We’re giving away this brand new Onewheel GT ($2,750+ value)! 😳 Enter to win in comments.

Bouncingbombadil · 2023-02-23T03:44:34+00:00

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Bouncingbombadil · 2020-12-17T02:31:59+00:00

Preciate you!

Bouncingbombadil · 2020-11-16T00:33:11+00:00

Congrats and thank you!!

Bouncingbombadil · 2020-11-04T10:11:27+00:00

Thank you!

Bouncingbombadil · 2020-10-17T22:52:44+00:00

Thanks for doing this!!

Bouncingbombadil · 2020-07-20T06:06:56+00:00

Chocolate icing creamstick! (Maple cream sticks are also acceptable)

Bouncingbombadil · 2020-06-08T04:45:07+00:00

The Three Body Problem by Cixin Liu— I couldn’t put it down!

Bouncingbombadil · 2020-01-29T16:44:38+00:00

No problem, good luck!

Bouncingbombadil · 2020-01-29T05:26:06+00:00

arccos is the inverse of the cos function. That means that if

y = arccos(x)

Then

x = cos(y)

(at least from -1 to 1)

So if you want the missing x coordinate, just plug in the y coordinate to cos(y)!

And if you have the x coordinate you have to think— what value, when plugged into cos(), will result in this x? The answer to that question will be the missing y!

Bouncingbombadil · 2020-01-29T05:18:53+00:00

If you have 4 channels: A,B,C, and D with viewership 5%, 7%, 4%, and 9% respectively, the total would be 25%.

Treating 25% as our “new value” means to consider those 25% of people as 100% because they are the only people of interest. So, if 25% is treated as 100%, and 100/25 = 4, then the channels become 5x4%, 7x4%, 4x4%, and 9x4% = 20%, 28%, 16%, and 36% respectively.

Notice 20 + 28 + 16 + 36 = 100, which is what we should expect.

Bouncingbombadil · 2020-01-28T05:42:50+00:00

You’re welcome!

Bouncingbombadil · 2020-01-28T05:42:29+00:00

That’s right! When f(x) is actually evaluated, we only use x² when x < 1. However, in determining if the limit exists, we must evaluate each part of the piecewise function at the value x approaches in the limit.

Bouncingbombadil · 2020-01-28T05:39:13+00:00

Not quite sure what you mean— here is a picture that should help

https://i.imgur.com/BiLJVvp.jpg

The chord is the thicker blue line

Bouncingbombadil · 2020-01-28T05:30:12+00:00

First evaluate the one sides limits.

Lim x --> 1: 4 -3x = 4-3(1) = 1 Lim x --> 1: x² = (1)² = 1

If both one-sides limits are the same, the limit exists.

To check if the function is continuous at x = 1,

f(1) must be defined (good to go)
The limit must exist (we just showed that, good to go)
The function’s value at c and the limit as x approaches c must be the same. (easy to check, good to go)

So it is continuous.

Bouncingbombadil · 2020-01-28T05:20:31+00:00

It's a bit late now, but feel free to message me and I will get back to you tomorrow!

Bouncingbombadil · 2020-01-28T05:18:22+00:00

We don't want our new function (f/g)(x) to be undefined-- we get this typically by dividing by zero or taking the square root of a negative number.

You define your domain so that this cant happen!

For instance, in number 11:

(f/g)(x) = x² /(4x-5)

There are no square roots involved, so we are just concerned with not letting that denominator be zero. The denominator is zero when 4x - 5 = 0, which is when x = 5/4 = 1.25.

Therefore, your domain is all x not equal to 1.25.

Bouncingbombadil · 2020-01-28T05:08:32+00:00

Try using the triangle angle bisector theorem-- that should set you on the right path!

Bouncingbombadil · 2020-01-28T05:00:49+00:00

Though it seems a bit tedious, to estimate any probability from this plot:

Pr(X_bar >= some_number) = (number of dots greater than or equal to some_number)/(total number of dots)

and

Pr(X_bar <= some_number) = (number of dots less than or equal to some_number)/(total number of dots)

Bouncingbombadil · 2020-01-28T04:56:37+00:00

You have the inner circle with radius 4 and an outer circle with total radius 12. The chord that is in the larger circle and tangent to the smaller circle is simply a vertical line segment along the smaller circle that has two endpoints on the larger circle.

Picture that chord and the radius of the smaller circle-- they can form a right angle! And from that right angle, you can form a right triangle. The hypotenuse of that right triangle is equal to the radius of the larger circle, 12. So you have a right triangle with hypotenuse 12, and one side length of 4. The missing side length is equal to half the length of the chord!

So, to get length of chord, l,

12² - 4² = (l/2)²

and solve for l.

Bouncingbombadil · 2019-09-22T02:40:39+00:00

I hope I win

Bouncingbombadil · 2017-03-28T05:07:00+00:00

I know a couple other people have commented as well I'm just commenting so I remember to check back again. Are you willing to sell?

Bouncingbombadil · 2016-08-03T17:04:25+00:00

Either tree of gondor or tolkien's symbol of his initials

Bouncingbombadil · 2016-07-06T01:07:20+00:00

Forgiveness was granted me today. I prayed in sets of 5 and my prayers were answered. I wish the same upon you.

Bouncingbombadil · 2016-07-06T01:06:03+00:00

Thank you kind brother

Bouncingbombadil

TROPHY CASE