Recall the well-known series
[tex]\displaystyle 2 \arcsin^2(x) = \sum_{n=1}^\infty \frac{(2x)^{2n}}{n^2 \binom{2n}n}[/tex]
Replace x with √x :
[tex]\displaystyle 2 \arcsin^2(\sqrt x) = \sum_{n=1}^\infty \frac{(4x)^n}{n^2 \binom{2n}n}[/tex]
Differentiate both sides:
[tex]\displaystyle -\frac{\arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^n}{n \binom{2n}n}[/tex]
Multiply by 4x :
[tex]\displaystyle -\frac{4x \arcsin(\sqrt x)}{2\sqrt{x-x^2}} = \sum_{n=1}^\infty \frac{(4x)^{n+1}}{n \binom{2n}n}[/tex]
All the series I've mentioned converge for |x| < 1, so we can take x = -1/4 to find the value of the sum we want.
[tex]\displaystyle \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n \binom{2n}n} = -\frac{4 \times \left(-\frac14\right) \arcsin\left(\sqrt{-\frac14}\right)}{2\sqrt{-\frac14-\left(-\frac14\right)^2}} = -\frac{\arcsin\left(\frac i2\right)}{\frac{\sqrt5\,i}2}} = \boxed{\frac2{\sqrt5} \mathrm{arsinh}\left(\frac12\right)}[/tex]
where
[tex]\arcsin\left(\frac i2\right) = z \iff 2\sin(z) = -2i\sinh(iz) = i \implies z = i \, \mathrm{arsinh}\left(\frac12\right)[/tex]
what should be the rate of interest to earn an 45000 as interest wale rupees 50000 easy in investment for 6 year
Answer:
5
Step-by-step explanation:
Find the differential of
f
(
x
,
y
)
=
x
2
+
y
3
at the point
(
2
,
1
)
.
[tex]f(x,y)=x^2+y^3\implies \left.\cfrac{}{} 2x+3y^2 \right]_{\stackrel{\textit{\small x=2}}{\textit{\small y=1}}}\implies 2(2)+3(1)^2\implies 7[/tex]
which of the following are polynomials
Answer:
I think so Option D is the correct answer
An athlete runs in a straight line along a flat surface. He starts from rest and for 20 seconds accelerate at a constant
rate. In this first 20 seconds he covers a distance of 100m. For the next 10 seconds he runs at a constant speed and
then decelerates at a constant rate for 5 seconds until he stops.
a) What is the total distance that he ran?
[5]
Another athlete runs along the same track, starting from rest and she accelerates at the same rate as her friend. She
however only accelerates for 10 seconds before running at a constant speed.
Answer:
probably 200
Step-by-step explanation:
or something like that
How does Algebra act as a tool to improve communication
It is a tool as it represents the language of patterns.
It is also a means of working with abstract notions and then applying them, which frequently leads to the formation of generalisations and insights outside of the original context.
if you answer this question you will get 30 points
Answer:
2 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Step-by-step explanation:
1+1 is 2
what does Y=
what does z=
Answer:
Hope the picture will help you
Think about each of the following. Which of these three triangles is impossible to draw?
Check by using sum of angles of triangle = 180°
20+45 < 180 so third angle will make it 180 which means it's possible to draw 120+50 = 170< 180 so third angle being 10 will complete the triangle90+100 = 190 > 180 so third angle being (-10) is impossible for the triangle so it can't be possibleRiley has completed 6 of the 30 pages she was assigned for homework. What percentage of her homework does Riley have left to complete?
Answer:
80 Percent
Step-by-step explanation:
Since she has done 6/30 pages, she has 24/30 more pages to complete. Convert 24/30 to a decimal by dividing 24 by 30 to get the percentage, which is 80 percent
Hopefully this helps - let me know if you have any questions!
Perimeter of following rectangle mixed number in simplest form 1 1/3 ft 5/8 ft
Answer: 3 11/12
Step-by-step explanation:
1 1/3 * 2 = 2 2/3
5/8 * 2 = 1 1/4
2 2/3 + 1 1/4 = 3 11/12
I need help...you will be mark brainliest if it's right ty
Answer:
Median: 5
Interquartile range: 4
Have an amazing day!
Please rate and mark brainliest!!
What is the area?
2 yd
8 yd
5 yd
Answer:
28
Step-by-step explanation:
I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.
area of trapezoid = (base1 + base2)h/2
area = (2 yd + 5 yd)(8 yd)/2
area = 28 yd²
The sphere below has a radius of 25 cm.
O
25 cm
Work out the volume of the sphere.
Give your answer correct to 1 decimal place.
Volume of sphere= tr3
cm3
Answer:
65449.8 cm3
Step-by-step explanation:
We start with the volume formula for a sphere: 4/3 πr3
We start with subbing in 25 to r, then we cube 25, which is equal to 15625.
We multiply 4/3 and pi. And lastly we multiply what we got by 15625 and either round the answer or fphaving fixed your calculator.
Briana has 3/4 pound of rabbit food. She feeds her rabbit 1/12 pound each day. How many days can Briana feed her rabbit with the food she has?
Four divided by 1,000 rounded to the nearest whole number
Answer:
4 ÷ 1,000 = 0.004
Rounding up to 0 as the nearest whole number
3
0.33 points
Suppose you form 5-letter strings from the letters C,O, M, P, U, T, I, N, and G. What are the number of permutations as a ratio of factorials?
type your answer...
Using the permutation formula, it is found that it's number as a ratio of factorials is given by:
[tex]N = \frac{9!}{4!}[/tex]
The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, five letters will be chosen from a set of nine, hence:
[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]
More can be learned about the permutation formula at https://brainly.com/question/25925367
find the area of circle o if DCBO is a rectangle and DB measure 10 units
Answer:
[tex]100\pi[/tex]
Step-by-step explanation:
Step 1: Identity the radius.
Since O is the center of the circle, and C and E lie on the circumference, OC and OE are the radii of the circle and thus,
OC=OE.
Step 2: Consider the rectangle.
All diagonals in a rectangle are congruent so this means
DB= OC ( OC is also a diagonal).
Thus, OC= 10 units.
Step 3: Analyze
So this means OE is also 10 units as well.
Since we know the length of the radius, Use the area of circle,
[tex]\pi {r}^{2} [/tex]
[tex]\pi( {10}^{2} ) = 100\pi[/tex]
So the area of a circle is 100 pi.
Answer:
314.2 square units
Step-by-step explanation:
The diagonals of a rectangle are the same length, so segment OC is the same length as segment DB: 10 units. OC is a radius of the circle, which means the circle's radius is 10 units.
The area of a circle is given by ...
A = πr²
A = π(10 units)² = 100π units²
A ≈ 314.2 units²
The area of circle O is about 314.2 square units.
26.95 divided by -5 1/2. can someone show me how to do it please?
Answer:
-4.9
Step-by-step explanation:
Since the number 26.95 has two decimal places, it can be turned into a whole number with a denominator having two zeroes; 100
2695
100
Then change -5 1/2 into an improper fraction; = -5 × 2 + 1
2
= -11/2
2695 ÷ ( -11 )
100 2
Reciprocate (put denominator as numerator and vice-versa ) the equation after the ÷ sign. After doing so, the ÷ sign changes to × sign.
Hence: 2695 × ( 2 )
100 -11
Then, cross multiply.
2695 ÷ ( -11 ) = -245100 ÷ 2 50
-245 ÷ 50
= -4.9
Answer: its -4.9
Step-by-step explanation:
Consider the function RX) = 3x + 1 and the graph of the function g(x) shown below.
у
4
6
4
2
X
-6 -4
- 2
12
4
6
-2
4
6
The graph g(x) is the graph of f(x) translated
✓ units
✓, and g(x) =
Step-by-step explanation:
f(x) goes through the point (0, 1).
g(x) goes through (2, 1) for the same y value.
that means g(x) is f(x) translated 2 units to the right.
but we could also look at the same x value (0).
then g(x) goes through (0, -5).
and that means g(x) is f(x) translated 6 units down.
since it is a line function, shifting it left/right or up/down makes no difference to the shape or position of the new curve itself.
as it looks like you don't have 6 in the drop-down menu, then 2 units (to the right) is the desired correct result.
that means g(x) = f(x-2) = 3(x-2) + 1 = 3x - 6 + 1 = 3x - 5
and that is what the graph is showing us.
It has been found that 50.3% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 171 owned some type of stock. At what level of significance in a two- tailed test would you conclude that this was a significant difference
Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.
What are the hypothesis test?At the null hypothesis, we test if the proportion is of 50.3%, hence:
[tex]H_0: p = 0.503[/tex]
We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:
[tex]H_1: p \neq 0.503[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, the parameters are:
[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]
[tex]z = 2.32[/tex]
What is the p-value?Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Sonya took out a mortgage of $65,000 at 7% for 25 years. What is the cost of the mortgage?
The cost of the mortgage is $81250
What are interests?
Interests are percentages of a principal
Given the following parameters
Principal = $65000
Rate = 7% = 0.07
Time = 5 years
I = PRT/100
I = 65000*0.07*25
I = 16,250
Cost of mortgage = Principal + Interest
Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250
Hence the cost of the mortgage is $81250
Learn more on mortgage here: https://brainly.com/question/22846480
Answer:
$72,823
Step-by-step explanation:
just took test
what is 7 times 3 fiths
Answer:
4-1.5 or 21/5 or 4.2
Step-by-step explanation:
Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - seven multiplied by three fifths = twenty-one fifths.
the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width
Answer:
Length and width of rectangle is 24 and 8 inchesStep-by-step explanation:
Given:
Length of rectangle is three times the widthPerimeter of rectangle is 64 InchesTo Find:
Length and WidthSolution:
Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:
Perimeter of rectangle = 2(L + B)
→ 64 = 2(3x + x)
→ 64 = 2(4x)
→ 64/2 = 4x
→ 32 = 4x
→ 32/4 = x
→ 8 = x
Hence,
Length of the rectangle = 3x = 3(8) = 24 inchesWidth of the rectangle = x = 8 inchesAnswer:
Length = 24 inchesWidth = 8 inches⠀
Step-by-step explanation :
⠀
As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle is 8 inches .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 24 inches .⠀
R\ {0}→→ Ris defined by Jff: 1 f(x)=x³-1/x³-1then show that 2 f(x) + f(1/x)=0.
[tex]\orange\bigstar \bold{ solution}[/tex]
[tex]\bold{f(x) = x³ - \frac{1}{x³ } }[/tex]
[tex]\bold{f ( \frac{1}{x} )= \frac{1}{x³} -x³ } [/tex]
[tex]\bold{f (x) + f (\frac{1}{x}) = (x³- \frac{1}{x³} ) + ( \frac{1}{x³} -x³)}[/tex]
[tex]\bold{ = 0 }[/tex]
Which angle is an x-intercept for the function y = cos(1)
A.0
B.2
C. £
D. 2£
Answer: C. [tex]\pi[/tex]
=======================================================
Explanation:
The x intercept always occurs when y = 0.
Use the unit circle to determine that [tex]\cos(\theta) = 0[/tex] when [tex]\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}[/tex]
So if [tex]x = \pi[/tex], then we have
[tex]y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0\\\\[/tex]
which shows us that [tex](\pi, 0)[/tex] is the location of one of the infinitely many x intercepts for this function.
Please help Math-correct answers only!!
Have number with correct answers/letters!
I'll do the first three questions to get you started.
==========================================================
Question 1
x = horizontal component of the triangle
cos(angle) = adjacent/hypotenuse
cos(theta) = horizontal/hypotenuse
cos(40) = x/30
x = 30*cos(40)
x = 22.98133329 approximately
This is the horizontal force applies to the suitcase.
Work = force*displacement
Work = 22.98133329*120
Work = 2,757.7599948
Work = 2,758
Answer: 2,758 Nm (choice B)==========================================================
Question 2
Add the drone's relative air velocity and the wind velocity vectors.
v+w = (13i + 3j) + (-7i - 2j)
v+w = (13i-7i) + (3j-2j)
v+w = 6i + j
Answer: 6i + j (choice B)==========================================================
Question 3
Check out the diagram below. Focus on the smaller triangle. Notice the placement of angle theta.
sin(theta) = opposite/hypotenuse
sin(40) = x/200
x = 200*sin(40)
x = 128.557521937308
x = 128.558
Answer: 128.558 pounds (choice A)Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Answer:
1/2
Step-by-step explanation:
The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].
Hope this helps :)
Answer:
1/2
Step-by-step explanation:
took the test
Write the given expression in terms of x and y only sin(tan^-1(x)+tan^-1(y)
Answer:
Step-by-step explanation:
Let a = tan⁻¹(x), so tan(a) = x,
[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]
Let b = tan⁻¹(y), so tan(b) = y,
[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]
sin( tan⁻¹(x) + tan⁻¹(y)) = sin(a + b)
= sin(a) cos(b) + cos(a)sin(b)
= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]
[tex]=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}[/tex]
Find the values of x for which the denominator is equal to zero for y=3x+5/x-6.
x = −5
x = 6
x = −6
none
Answer:
x=6 is the answers for the question
Step-by-step explanation:
please mark me as brainlest
Work out the highest common factor (HCF) of 18 and 30
[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]