two angle are complementary if the um of their meaure i 90 degree°. Find the meaure of two complementary angle if one angle i 20 degree° more than forty four time the other angle
The measure of one angle is 1.56° and another angle is 88.64°.
Complementary angles are two angles whose combined angle is 90 degrees.
Let's consider the smaller angle as A and the larger angle as B.
Given that the two angles are complementary, then their sum is A+B = 90°.
The angle B is 20° more than and 44 times angle A. Then B = 44A+20°. Substituting this equation in the A+B = 90° equation, we get,
A+44A+20° = 90°
45A = 90°-20°
A = 70°/45
A = 1.56°
Substitute A = 1.56°in B = 44A+20°, we get,
B = 44(1.56°)+20°
B = 88.64°
The answers are 1.56° and 88.64°. The sum of these two angles gives 90.2°. By rounding off, we will get 90°.
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Solve for m.
m/2 = m+5/4
Answer:
m = -5/2 or -2.5
Pls choose me as brainliest!
Which of the following represents 1 amu?AMass of a Câ12 atomBMass of a hydrogen atomC1/12th of the mass of Câ12 atomDMass of Oâ16 atom
option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.
First, let us study the definition of Atomic Mass,
Atomic mass -
The total weight of any matter perceived in an atom or any element.1 atomic mass is equal to [tex]1.660539040 * 10^{-24}[/tex] grams.The atomic mass that is derived is slightly lesser than that of the masses of neutrons, protons, and electrons.This slight difference in masses is termed as mass defect.The number of protons and neutrons decides the atomic mass of any particle.The standard unit to measure atomic mass is called Dalton.So we can also conclude that the 1 atomic mass unit is equal to 1/12 of the mass of the C-12 atom
Therefore, option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.
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2
x² + 14x − 24 = 4x
The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
x² + 14x − 24 = 4x
Simplify the equation, then we have
x² + 14x − 24 = 4x
x² + 10x − 24 = 0
Factorize the equation, then we have
x² + 10x − 24 = 0
x² + 12x − 2x − 24 = 0
x(x − 12) − 2(x − 12) = 0
(x − 2)(x − 12) = 0
x = 2, 12
The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.
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Suppose you walk at the rate of 210 ft/min. You need to walk 10,000 ft.
How many more minutes will it take you to finish if you have already walked 550 ft?
Answer:
Step-by-step explanation:
210x550=115500
115,500 divide 10,000=11.55?
Two people are at an elevator. At the same time one person starts to walk away from the elevator at a rate of 2 ft/sec and the other person starts going up in the elevator at a rate of 7 ft/sec. What rate is the distance between the two people changing 15 seconds later?.
The rate at which the distance between the two people is changing 15 seconds later is 7.28 ft/sec.
Here, we note the following
Let the person walking away from the elevator be X
Let the other person going up in the elevator be Y
Therefore after 15 seconds, their positions will be;
For X, 2 ft/sec × 15 s = 30 ft away from the elevator
For Y, 7 ft/sec × 15 s = 105 ft up in the elevator
At that instant, the distance between them is given as
d² = x² + y²
d=√ 30² +105² = 11925 ft²
d = √11925 ft² = 109.202 ft
The rate of change of the distance between the two people, X and Y is given as
[tex]\frac{dd^2}{dt} =\frac{dx^2}{dt} +\frac{dy^2}{dt} \\Therefore,2d\frac{dd}{ydt} =2x\frac{dx}{dt} +2y\frac{dy}{dt} \\[/tex]
(or)
[tex]d\frac{dd}{dt} =x\frac{dx}{dt} +y\frac{dy}{dt} \\[/tex]
Since dx/dt is given as 2ft/sec and dy/dt is 7ft/sec
Then [tex]d\frac{dd}{dt} =30*2+105*7=975\\\frac{dd}{dt} =\frac{795}{105*202} =7.28ft/sec[/tex]
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Tomorrow, Mrs. Wendel's class will be using toothpicks for a science project. Each student must use at least 6 toothpicks for the project.
Mrs. Wendel knows that there is already a bag of 50 toothpicks in the class storage room. She plans to buy x additional toothpicks this afternoon to make sure her class will have enough.
If her class has 28 students, which number sentence represents this situation?
for the polynomial below -3 is a zero g(x)= x^3+5x^2+56x+150 express g(x) as a product of linear factors
The product of linear factors of the given polynomial are;
(x + 3 )*(x² + 2x + 50 + (−100/(x + 3)))
How to find the linear factor of a polynomial?We are given the polynomial expression as;
g(x)= x³ + 5x² + 56x + 150
Now, we are told that -3 is a zero. Thus, if -3 is a zero that means x = -1
and x + 3 is a factor.
Using online polynomial division calculator, the the polynomial is divided by (x + 3) to get;
(x³ + 5x² + 56x + 150)/(x + 3) = x² + 2x + 50 + (−100/(x + 3))
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Arturo was comparing the price of apple juice at two stores. The equation y=0.29x represents what Arturo would pay in dollars and cents, y, for x bottles of apple juice at store A. Arturo can buy 13 bottles of apple juice at Store B for a total cost of $8.84. How much more is a bottle of apple juice at Store B than at Store A?
Answer:
$0.39
Step-by-step explanation:
First find the unit rate for store B ( $8.84/13)
At store B Artuto spends $0.68 for one bottle of apple juice
At store A they spent $0.29
0.68-0.29= 0.39
Find the measure of <1
A. 77 degree
B. 38 degree
C. 65 degree
D. 142 degree
Please help!!!!
(Picture provided)
Answer:
D. 142 degree
Step-by-step explanation:
A triangle has 180 degree
77 + 65 = 142 degree
180 - 142 = 38 degree
38 degrees is the missing angle of the triangle. This angle must add with angle 1 outside equal to 180
180 - 38 = 142 degree
So, the answer is D
the radius of a spherical ball is increasing at a rate of . at what rate is the surface area of the ball increasing when the radius is cm?
Although part of your question is missing, you might be referring to this full question: The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm? The surface area of a sphere with radius r is given by 4πr².
The rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.
Given A = 4πr²
So, we have:
dA/dt = d/dt (4πr²)
= 4π * d/dt * (r²)
= 4π * 2r * dr/dt
= 8πr * dr/dt
Now, we have that dr/dt = 2 cm/min. So, when the radius of the ball is 8 cm, we have that:
dA/dt = 8πr * dr/dt
= 8π * 8 * 2
= 128π
Since we are measuring area, our unit is cm²/min, not cm/min.
Thus, the rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.
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Nataha wa thinking of a number. Nataha add 2. 5 to the number, then double the reult to get an anwer of 61. Form an equation with x from the information
The equation with x about the number thought by Natasha is (x + 2.5) × 2 = 61
Let the number thought by Natasha be x. To formulate the equation, we will perform the same operations as done by Natasha. Forming the equation now -
(x + 2.5) × 2 = 61
Performing multiplication on Left Hand Side of the equation
2x + 5 = 61
Rewriting the equation
2x = 61 - 5
Performing subtraction on Right Hand Side of the equation
2x = 56
Rewriting the equation
x = 56/2
Performing division on Right Hand Side of the equation
x = 28
Thus, the equation is (x + 2.5) × 2 = 61 and the number thought by Natasha is 28.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(0,7) and (4,9)
Craig collect coin, He collected a total of 175 coin. If 72% of the coin he collected were foreign, how many other coin did he collect?
The number of coins which Craig collected as calculated from the given data is 49.
Given ,
percentage of foreign coin = 72%
Therefore the percentage of normal coins will be 28%.
Hence , the number of normal coins which he collected can be found out as ,
28% of 175
= 28% × 175
= 28/100 × 175
= 0.28 × 175
= 49
When we divide a given number by 100 as a fraction , the result we get is known as percentage .
It is represented by the percentage sign which is "%".
The percentage is denoted by the letters "pct" or "pc," respectively. In other words, the percent or % is calculated at a value of around 100 and represents the proportion of one quantity made up of another.
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What is the area of the rectangle shown on the coordinate plane?
Enter your answer in the box. Do not round at any step.
The area of the rectangle shown on the coordinate plane is 12 square units.
What is the area of the rectangle shown on the coordinate plane?
To calculate the area of a rectangle, multiply the length by the width of the rectangle.
To find the area of the rectangle shown on the coordinate plane, first, we need to calculate the distance between the points that conforms two of the sides of the rectangle (base and height).
We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:
1 - (-4, 1)
2 - (-1,-2)
3 - (-3,-4)
4 - (-6, -1)
Then, calculating the length of the sides,
Consider rectangle ABCD with vertices A(-4, 1), B(-1, -2), C(-3, -4) and D(-6, -1). The area of the rectangle is
A = length * Width
Find the length and the width:
AB = √(-1 - (-4))² + (-2 - 1)² = √9 + 9 = √18
BC = √(-3 - (-1))² + (-4 - (-2))² = √4 + 4 = √8
Then the area of the rectangle ABCD is
A = √18 * √8
A = 12 unit²
Hence, the area of the rectangle shown on the coordinate plane is 12 square units.
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question 7 a data analyst adds labels to their line graph to make it easier to read even though they already have a legend on their visualizations. how does labeling the data make it more accessible?
Labels on a line graph can make the visualization more accessible in a few ways:
Labels can provide additional context for the data. For example, if the y-axis of the line graph represents the temperature in degrees Celsius, labeling each line with the location or type of temperature measurement can help the viewer better understand the data.Labels can help the viewer more quickly identify the data they are interested in. If the line graph has many lines and a legend, it can be time-consuming to locate the specific line of interest. By labeling each line directly on the graph, the viewer can more easily find the data they are looking for.Labels can improve the clarity and readability of the graph. If the lines on the graph are close together or overlap, labels can help the viewer distinguish between the different lines.Overall, labels can help make a line graph more accessible by providing additional context, improving readability, and helping the viewer quickly find the data they are interested in.
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Write a situation for 4.63 x 9 and a picture that goes with it
A problem that could be solved by multiplying 4.63 x 9 is "the product of 4.63 and 9"
How to determine the productFrom the question, we have the following parameters that can be used in our computation:
4.63 x 9
In the above expression, we can see that
4.63 and 9 are multiplied
This means that the problem is a product expression
And a problem that can represent 4.63 x 9 is "the product of 4.63 and 9"
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Which division problem can be described using this model?
Answer:
12/3=4
Step-by-step explanation:
You have 12 blocks in total, and 3 sections each. It is asking you how many blocks per section.
12 blocks in total/ 3 sections each = 4 blocks per section
The cost a sofa set is $9352. how much will 125 such sofa sets cost?
Find the measures of two complementary angles if the measure of the larger angle is 2 less than 3 times the measure of the smaller angle.
Answer:
Let x be the larger angle and y be the smaller angle
Larger angle is 2 less than 3 times the smaller angle that is x = 3y - 2
As the angles are complementary, their sum equals 90°
or, x + y = 90°
or, 3y - 2 + y = 90°
or, 4y = 92°
or, y = 23°
So, x = 3 * 23 - 2 = 67°
Larger angle = x = 67°
Smaller angle = y = 23°
A circle with a radius of 1 cm sits inside a 3 cm x 4 cm rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answer:
below
Step-by-step explanation:
Area of rectangle ( 3 x 4 ) minus the area of the circle (pi * 1^2) =
= shaded area = 8.86 cm^2
10.1 approximately how many more calories are there in 2 slices of bacon than there are in 3 slices of trasted turkey? why is there a difference?
Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.
What does equation mean?a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.
Here,
One piece of bacon has 42 calories in it.
There are 60 calories in 1 slice of turkey.
2 slices of bacon are 2 calories each (42)
So 84 calories in 2 slice of bacon
3 slices of roasted turkey have 3 calories each slice (60)
Three slices of roasted turkey have 180 calories each.
180-84 is the difference in the amount of calories.
96 calories are added due to the calorie difference.
Two slices of bacon had 96 less calories than three slices of roasted turkey.
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I need help with this problem
Answer:
x = 6
Step-by-step explanation:
We have a 30°-60°-90° right triangle here, so the length of the hypotenuse (12) is twice the length of the shorter leg (6). So x = 6.
please helppp
my brain is not working
Answer:
Below
Step-by-step explanation:
27 = 3^3 and 9 = 3^2
3^3 * (3^2)^3x
3^3 * 3^6x
3^(3+6x) so k = 3+6x
The speed of sound, S, in meters per second, is a linear function of the temperature of the air through which
the sound travels. Air temperature, T, is measured in degrees Celsius and S=0.6T+331.4. Which of the
following is the best interpretation of the number 331.4 in the context?
a) The speed of sound in meters
per second at 0.6 degrees Celsius
c) The speed of sound in meters
per second at 0 degrees Celsius
b) The increase in speed of sound at 331.4 degrees
per degree of temperature
d) none of the above
Answer:
C
Step-by-step explanation:
S = .6T + 331.4
When S = 331.4:
331.4 = .6T + 331.4 <=====you should be able to see this is true when T= 0