Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Luigi0210 Group Title

A particle travels along the curve y= sqrt(x+4) a.) how far is the particle closet to the point (6,0) b.) How far is it from (6,0) at the moment?

  • one year ago
  • one year ago

  • This Question is Closed
  1. ZeHanz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You could write the distance of a point P(p, sqrt(p+4)) to (6,0) as a function, and try to calculate the minimum of that function using the derivative. Here is hou it would look: \[d(p)= \sqrt{(p-6)²+(\sqrt{p-4}-0)^2}=\sqrt{(p-6)^2-(p-4)}\]However, the root makes it more difficult. But if you realize d(p) is minimal if the number under the root sign has its minimum, you can focus on just that one. So define the following function: f(p)=(p-6)²-(p-4)=p²-12p+36-p+4 So f(p)=p²-13p+40. Where f has its minumum, just calculate the root of that p to find the minimal distance.

    • one year ago
  2. ZeHanz Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    f'(p)=2p-13=0, so p=6½. The minimum distance would then be \[\sqrt{\frac{ 13 }{ 2 }}=\frac{ \sqrt{13} }{ \sqrt{2} }=...=\frac{ 1 }{ 2 }\sqrt{26}\]

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.