Question

A particle is moving along the curve y=2*sqrt(5x+11). As the particle passes through the point (5,12) , its x -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant. I'm having trouble getting dy/dt and y

Answer 1

distance = sqrt (x^2 +y^2)
=sqrt (x^2 +(2*sqrt(5x+11))^2)

differentiate with respect to t...

Answer 2

Sounds like a related rates situation, right?

Answer 3

plug in dx/dt and x...

Answer 4

yes related rates

Answer 5

...simplify a bit and you're done:)

Answer 6

OK, good, I thought it was going to get all parametric and crap.
Looks like @Algebraic! laid the course for you well.

Answer 7

why would the y coordinate not be 12?

Answer 8

you mean just plug in y=12 into sqrt (x^2 +y^2) ?

Answer 9

yes

Answer 10

that would be easy but wrong:)

Answer 11

ok I calculated that y=72, so I'll try this......

Answer 12

what?

Answer 13

when finding y, do I plug in 5 for x for 2sqrt(5x+11)?

Answer 14

into 2sqrt(5x+11), i mean....

Answer 15

that's already been done for you. y=12

Answer 16

you should really try finding the derivative of:
sqrt (x^2 +(2*sqrt(5x+11))^2)

that's how you complete this problem.

Answer 17

simplify it a little and differentiate. use the chain rule. the derivative of 'x' leave as dx/dt

Answer 18

alright i'm going to try and start over

Answer 19

when i try to differentiate y=2sqrt(5x+11) i get 5(5x+11)^(-1/2) using the chain rule. This has to be what I keep getting wrong.

Answer 20

You need to differentiate that function WRT time because you need to know dy/dt

Answer 21

\[\frac{ d }{ dt } \sqrt{ (x^2 +(2*\sqrt(5x+11))^2)}) = \frac{ d }{ dt } \sqrt{ (x^2 +20x+44})\]
\[ \frac{ d }{ dt } \sqrt{ (x^2 +20x+44}) =\frac{ (2x+20)\frac{ dx }{ dt } }{2 \sqrt{ (x^2 +20x+44}) }\]

plug in values of x and dx/dt

Answer 22

the computer system must be wrong, i got that answer too. thank you for your patience and help

Answer 23

what did you get for the final answer?

Answer 24

2.307692308

Answer 25

30/13

Answer 26

it can be entered as a fraction or in radians, so yes, samething

Answer 27

\[y=2(5x+11)^{\frac{ 1 }{ 2 }}\]
\[\frac{ dy }{ dt }=5(5x+11)^{\frac{ -1 }{ 2 }}\frac{ dx }{ dt }\]
dx/dt = 2 (given), x=5

Solve for dy/dt. Then:

\[x ^{2}+y ^{2}=g ^{2}\]

Answer 28

Differentiate WRT time, solve for dg/dt, plug in values, and have a cigar.

Answer 29

Thank you!