Let
[tex]\displaystyle f(x) = \sum_{n=1}^\infty (-1)^{n-1} \frac{x^{2n-1}}{(2n-1)! (2n+1)}[/tex]
The exponent is indeed [tex]2n-1[/tex] - not a typo!
Take the antiderivative of [tex]f[/tex], denoted by [tex]F[/tex]. This recovers a factor of [tex]2n[/tex] in the denominator, which lets us condense it to a single factorial.
[tex]\displaystyle F(x) = \int f(x) \, dx = C + \sum_{n=1}^\infty (-1)^{n-1} \frac{x^{2n}}{(2n+1)!}[/tex]
Recall the series expansion of sine,
[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{(2n+1)!}[/tex]
Then with a little algebraic manipulation, we get
[tex]\displaystyle F(x) = \int f(x) \, dx = C + 1 - \frac{\sin(x)}x[/tex]
Differentiate to recover [tex]f[/tex].
[tex]f(x) = \dfrac{\sin(x) - x\cos(x)}{x^2}[/tex]
Finally, [tex]f(\pi) = \frac1\pi[/tex], so our sum is
[tex]\displaystyle \pi^2 f(\pi) = \sum_{n=1}^\infty (-1)^{n-1} \frac{\pi^{2n+1}}{(2n-1)! (2n+1)} = \boxed{\pi}[/tex]
I need to solve this problem using the he quadratic formula
Answer:
the quadratic formula is
-b + {the square root of} b^2 - 4ac / 2a
-
or just
(-b±√(b²-4ac))/(2a)
Step-by-step explanation:
yh
Water comes out of a pipe at a rate of 16 gallons per minute.
How many gallons have come out after 4 minutes?
Answer:64
Step-by-step explanation:16 × 4
what percent of 55 is 11 ?
Answer:
20% try this I think this is the answer
D=33+31g. Determine the distance the car can travel using 4 gallons
Answer:
The distance d (in miles) you travel in a car is given by d=55t where t is the time (in hours)
The distance d (in miles) you travel in a car is given by d=20g where g is the number of gallons of gasoline the car uses.
1. Write an equation that relates g & t.
2. Solving for g.
=>
Hence,
3. You travel for six hours. How many gallons of gasoline does the car use
We will use this equation to solve the question.
Putting t = 6
g = 16.5 gallons
4. How far do you travel?
We can use equation here
miles
Step-by-step explanation:
this is what you wanted right?
In ΔABC, what is the value of cos B?
In right-angled triangle (ΔABC), the value of cos(B) is equal to 12/13.
What is a right angle?A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.
How to calculate the magnitude of cos θ?In order to determine the magnitude of cos θ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.
cos(θ) = Adj/Hyp
Where:
Adj represents the adjacent side of a right-angled triangle.Hyp represents the hypotenuse of a right-angled triangle.θ represents the angle.Substituting the parameters into the formula, we have;
cos(B) = 12/13
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The distance in feet that a ball rolls down an incline is modeled by s(t) = −2t^2 − 2 , where t is seconds after the ball begins rolling. Find its instantaneous velocity at t = 4 seconds.
Answer:
5
Step-by-step explanation:
because im a genious.
2x+5-19 division property of equality
Answer:
Step-by-step explanation:
it is the steps to get to that certain step
some of the steps are out of order
I'm going to assign letters
the order is
A: 2x+5=19
B: 2x+5-5=19-5
C: 2x=14
D: 2x/2=14/2
E: x=7
A: given
B: we subtracted 5 from both sides so subtraction property of equality
C: subtract
D: divison property of equality (we divide both side by 2)
E: divide
add to lowest terms
6 4/5 + 3 7/10
answer:
[tex]10 \frac{1}{2} [/tex]
Y over 5 + 6 = 21, what is y?
Answer:
y=231
Step-by-step explanation:
to solve for y simplify both sides of the equation by isolating the variable
When traveling to Great Britain, Bethany exchanged $635 US dollars into £580 British pounds. How many pounds did she receive for each US dollar?
After the exchange from the U.S dollar to British pounds, Bethany received £0.91 for each U.S. dollar.
What is an exchange rate?An exchange rate is a rate or a price of one country's currency in terms of another.
The exchange rate describes how much each currency can be obtained when converting one currency to another.
In this instance, the exchange rate between the U.S. dollar and the British pound is $1 = £0.91.
Data and Calculations:Total US dollars with Bethany = $635
The total British pounds received by Bethany after the exchange = £580
Exchange rate per U.S. dollar = £0.91 (£580/$635)
Exchange rate per British pound = $1.095 ($635/£580)
Thus, Bethany received £0.91 for each U.S. dollar.
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Special Angle Pairs
Find m<1
Please help !
Special Angle Pairs, m<1, then the expression is,
(4x + 16)° = (2x + 34)° = 52° where, x = 9°
⇒ As shown in Graph,
⇒ (4x + 16)° is congruent to (2x + 34)°
⇒ Because they are vertical angles.
The angles opposite each other when two lines cross. They are always equal. In this example a° and b° are vertical angles. "Vertical" refers to the vertex (where they cross), NOT up/down.
These are vertical angles.
So,
We can write,
(4x + 16)° = (2x + 34)°
Calculate the equation,
(4x - 2x)° = (34 - 16)°
We can use sum or difference,
(2x)° = (18)°
We can divide the values,
(x)° = (18/2)°
x° = 9°
Hence,
x° = 9°
We can substitute x = 9° value in (4x + 16)° and (2x + 34)° expression,
So,
We can use,
= (4x + 16)°
= (4*9 + 16)°
= (36 + 16)°
= 52°
Therefore,
(4x + 16)° = 52°
We can use,
= (2x + 34)°
= (2*9 + 34)°
= (18 + 34)°
= 52°
Therefore,
(2x + 34)° = 52°
Hence,
Special Angle Pairs, m<1, then the expression is,
(4x + 16)° = (2x + 34)° = 52° where, x = 9°
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What should be added to 52 to get -79?
Answer:
-131
Step-by-step explanation:
52+-131=-79
HELP QUICK!
Which rectangle is not an enlargement of rectangle A?
A
B
C
D
Answer:
The answer is D.
Find the scale of each dimension:
B: 6/3 = 2 and 10/5 = 2, both dimensions have the same scale factor of 2.
C: 15/3 = 5 and 25/5 = 5, both dimensions have the same scale factor of 5.
D: 60/3 = 20 and 90/5 = 18, each dimension has a different scale factor so is not an enlargement.
hope it helped:)!
Answer: answer a is wrong answer b is right answer c is wrong answer d is right
Step-by-step explanation:
d and b are right why? bc b saids this; 6 ft for b; 10 ft d; 60 ft and 90 ft
Find the ratio created when BA is partitioned by C.
Write your answer as a ratio with a colon and no spaces. Example 10:3
The ratio of the point C on the line segment is 2 : 3
How to determine the ratio of the point C on the line segment?The line segment that completes the question is added as an attachment
On the attached line segment, we have the following points assuming that the point A is at A = 0
So, we have
A = 0
C = 2
B = 5
The above means that
AB : CB = C - A : B - C
So, we have
AB : CB = 2 - 0 : 5 - 2
Evaluate the difference
AB : CB = 2 : 3
Hence, the ratio of the point C on the line segment is 2 : 3
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Please help !! Maurice walks 262 miles due south, then 168 miles due west and finally 422 miles due north. How
far is Maurice from his starting point?
miles
Maurice is a distance of 232 miles away from his starting point.
What is the final distance of Maurice from his starting point by using vectors and Pythagorean theorem?
Let suppose the existence of a coordinate system whose orthogonal axes are represented by north and east directions, which means that both north and east directions have positive signs. Then, the vector position of Maurice relative to his starting point is:
r = ∑ Δx i + ∑ Δy j
Where:
Δx - Net change in the east direction.Δy - Net change in the north direction.Then, the vector position of Maurice relative to his starting point is:
r = (- 168) i + (- 262 + 422) j
r = - 168 i + 160 j
And the distance is found by using the Pythagorean theorem:
r = √[(Δx)² + (Δy)²]
r = √[(- 168)² + 160²]
r = 232
Maurice is a distance of 232 miles away from his starting point.
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According to the following table, what is the federal income tax due for Mr. and Mrs. Jones filing their federal income tax return jointly who make a combined $92,400 in taxable income?
Based on the fact that Mr. and Mrs. Jones are filling their federal tax return jointly, their federal income tax due is $11,737
How to find the federal income tax?There was no table included so I will use the federal income tax rates for those filing in April 2022.
For a married couple filing jointly like Mr. and Mrs. Jones with a combined $92,400 taxable income, the federal income tax due is:
= 9,328 + 22% of income over $81,050
= 9,328 + (22% x (92,000 - 81,050))
= 9,328 + (22% x 10,950))
= 9,328 + 2,409
= $11,737
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Simplify 15^5/ -5^-6
Answer:
Step-by-step explanation:
Factor 15^5: 5^5 x 3^3
[tex]\frac{5^5*3^5}{-5^-6} = 5^1^1\\ \\ \frac{5^1^1*3^5}{-1} =-5^1^1*3^5\\ \\ =-11865234375[/tex]
Either: -5^11(3^5) or -11865234375
(depending on how you're supposed to write it)
I think at least
twenty more than a number is less than twice the same number
Answer:
x+20<2x
Step-by-step explanation:
20 more than a number implies that twenty must be added to the variable. Then, because it says less than you add a less than symbol. Finally, twice the same number tells you to use x again but since it’s being multiplied by 2, typing 2x makes it easier to understand.
Solve for x
3x = 4y
What is the 99th digit of pie?
The approximation of pi to 99 decimal places is 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679.
We have,
Determining the 99th digit of pi requires an understanding of the properties of pi and how it is calculated.
Pi is an irrational number, which means it has an infinite number of non-repeating decimal digits.
Since pi has an infinite number of digits, it is not possible to directly state the 99th digit without extensive computation.
However, various methods and algorithms have been developed to approximate the value of pi to a specific number of decimal places.
The 99th digit of pi has not been explicitly determined.
Thus,
The approximation of pi to 99 decimal places is 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679.
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Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth multiplier (i.e. common ratio) was around 2.0. In 1983, about 1800 people in the U.S. died of AIDS. We can use the exponential model:
P
n
=
1800
(
2.0
n
)
.
If the trend had continued unchecked, how many people would have died from AIDS in 2004?
If the trend had continued unchecked, 3,774,873,600 people would have died from AIDS in 2004
How many people would have died from AIDS in 2004?The equation of the function is given as
P(n) = 1800(2.0)^n
Where n represents the number of years since 1983
There are 21 years from 1983 to 2004
This is calculated as
n = 2004 - 1983
n = 21
Substitute 21 for n in the equation P(n) = 1800(2.0)^n
So, we have
P(21) = 1800(2.0)^21
Evaluate
P(21) = 3774873600
Hence, if the trend had continued unchecked, 3,774,873,600 people would have died from AIDS in 2004
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A rectangular board is 1100 millimeters long and 700 millimeters wide. What is the area of the board in square meters?
Answer:
its 300000000
Step-by-step explanation:
the 5th dimensions negate your father out of existence
ill give brainly and 10 points hurry please
Answer:
B
Step-by-step explanation:
it cant be a or c because if it is a negative then there is no need to put a + sign or add another - sign
Answer:
A
Step-by-step explanation:
Let's get the answer.
Suppose the question was the distance between 12 and 1. You would write it as 12 - 1 = 11. So you have to pick an answer that looks like this example.
B: is actually 11 12 -1 = 11
C: is 12 +(-1) = 12 - 1 which also gives 11
D: -1 -12 = -13. You are not really really with a distance here. You are combining 2 negative numbers.
So the answer is A.
-12 - (-1) = -12 + 1 = - 11
Which of the following shows examples of things that convert light energy to electrical energy? (5 points)
•Fan and wind turbine
•Light bulb and blender
•Airplane and human body
•Solar panels and solar cells.
The electrical device which shows an example of the conversion of light energy into electrical energy is: D. solar panels and solar cells.
What is a PV panel system?A PV panel system is an abbreviation for photovoltaic (PV) panel system and it is also referred to as a photovoltaic module, solar cell panel, or solar electric panel.
In Electrical engineering, the photovoltaic (PV) panel system are typically designed and developed to convert the light energy received from the Sun into electrical energy, which can be used specific electrical devices and home appliances.
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please help me please dont ignore
Answer:
2
Step-by-step explanation:
Given a graph of an original object and its image after dilation, you want to know the scale factor of the dilation.
DilationThe scale factor multiplies each of the coordinates.
The original coordinates of point A are (0, 1).
The coordinates of dilated point A' are (0, 2).
The factor that multiplies 1 to make it be 2 is 2/1 = 2.
The dilation scale factor is 2.
__
Additional comment
As a check, you can consider another point:
C(4, 3) × 2 = C'(8, 6) . . . . matches the point on the graph
16.
A quote you received from a local restaurant is $625 for a business luncheon. The restaurant owner tells you the price with gratuity is $720. How
much did the owner add for gratuity?
A. $75
B. $105
C. $85
O D. $95
Which list shows these lengths in order greatest to least?
Using the conversion of fraction to decimal, the list that shows these lengths in order greatest to least is:
[tex]\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}[/tex]
How a fraction is converted to decimal?A fraction is converted to decimal dividing the numerator by the denominator.
Hence the numbers in this problem are given as follows:
9/100 = 0.09.π/24 = 0.131.3/25 = 0.12.sqrt(3)/11 = 0.1575.Hence, considering the conversions to decimal above, the list that shows these lengths in order greatest to least is:
[tex]\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}[/tex]
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0.003 as a percentage.
Answer:
.3 %
Step-by-step explanation:
.003 x 100% = .3 percent
Given m || n, find the value of x and y.
X=
(5y+19)
(2x+1)
y =
(3x-19)
m2
72
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Is 5x+3y=0 linear or nonlinear
Answer:
3.33333
Step-by-step explanation:
It is a Linear