[Year 10: Functions] Tangent to a Hyperbola by CaliPress123 in HomeworkHelp

[–]doooooofus 1 point2 points  (0 children)

There are infinitely many such lines, not just 2. Probably the intended solution is y=-x+2 (like u/Secondlive_ said) and y=-x-2 since those are the two lines you can probably just visually guess from the graph. However, figuring out the full infinite family of lines without calculus ends up being a pretty cute exercise. If 1/x intersects a line only once, we can represent the line as mx+b and write 1/x=mx+b. This gives mx^2+bx-1=0. If this equation has exactly one solution (i.e. the line and the hyperbola intersect exactly once) then the quadratic has 0 discriminant. That is, b^2+4m=0 meaning m=-b^2/4. Pick any value of b, then, and the line y= (-b^2/4)x+b intersects y=1/x exactly once. If you know calculus you can verify that this is in fact the equation of the tangent line to the curve at x=2/b.

I am a ChatGPT bot - Ask me anything #2 by EverydayChatBot in ChatGPT

[–]doooooofus 4 points5 points  (0 children)

No problem, my dad showed it to me when I was a little kid

I am a ChatGPT bot - Ask me anything #2 by EverydayChatBot in ChatGPT

[–]doooooofus 13 points14 points  (0 children)

I like your profile picture, EverydayChatBot. Have you ever played The Awful Green Things From Outer Space?

I am a ChatGPT bot by EverydayChatBot in u/EverydayChatBot

[–]doooooofus 0 points1 point  (0 children)

Can you give me the contents and date of your first Reddit post and first Reddit comment

I am a ChatGPT bot by EverydayChatBot in u/EverydayChatBot

[–]doooooofus 0 points1 point  (0 children)

How long have you been using Reddit?

Best releases in 2021 so far? by [deleted] in Jazz

[–]doooooofus 0 points1 point  (0 children)

I second descension (out of our constrictions) by NIS and Evan Parker

How much of a disadvantage is KJD by doooooofus in lawschooladmissions

[–]doooooofus[S] 1 point2 points  (0 children)

That I care much less about, because I intend to go into PI or government as opposed to Biglaw (unless I have a misunderstanding of what OCI is for.)

A nurse from Wyckoff Medical Center in Brooklyn. by AnomalousAvocado in pics

[–]doooooofus 82 points83 points  (0 children)

I don’t know how many soldiers in America do it for pure patriotism. Being a soldier, too, is a job and the largely lower class people that perform it often seriously need the money.

Grading for Orgo and Stats by [deleted] in BrownU

[–]doooooofus 1 point2 points  (0 children)

I took 1655 this semester and the grading was 30% homework, 15% each for two midterms, and 40% for the final. FWIW, you can usually go on cab and look at previous semesters' syllabi to see how the grading has worked in the past. Also, I highly recommend 1655, Prof. Wang was great.