Recall that for |x| < 1, we have
[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]
It follows that, for |-x²| = |x|² < 1, or just |x| < 1,
[tex]\displaystyle \frac1{1+x^2} = \frac1{1-(-x^2)} = \sum_{k=0}^\infty (-x^2)^k = \sum_{k=0}^\infty (-1)^k x^{2k}[/tex]
Taking the antiderivative of both sides gives us
[tex]\displaystyle \arctan(x) = C + \sum_{k=0}^\infty \frac{(-1)^k}{2k+1} x^{2k+1}[/tex]
where C is a constant, which we determine to be 0, since taking x = 0 on both sides makes the series vanish, while arctan(0) = 0 since 0 = tan(0). So
[tex]\displaystyle \arctan(x) = \sum_{k=0}^\infty \frac{(-1)^k}{2k+1} x^{2k+1}[/tex]
Since tan(π/4) = 1, it follows that π/4 = arctan(1), so in the series we replace x = 1, then solve for π :
[tex]\displaystyle \arctan(1) = \sum_{k=0}^\infty \frac{(-1)^k}{2k+1} 1^{2k+1}[/tex]
[tex]\displaystyle \frac\pi4 = \sum_{k=0}^\infty \frac{(-1)^k}{2k+1}[/tex]
[tex]\displaystyle \pi = \sum_{k=0}^\infty \frac{4(-1)^k}{2k+1}[/tex]
[tex]\pi = 4 - \dfrac43 + \dfrac45 - \dfrac47 +\cdots[/tex]
The amount of a pair of designer pants was decreased from $150 to $120. What is the percent decrease of the pants?
Answer:
40% (decrease)
Step-by-step explanation:
150 - 250
|250|
× 100% =
8. To make a homemade all-purpose household cleaner, you can mix the
ingredients shown in the table. Samuel has 1 cup of rubbing alcohol
and will use the entire amount. He plans to store the cleaning solution
in containers that each hold a maximum of 6 cups. How many
containers does he Need?
Answer:
Could you link the table?
Step-by-step explanation:
Find two consecutive negative odd integers whose product is 35?
Answer:36
Step-by-step explanation:
Step-by-step explanation:
let, a required negative number be x
then it's cnsecutive odd negative. be x+2
now,
[tex] x \times ( x + 2) = 35 \\ or \: \: {x}^{2} \: + 2x = 35 \\ {x}^{2} + 2x = 35 \\ {x}^{2} + 2x - 35 = 0 \\ {x}^{2} + 7x - 5x - 35 = 0 \\ x(x + 7) - 5(x + 7) = 0 \\ (x + 7) (x - 5) = 0 \\ \\ now \: \: \: \: \: \: \:either \: \: x + 7 = 0 \\ x = - 7\\ \\or \: \: \: \: \: (x - 5) = 0 \\ x = 5[/tex]
since ,
we have supposed a negative number ,
,
we need negative odd number so,
x = -7
and it's consecutive number will be x+2
so, it is. -7+2 = -5
hence ,
-7 *and -5 are the required answer.
Jason is a project manager, He is dividing up work for his team. He gave Sarah 1/27th of the job, Brandon 0.32 of the job and Kelly 21% of the job. Jason will do the rest of the job himself. Including himself, who worked most of the job? Show all your work.
Answer:
Jason did the most, at about 43.3%
Step-by-step explanation:
Sarah did 1/27th of the work, which is about 0.037
Brandon did 0.32
Kelly did 21%, which is 0.21
Jason did the rest, which is 1-0.037-0.32-0.21=0.433
Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options. x = 5 –15 = –5x 5x = 15 –15 = 5x x = -5
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The given expression is ~
[tex]3x - 5 = - 2x + 10[/tex][tex]3x + 2x = 10 + 15[/tex][tex]5x = 15[/tex][tex]x = 15 \div 3[/tex][tex]x = 5[/tex]So, the Correct options are ~
[tex]x = 5[/tex]and
[tex]5x = 15[/tex]Answer:
A and C
Step-by-step explanation:
consider the graph of f(x) = x^2 -4x +5
hope this helps :) !!
What’s m= 10- -2-11 -19
Answer:
-18
Step-by-step explanation:
10-(-2)=12
12-11=1
1-19=-18
Can anyone help me ASAP!
Answer:
7.8
Step-by-step explanation:
the answer is
[tex] \sqrt{61} [/tex]
easy one - giving brainly if correct - show work.
Answer:
2/3
Step-by-step explanation:
Answer:
you need to do the math then divide numerator by dumerstor then x 100
aiden runs 5 laps around a track in 8 minutes how many laps per minute is that
Answer:
8/5 1.6 minutes per lap
5/8 0.625 lap per minutes
Solve each system of equations using substitution or elimination.
x + y = 3
2x - 3y = 1
Answer:
x=2
y=1
Step-by-step explanation:
is this righttt? below
Step-by-step explanation:
yes
Answer:
yes
I think
oorrrrrrr
Simplify.
0.156 - 0.12
A. 13
B. 1.3
C. 0.13
D. 0.013
Please select the best answer from the choices provided
B. 1.3
Hope that helped:)
factorize 2x²y⁴-6xy³
Answer:
=2xy^3x(xy-3)
Step-by-step explanation:
2x^2y4-6xy^3
=2xy^3x(xy-3)
=2xy^3x(xy-3)
What is the least common multiple of 6/30
Answer:
LCM of 6 and 30 is 30
ya'll help me w/slope, please
I got ECHA... hope it's right:)
Identify all values of x that make the equation true:
?
+3
Answer:
where is the equation??
A grocer can buy strawberries for $1.38 per pound
The order of strawberries cost $241.50. How many pounds did the grocer order?
I know the answer is 175 I just don’t know how to explain how I got it
Work Shown:
x = number of pounds of strawberries purchased
1.38x = cost of buying those x pounds of strawberries, at $1.38 a pound
1.38x = 241.50
x = (241.50)/(1.38)
x = 175
As a check,
1.38*x = 1.38*175 = 241.50
which confirms the answer
A town's population is currently 15,150. If the population doubles every 7 years, what will the population be 14 years from now?
Answer:
A population of 424,200
Step-by-step explanation:
Graph the following equation: y = -5x + 1
Answer: in your graphplot the point of the y-intercept(which in this case is 1, hence the “+1”)
Step-by-step explanation:
Next 5x is the same as -5/+1 which pretty much means you have to go down 5 times and 1 to the right in a repeated motion until you can no longer plot that point.
then you do the opposite of -5x which is -1/+5 which means you have to go up 5 times and 1 to the left in a repeated motion until you can’t
[tex]\small\bold\green{{help}}[/tex]
9514 1404 393
Answer:
y = -2/3x +5/3y = 2.4x -8Step-by-step explanation:
Solve for y. The slope (m) is the coefficient of x. The y-intercept (b) is the constant.
1. 3y = -2x +5
y = -2/3x +5/3 . . . . . m = -2/3, b = 5/3
__
2. y = 2.4x -8 . . . . . . . m = 2.4, b = -8
Cecile picked 219 apple. She divided the apple equally into 3 baskets. How many apple is in each basket
Answer:
73 apples
Step-by-step explanation:
What is the radius of the circle ?
Answer:
Step-by-step explanation:
60 degrees angles 2
2x equal over five so ur answer will be c
Evaluate 2xy when x=−14 and y=3. Help!!!!
Answer:
-84
Step-by-step explanation:
Help is on the way! Plug in the values of x and y into the expression and then simplify with multiplication.
2(-14)(3)
-84
And you're done!
Monica wants to rent online movies. The company Movies Plus charges a one-time fee of $20 plus $5 per movie. Movies-2-Go charges $7 per movie and has no one- time fee. For how many movies is the cost of renting movies from Movies Plus and Movies-2-Go the same?
Answer:
Step-by-step explanation:20+5+7=32
4
Two of the dozen eggs in a carton
are cracked. About what percent of the
carton is cracked?
Answer:
am 50%
Step-by-step explanation:
I try my best
Answer:
10%
Step-by-step explanation:
10
2
What are the new coordinates of B after a dilation with a scale factor of 4?
Hiii can some please help me!!! Thank you!!! I will mark you branlist !!
Explanation:
The diagram shows that point B is at (3, -1).
Multiply each coordinate of point B by the scale factor 4
3*4 = 12-1*4 = -4The point B(3,-1) moves to B ' (12, -4)
This trick only works if the center of dilation is the origin.
Perform the following operation
Answer:
When you multiply an odd number of negatives you get a negative result. When you multiply an even number of negatives you get a positive result.
First, multiply normally.
25x10x5
1100
Then determine whether the sign is positive or negative. Since there is an odd number of negatives, the sign is negative.
So, the answer is -1100.
:)
2p2 - 5p + 3
pliss anwered this for me
Answer:
2p²-5p+3 is the final answer as they aren't any like terms to collect in order to simply the solution further.
Step-by-step explanation:
Wishing you a splendiferous day,
stay salty...
For the Recursive Formula An = an-1 + d, what does the An-1 represent?
A) the last term
B) the first term
C) the previous term
D) the next term
Answer:
answer is d
if this helps can i get brainliest
