The sum of the series Σn=1 to ∞ n(n-1)x^(n) is:
(2x^2(1-x)^3 + 6x^3(1-x)^2)/(1-x)^6
We can differentiate both sides of the equation 1/(1-x)^2 = Σn=1 to ∞ nx^(n-1) with respect to x to obtain:
[1/(1-x)^2]' = [Σn=1 to ∞ nx^(n-1)]'
Then, using the power rule of differentiation, we get:
2/(1-x)^3 = Σn=1 to ∞ n(n-1)x^(n-2)
Multiplying both sides by x, we obtain:
2x/(1-x)^3 = Σn=1 to ∞ n(n-1)x^(n-1)
Differentiating both sides of the equation 2x/(1-x)^3 = Σn=1 to ∞ n(n-1)x^(n-1) with respect to x, we obtain:
[2x/(1-x)^3]' = [Σn=1 to ∞ n(n-1)x^(n-1)]'
Using the power rule of differentiation, we get:
(2(1-x)^3 + 6x(1-x)^2)/(1-x)^6 = Σn=1 to ∞ n(n-1)x^(n-2)
Multiplying both sides by x^2, we obtain:
(2x^2(1-x)^3 + 6x^3(1-x)^2)/(1-x)^6 = Σn=1 to ∞ n(n-1)x^(n)
Therefore, the sum of the series Σn=1 to ∞ n(n-1)x^(n) is:
(2x^2(1-x)^3 + 6x^3(1-x)^2)/(1-x)^6
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2(-2-4) = use the distributive property to expand the expression below.
Answer:
-12
Step-by-step explanation:
First, solve in parentheses.
2(-2-4)
=
2(-6)
Next, multiply 2 by -6.
Which equals -12.
So therefore using the distributive property shown above, the answer would be -12.
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What is the distributive formula?}[/tex]
[tex]\mathsf{a(b + c)}[/tex]
[tex]\mathsf{= a(b) + a(c)}[/tex]
[tex]\mathsf{= ab + ac}[/tex]
[tex]\huge\textbf{What is the equation?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\huge\textbf{What are we simplifying?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-2) + 2(-4)}[/tex]
[tex]\mathsf{= -4 - 8}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{How are you going to translate to}\\\\\huge\textbf{easier terms?}[/tex]
[tex]\mathsf{2(-2 - 4)}[/tex]
[tex]\mathsf{= 2(-6)}[/tex]
[tex]\mathsf{= -12}[/tex]
[tex]\huge\textbf{What is the ANSWER to the question?}[/tex]
[tex]\huge\boxed{\mathsf{-12}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Find the circumference and the area of a circle with diameter equal to 8.6 inches. Use 3.14 for pie.
The circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.
How to calculate the circumferenceThe formula for circumference of a circle is given as;
Circumference = 2 π r
We have diameter = 8. 6 inches
Radius = diameter/ 2
Radius = 8.6/2 = 4. 3 inches
Circumference = 2 × 3. 14 × 4. 3 = 27. 0 Inches
The formula for area of a circle = π r ^2
Area = 3. 14 × 4. 3 × 4. 3
Area = 58. 0 Inches square
Thus, the circumference and area of the circle are 27. 0 inches and 58. 0 inches square respectively.
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PLEASE HELP 50 POINTS
Step-by-step explanation:
The initial velocity of a particle moving along x−axis is u (at t=0 and x=0) and its acceleration a is given by a=kx.What is the standard deviation of the data set? 6.5, 11.2, 13, 6.3, 7, 8.8, 7.4
Using it's concept, the standard deviation of the data-set is of 2.39.
What are the mean and the standard deviation of a data-set?The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.The mean of the data-set in this problem is given by:
M = (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4)/7 = 8.6.
Hence the standard deviation is:
[tex]S = \sqrt{\frac{(6.5-8.6)^2+(11.2-8.6)^2+(13-8.6)^2+(6.3-8.6)^2+(7-8.6)^2+(8.8-8.6)^2+(7.4-8.6)^2}{7}} = 2.39[/tex]
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In convex pentagon $ABCDE$, angles $A$, $B$ and $C$ are congruent and angles $D$ and $E$ are congruent. If the measure of angle $A$ is 40 degrees less than the measure of angle $D$, what is the measure of angle $D$
In a convex pentagon, the measure of angle D is 132°.
What is convex pentagon?If a planar polygon has all the line segments connecting any given pair of its points, it is said to be convex pentagon.
Properties of a Convex Polygon are-
Any polygon whose inner angles are all smaller than 180 degrees is said to be convex.A concave polygon is one in which at least one of the angles is bigger than 180°.A convex polygon's diagonals are located inside the polygon.A polygon is considered convex if the line connecting every pair of its points lies entirely within it.Calculation for the measure of angle D.
The sum of the interior angles = 540°
Let A, B , C = D - 40
And let E = D
So we have
A + B + C + D + E = 540
(D - 40) + (D - 40) + (D - 40) + D + D = 540
5D - 120 = 540
5D = 660
D = 660 / 5
D = 132°
Therefore, the measure of angle D is 132°.
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142857/500000 simplified
Using your own examples, explain why all statements are sentences but not all sentences are statements. Clearly indicate which type of non-statement you have used in each case. (Your response should be between 500 and 600 words).
Answer:
0.285714 -> 0.29
Step-by-step explanation:
Enter the degree of the polynomial below.
5,5 + 8,2 + 2x - 319 - 8x1 -4,5
Based on the given polynomial, the degree of the polynomial can be calculated to be 1.
what is the degree of the polynomial?the degree of the polynomial is defined as the highest exponential degree or power in a polynomial.
from the above, we see that the highest power is 1 from 8x¹.
the degree of the polynomial is therefore 1.
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If Robbie has twenty-five apples and he wants to share them equally with four other friends, how many apples must he give to each of his friends so that he will have the same number of apples as each of his friends
Answer:
5 apples
Step-by-step explanation:
4 friends + Robby = 5 people
25 apples in total ÷ 5 people
= 5 apples per person
Select the correct answer.
Consider these functions:
f(x) = 4x³ - 10
g(x) = 3x - 4/2
What is the value of g(f2))?
Answer:
3x - 4/2
Step-by-step explanation:
2 result(s) for "f(x) = 4x³ - 10 g(x)
3x^2=7x solve the equation
Answer:
3x^2 - 7x =0
x(3x-7) = 0
3x - 7 = 0
3x =7
x= 7/3
The angle measurements in the diagram are represented by the following expressions.
Answer:
Angle A= 30
Step-by-step explanation:
Angle A and B are same side interior
So A + B = 180
x = 8
6(8)-18=30
Answer:23
Step-by-step explanation:
jaja
-x^2 +x+6=0 (Please solve by completing the square, and show steps)
The solution to the equation using the completing the square are 2 and -3
Quadratic equationThese are equation that has a leading degree of 2. Given the equation below
-x^2 +x+6=0
This can also be written as
x^2-x-6 = 0
Complete the square
x^2-x = 6
x^2-x+ (1/2)^2 = 6 + (1/2)^2
(x-1/2)^2 = 6 + 1/4
(x+1/2)^2 = 25/4
x+1/2 = ±√25/4
x = 5/2 -1/2 or -5/2-1/2
x = 4/2 or -6/2
x = 2 and -3
Hence the solution to the equation using the completing the square are 2 and -3
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The piece of music that I am learning is 60 measures long. There are 13 beats in every measure, and every eighth note lasts for 1 beat. The last 17 measures of this piece are the finale. In every measure of the finale, there are 7 eighth notes played at middle C. If middle C never occurs in this piece outside of the finale, for what fraction of the whole piece do I play middle C
[tex]\frac{119}{780}[/tex] fraction of the whole piece you play middle C.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction consists of a numerator above a line and a non-zero denominator below (or after) that line. Numerators and denominators are also employed in uncommon fractions such as compound fractions, complex fractions, and mixed numerals.To find for what fraction of the whole piece do you play middle C:
Since 7 out of every 13 beats in the finale are played at middle C, [tex]\frac{7}{13}[/tex] the finale is played at middle C.
The finale is 17 measures out of a 60-measure piece or [tex]\frac{17}{60}[/tex] of the whole piece.
[tex]\frac{7}{13}[/tex] of [tex]\frac{17}{60}[/tex] is [tex]\frac{7}{13}[/tex] x [tex]\frac{17}{60} = \frac{119}{780}[/tex]
Therefore, [tex]\frac{119}{780}[/tex] for a fraction of the whole piece you play middle C.
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What is the percent rate??
Kryton -85 is a radioisotope of krypton that has a half-life of about 10.75years. This isotope is produced by the nuclear fission of uranium and plutonium in nuclear weapons and in nuclear reactors, as well as cosmic rays. An important goal of the Limited Nuclear Test Ban Treaty of 1963 was to eliminate the release of such radioisotopes into the atmosphere. At present, the activity of Krypton -85 in the atmosphere is about 135 mCi.
Using an exponential function, it is found that the decay rate is of 6.24% a year.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]0.5A(0) = A(0)(1 - r)^{10.75}[/tex]
[tex](1 - r)^{10.75} = 0.5[/tex]
[tex]\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}[/tex]
[tex]1 - r = (0.5)^{\frac{1}{10.75}}[/tex]
1 - r = 0.9376.
r = 1 - 0.9376.
r = 0.0624.
The decay rate is of 6.24% a year.
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The perimeter of a rectangle is 99 ft, and the length is twice the width. what are its dimensions?
The dimension of the length and width of the rectangle with the given perimeter are 33ft and 16.5ft respectively.
What are the dimensions of the rectangle?Perimeter of rectangle is expressed as;
P = 2( l + w )
Given that;
Perimeter P = 99ftLet width w = xLength l = 2xWe substitute into the formular above.
P = 2( l + w )
99ft = 2( x + 2x )
99ft = 2x + 4x
99ft = 6x
x = 99ft/6
x = 16.5ft
Width = x = 16.5ft
Length = 2x = 2( 16.5ft ) = 33ft
Therefore, the dimension of the length and width of the rectangle with the given perimeter are 33ft and 16.5ft respectively.
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The bars in a _____________ do not touch since data is ______________.
A. bar graph ; continuous
B. bar graph ; discrete
C. histogram ; continuous
D. histogram ; discrete
Answer:
b
Step-by-step explanation:
Bat Graphs represent discrete data. They are spaced and don't touch to represent a discrete value.
Histograms represent continuous data. They are close and connected to represent variation in continuous data.
The distance from the Sun to Mercury is approximately 57910000 km.
Assuming Mercury has a circular** orbit around the Sun, find the distance Mercury travels in orbiting the Sun through an angle of 2.65 radians.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
How much distance did Mercury travel on its orbit?
The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:
s = (2.65 rad) · (57 910 000 km)
s = 153 461 500 km
Please notice that the radius of translation is the distance from the Sun to Mercury.
Mercury travels a distance of 153 461 500 kilometers on its orbit.
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Find the quotient: look at pic
Answer:
2y+6
Step-by-step explanation:
first, pull out the 2 from the top to separate the equation
second, factor out y
third, cancel out the common factor of y-1
fourth, remove the parenthesis from 2(y+3)
answer = 2y+6
Model the situation with the sun of the polynomials. Then simplify their sum.
A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame.
Answer: 16x - 2
Step-by-step explanation:
The perimeter of a figure is the total length of all sides of the figure. Since this figure is a rectangle, opposite sides have the same length.
Therefore, the perimeter of the picture frame can be modeled by
[tex]6x+3+2x-4+6x+3+2x-4[/tex]
Moving all like terms together, we get
[tex]6x+2x+6x+2x+3-4+3-4[/tex]
Finally, combining these terms, we get
[tex]16x -2[/tex]
How to use the distributive property to multiply two variables together
Distributive property states that A × (B + C) = AB + AC. are always equal.
According to the statement
we have to explain the distributive property over multiplication.
Distributive property is the multiplication property.
According to this property, it generalizes the Distributive Law and it tells us that the an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
It means that From distributive property
A × (B + C) = AB + AC.
These are always equal with each other.
Now we will explain with an example,
Let A = 2, B = 3 and C = 4
Then
2 × (3 + 4) = 2(3) + 2(4).
2 × (7) = 2(3) + 2(4).
14 = 6 + 8.
14 = 14.
It proves that the A × (B + C) = AB + AC.
So, Distributive property states that A × (B + C) = AB + AC. are always equal.
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PLEASE HELP!!!!
This year, the Nature Club made 3 exhibits per month for its annual fair. This year's fair has twice as many exhibits as last year's. How many exhibits were there in last year's fair?
Answer: 18
Step-by-step explanation:
There are 12 months in a year. The club made 3 exhibits each month. 3 times 12 is 36. They made twice as many as last year, so divide 36 by 2 and you get 18.
I hope this helps!
slope:
y-intercept:
PLSPLSPLS HELP
Answer:
Slope: 1
Y-intercept: -1
Step-by-step explanation:
The line passes the y-axis at -1, the rise/run, which is used to calculate the slope is 2/2, and it equals to 1, so the slope is 1.
I hope it helps! Have a great day!
bren~
1 1/6 + (x/3 · 1/4) = 1 3/4
solve for x
Answer:
x = 7Step-by-step explanation:
1 1/6 + (x/3 · 1/4) = 1 3/4
solve for x
1 1/6 + x/12 = 1 3/4
1 1/6 - 1 3/4 = -x/12
-7/12 = -x/12
-7 = -x
x = 7
----------------
check
1 1/6 + (7/12 * 1/4) = 1 3/4
1 1/6 + 7/48 = 1 3/4
1 15/16 = 1 3/4
1 3/4 = 1 3/4
the answer is good
please help asap i am so confused
The table so fined below based on the information given about the function.
How to illustrate the information?The table based on the function given will be:
Plan A. Plan B
Monday. 10. 30
Tuesday. 20. 40
Wednesday. 40. 50
Thursday. 80. 60
Friday. 160. 70
A is illustrated as it's double minutes for each day. B is illustrated by adding 10min each day.
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Find the x - and y -intercepts of the graph of the linear equation 2 x plus 3 y is equal to 2x+3y=12
Answer:
x-intercept is 6 [(6, 0) is the point]
y-intercept is 4 [(0, 4) is the point]
Step-by-step explanation:
To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:
[tex]2x+3(0)=12\\2x=12\\x=6[/tex]
So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0
To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:
[tex]2(0)+3y=12\\3y=12\\y=4[/tex]
So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0
Quick algebra 1 assignment for 50 points!
Experts and Geniuses please help asap, TYSM!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
Step-by-step explanation:
Direct variation is essentially a linear equation, where there is a constant rate. Direct variation can be applied to many things, and we can use it to represent how much money someone has in their bank account after "x" weeks if they're depositing a constant amount of money each week.
So a practical example would be: If someone just opened a bank account and deposits $50 every week, how many weeks will it take for them to have $400 in their account.
So the slope is given in the question, it's $50, since their depositing that constant amount each week. So this gives us the equation: [tex]y=50x[/tex] where x represents the amount of weeks. The y represents the amount of money they have, and since we want to find when this equals 400, we set the y=400, and then solve for x. This gives us the equation: [tex]400=50x[/tex]. Dividing both sides by 50 you get: [tex]8=x[/tex]. So it'll take 8 weeks to have $400 dollars, if you deposit 50 dollars each week.
A group of friends wants to go to the amusement
park. They have no more than $420 to spend on
parking and admission. Parking is $8.75, and
tickets cost $25.75 per person, including tax.
Which inequality can be used to determine x, the
maximum number of people who can go to the
amusement park?
Answer:
The maximum amount of people that can go to the amusement park is 15.
Step-by-step explanation:
First you create an equation to represent the question
8.75+25.75x≤420
You put the less than or equal to sign because 420 is the maximum amount of money.
Now you just solve the equation.
25.75x≤420-8.75
25.75x≤411.25
x≤411.25/25.75
x≤15.9708738
Then you have to round down because you cant have .9 of a person.
So x≤15
Then, Check your solution
8.75+(25.75 x 15)≤420
8.75+386.25≤420
395≤420
That is true. But to make sure that is the maximum add another 25.75
395+25.75≤420
420.75≤420
This is equation is false so, our answer is correct.
The maximum amount of people that can go to the amusement park is 15.
The pen is 2 cm shorter than the scale. if the scale is 7 inches long. how long is the pen?
The pen is [tex]15.78[/tex] centimeters long when scale is [tex]7[/tex] inches long and pen is [tex]2cm[/tex] shorter then the scale.
How to find the how much long is the pen ?
Scale is [tex]7 inches[/tex] long and
We know that
[tex]7inches=17.78cm[/tex]
And pen is [tex]2cm[/tex] shorten then the scale
So the length of the pen is
[tex]=17.78-2\\=15.78cm[/tex]
[tex]=6.21 inches[/tex]
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One can convert temperature from kelvin into fahrenheit using the formula . what is the temperature in kelvin corresponding to f degrees fahrenheit?
One can easily convert the temperature using temperature conversion formula given below
K = [tex]\frac{5(F - 32)}{9} + 273.15[/tex]
where F = degrees in Fahrenheit
K = degrees in Kelvin
What is temperature conversion? The measuring units of the temperature recorded in a particular unit can be converted with the aid of a temperature converter. The degree of heat or cold that a solid, liquid, or gas has is expressed by its temperature. A thermometer is used to determine temperature. Although the SI unit for temperature is Kelvin (K), most people measure temperature in Centigrade or Celsius (°C) and Fahrenheit (°F).Know more about temperature conversion https://brainly.com/question/13421795
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Please explain the answer before, and also help with number line!
The solution to the given inequality is x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
Number line and inequalityGiven the inequality expression as shown
6x + 6 < -30
Subtract 6 from both sides
6x < -30 - 6
6x < -36
Divide through by 6
x < -36/6
x < -6
For the number line, an open circle will be drawn on the value of -6 and the arrow pointing to the left side.
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