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2 years ago

Can anyone help me with geometry? I have a whole packet. You guys can add me on snap with my user taejichi

Mathematics

1 answer:

Alex777 [14]2 years ago

3 0

Answer:

Step-by-step explanation:

Yes but you can post here also

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<img src="https://tex.z-dn.net/?f=%20%20%5Crm%5Csum%20%5Climits_%7Bn%20%3D%200%7D%5E%7B%20%5Cinfty%20%7D%20%20%5Carcsin%20%5Clar

sineoko [7]

Recall that over an appropriate domain,

$\arcsin(x) \pm \arcsin(y) = \arcsin\left(x \sqrt{1-y^2} \pm y \sqrt{1-y^2}\right)$

Let $x=\frac1{n+1}$ and $y=\frac1{n+2}$ (these belong to the "appropriate domain", so the identity holds). We have

$\dfrac{\sqrt{n+3}}{(n+2)\sqrt{n+1}} = \dfrac1{n+1} \sqrt{\dfrac{(n+3)(n+1)}{(n+2)^2}} = \dfrac1{n+1} \sqrt{1 - \dfrac1{(n+2)^2}} = x \sqrt{1-y^2}$

and

$\dfrac{\sqrt n}{(n+1)\sqrt{n+2}} = \dfrac1{n+2} \sqrt{\dfrac{n(n+2)}{(n+1)^2}} = \dfrac1{n+2} \sqrt{1 - \dfrac1{(n+1)^2}} = y \sqrt{1-x^2}$

Then the sum telescopes, as

$\displaystyle \sum_{n=0}^\infty \arcsin\left(x \sqrt{1-y^2} - y \sqrt{1-x^2}\right) = \sum_{n=0}^\infty \left( \arcsin(x) - \arcsin(y) \right) \\\\ = \left(\arcsin(1) - \arcsin\left(\frac12\right)\right) + \left(\arcsin\left(\frac12\right) - \arcsin\left(\frac13\right)\right) + \cdots \\\\ = \arcsin(1) = \boxed{\frac\pi2}$

3 0

1 year ago

How do you draw a model that shows decimal 1.7

Pie

Answer:

We can model the decimal number 1.7 by drawing two squares and divide each of the two squares into 10 equal parts.

Then we start shading the square such that the first square is fully shaded and in the second square we shade 7 out of the 10 parts such that 0.7 of the figure is shaded.

Hence, the total portion of the figures that are shaded are:

1+0.7=1.7

3 0

2 years ago

Read 2 more answers

Which point of intersection is the solution to the equations y = 2/5x-1/2 and y = -1/3x + 2/3?

abruzzese [7]

The answer is B because it is the only one where the line intersects on the y - axis at -1/2 and 2/3, which are the y -intercepts

7 0

2 years ago

Express 55 in standard form

Lynna [10]

Answer:5*11

Step-by-step explanation:

5 0

3 years ago

Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylin

sp2606 [1]

Answer:

3,451 cm³

Step-by-step explanation:

The ball is a sphere.

Formula for finding the volume of a sphere = ⁴/3*πr³

Volume of the 3 balls = 3(⁴/3*πr³)

Where,

radius (r) = ½ of diameter = ½(13) = 6.5 cm

Plug in the values into the formula:

Volume of the 3 balls = 3(⁴/3*π*6.5³)

= 4*π*274.625

= 3,451.03953 ≈ 3,451 cm³

3 0

2 years ago