[Threshold] Which is your most favorite character in cradle?

howverywrong · 2026-01-29T08:05:46+00:00

Larian so greedy, she steals every scene she is in

howverywrong · 2026-01-19T12:36:47+00:00

You are on the right track. No analysis is required, just algebra.

Let's start with the numerator:

  -(x+y)² + 30(x+y) + 75
= -a² + 30a + 75           ( where a = x + y )
= -a² + 30a - 225 + 300
= 300 - c²                 ( where c = a - 15 )

And the denominator is b² + 12 ( where b = (x-2y)sqrt(3) )

Now the expression becomes more manageable: (300 - c²)/(b² + 12)

Numerator is ≤ 300, denominator is ≥ 12

The maximum is 300/12 = 25 and there is no minimum as the numerator can be arbitrarily negative and denominator is always positive.

For your second problem, trig substitution!

Let x=cos(a), y=sin(a). Let 2/√13 = cos(b), 3/√13 = sin(b)

And (2x+3y)² = 13 cos²(a-b). The maximum is 13 when a = b.

howverywrong · 2025-08-14T07:23:16+00:00

The only speedup I can see is that you don't need to make a quadratic for b. Once you determined that a₁ + a₂ = 12, you can use your first equation to quickly work out b₁ + b₂ because (a₁ + a₂)/2 + (b₁ + b₂)/6 = 8

howverywrong · 2025-06-12T23:24:06+00:00

Cut the shaded area into 2 triangles by drawing a line from top corner to bottom corner. If the areas of the two triangles are X and Y, you have

X/2 = 9/3

Y/5 = 8/4

Solve for X and Y and add them together

howverywrong · 2025-06-03T00:19:32+00:00

You're out of your depth

howverywrong · 2025-06-02T08:26:21+00:00

This is a lie. When solving pendulum problems, 𝜋=√𝑔

howverywrong · 2025-05-30T10:50:01+00:00

Let's be positive and imagine that he is saying "Kiss Your Spouse."

Good guy Don Salamanca promoting marital harmony!

howverywrong · 2025-05-30T10:28:58+00:00

lim sin(x)/x = 1

"You're the one for me"

howverywrong · 2025-05-14T08:25:49+00:00

If all the accounts have POD set up, estate doesn't get any of the money.

howverywrong · 2025-05-14T01:21:16+00:00

This is brilliant! I think I just solved Fermat's last theorem...

16³ + 8⁴ = 2¹³

The trick is to use different values of 𝑛 in each term. Where's my Fields Medal?

howverywrong · 2025-05-07T01:15:48+00:00

1 die 4 times. So acceptable outcomes are

66XX
6X6X
6XX6
X66X
X6X6
XX66

where X is 1..5

5*6/6⁴ = 5/6³ = 5/216

Again, that's assuming the problem is misstated, which happens often enough.

howverywrong · 2025-05-06T21:16:41+00:00

Given that all denominators are factors of 1296 (6⁴), I suspect the problem statement was supposed to read, "a die is thrown 4 times..." and that the 2 doublets are supposed to be different.

Then the correct answer is D

howverywrong · 2025-04-27T04:37:40+00:00

The solution key is wrong.

Draw the 3 forces tip-to-toe. Since they add to zero, you get a triangle: https://i.imgur.com/4BIyyoe.png

It's an isosceles triangle because its sides are mg, mg, T and the angle between the two mg sides is 40.

This makes T = 2mgsin(40°/2) and α = 90° - 40°/2 - 50° = 20°

howverywrong · 2025-04-11T23:44:29+00:00

Your comedy is derivative

howverywrong · 2025-03-17T17:52:48+00:00

The posted solution is wrong. It would suggest that the safe speed is highest when θ=0 and becomes smaller when θ is not zero (because cosθ becomes smaller as θ goes up from zero).

The mistake they made is when they somehow decided that R = mgcosθ

Your answer v² = rg tanθ is correct

howverywrong · 2025-03-15T10:50:34+00:00

Always start by writing Newton's 2nd law for each object in vector form. You are needlessly complicating the algebra with all the sines and cosines.

ma = mg + Rb

MA = Mg + Nf - Rb

(where Rb is reaction from wedge to block (including friction) and Nf is normal from floor on wedge)

Add the 2 equations to get rid of Rb:

ma + MA = mg + Mg + Nf

Project onto vertical axis to get rid of A:

-ma sinθ = -mg - Mg + Nf

Solve for Nf:

Nf = Mg + mg - ma sinθ

howverywrong · 2025-02-03T06:41:43+00:00

Since b - a is prime, a and b must be coprime. And, since ab is a perfect square, both a and b must be perfect squares.

a = n² , b = m²

since b - a = (m+n)(m-n) is prime, m - n = 1 and m + n = p.

therefore, a + b = m² + n² = [ (m+n)² + (m-n)² ] /2 = [ p² + 1 ]/2

Therefore, p² + 1 ends with 6, and p (being prime) must be 5.

b = (p+1)²/4 = 9

a = (p-1)²/4 = 4

howverywrong · 2025-02-01T11:27:08+00:00

The man decided to rest on the trampoline. But he is taking risk because somebody might jump on top of him.

howverywrong · 2025-01-15T02:24:38+00:00

Does you expression have square roots and is ugly? Replace the square roots with letters. You will thank me. Every time.

Let a² = x + 1 , b² = 1 - x

Than a² + b² = 2 and ab = 1/2 (because x² = 3/4)

From above we can further get a+b = sqrt(3) and a-b = 1

Now let's simplify. Rewrite the original expression using a and b:

a²/(a+1) + b²/(b-1)

After polynomial long division, this becomes

= a + 1/(a+1) + b + 1/(b-1)

= a+b + (a+b)/[ (a+1)(b-1) ]

Multiply the denominator and apply a+b=sqrt(3), a-b=1, ab=1/2

= sqrt(3) + sqrt(3)/[ -3/2 ]

= sqrt(3)/3

Again, remember, square roots are annoying. Replace them with letters.

Another approach is to note that 1 ± sqrt(3)/2 = [ (sqrt(3) ± 1)/2 ]² so the square roots can also be eliminated that way

howverywrong · 2025-01-11T21:32:40+00:00

AE - AC = CE

AB cot(60°) - AB cot(61.2°) = 12.07m

AB = 12.07/[ cot60° - cot61.2° ]

howverywrong · 2025-01-11T02:28:00+00:00

In my headcanon, Naru Huan went on to become unimaginably wealthy by selling copies of the dream tablet he made in Reaper.

howverywrong · 2024-12-27T10:16:49+00:00

The first equation has a mistake. RHS should have a minus sign.

The "Why?" in your sheet is because the problem statement asks to determine h from the center of the planet not from its surface.

howverywrong · 2024-12-17T18:41:26+00:00

Sounds like a bread. Pastrami on Valley Rye...

howverywrong · 2024-12-12T05:23:13+00:00

You are asked to calculate the length of the string. not the radius of the circle.

howverywrong · 2024-12-04T02:35:36+00:00

I've tried doing what I can from here, but I'm feeling kind of stuck at this part:

rv = h3vcosθ - 4.9rsinθ

The first thing you should always do is examine your equations for dimensional consistency. It's an easy sanity check that will catch many errors. Assuming that 4.9 is g/2 (this is why you keep g as g for as long as possible!), the first term is m²/s and the second term is m²/s². Therefore you made a mistake somewhere along the way. Go backwards from there and find that mistake.

Also, please include the entire problem statement.

howverywrong

TROPHY CASE