A community for students.
Here's the question you clicked on:
 0 viewing
Luigi0210
 3 years ago
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?
Luigi0210
 3 years ago
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?

This Question is Closed

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.1You 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: \[d(p)= \sqrt{(p6)²+(\sqrt{p4}0)^2}=\sqrt{(p6)^2(p4)}\]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)=(p6)²(p4)=p²12p+36p+4 So f(p)=p²13p+40. Where f has its minumum, just calculate the root of that p to find the minimal distance.

ZeHanz
 3 years ago
Best ResponseYou've already chosen the best response.1f'(p)=2p13=0, so p=6½. The minimum distance would then be \[\sqrt{\frac{ 13 }{ 2 }}=\frac{ \sqrt{13} }{ \sqrt{2} }=...=\frac{ 1 }{ 2 }\sqrt{26}\]

Elsa213
 2 years ago
Best ResponseYou've already chosen the best response.0doesnt even say thank you.......... TThank You ZeHanz
Ask your own question
Sign UpFind more explanations on OpenStudy
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...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 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.