Mathematics Asked on January 5, 2022

Came across a problem on social media,

Find the area of the region bounded by a parabola, $y = x^2 + 6$ and

line a line $y = 2x + 1$.

I tried to draw it on paper and they didn’t seem to intersect. So I drew them online (attached screenshot). My answer was 0, but someone said that we assume they meet at infinity and answer would be infinity. Parallel lines don’t diverge like these do, so I think we can assume that they would never interest at infinity.

$$x^2 + 6 = 2x + 1$$ $$x^2 - 2x + 5$$ $$frac{2 pm sqrt{4 - 4(5)}}{2}$$

As you can see by analyzing the discriminant, this quadratic has no real roots, so there are no points at which the two curves intersect. You could say that the area between the curves tends to infinity. As was stated in the comments, whoever posted this most likely intended to include more information/restrictions.

Also, these two curves will not "meet at infinity." Both diverge as $x$ gets arbitrarily large

Answered by N. Bar on January 5, 2022

0 Asked on August 13, 2020 by user_hello1

3 Asked on August 12, 2020 by yudop

1 Asked on August 12, 2020 by abhijeet-vats

1 Asked on August 11, 2020 by gfr

abstract algebra book recommendation homological algebra reference request

1 Asked on August 8, 2020 by m1996rg

0 Asked on August 7, 2020 by david-warren-katz

0 Asked on August 6, 2020 by yaniv765

1 Asked on August 5, 2020 by roi_saumon

4 Asked on August 5, 2020 by dharmendra-singh

1 Asked on August 4, 2020 by w-mu

differential geometry geodesic riemannian geometry smooth manifolds

1 Asked on August 4, 2020 by hash-man

1 Asked on August 3, 2020 by ifn47

2 Asked on August 3, 2020 by 2132123

1 Asked on August 3, 2020 by user

calculus of variations euler lagrange equation functional analysis reference request

1 Asked on August 2, 2020

cyclotomic polynomials elementary number theory primality test prime numbers

1 Asked on July 31, 2020 by twentyyears

1 Asked on July 30, 2020 by pea-terzi

elementary number theory examples counterexamples prime numbers

2 Asked on July 28, 2020 by lucas

Get help from others!

Recent Answers

- haakon.io on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- Peter Machado on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP