related rates with square roots
$begingroup$
A particle is moving along the curve $y=2sqrt{5x+11}$. 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 got $frac{298}{13}$ which is incorrect. I think what I am having the most trouble with is finding the $frac{dy}{dt}$ value.
calculus
edited Jan 25 at 2:51
NolantheNerd
134
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
$endgroup$
add a comment |
$begingroup$
A particle is moving along the curve $y=2sqrt{5x+11}$. 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 got $frac{298}{13}$ which is incorrect. I think what I am having the most trouble with is finding the $frac{dy}{dt}$ value.
calculus
edited Jan 25 at 2:51
NolantheNerd
134
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
$endgroup$
3
$begingroup$
try to include your attempt so that we can point out your mistake?
$endgroup$
– Siong Thye Goh
Jan 25 at 2:20
add a comment |
$begingroup$
A particle is moving along the curve $y=2sqrt{5x+11}$. 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 got $frac{298}{13}$ which is incorrect. I think what I am having the most trouble with is finding the $frac{dy}{dt}$ value.
calculus
edited Jan 25 at 2:51
NolantheNerd
134
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
$endgroup$
A particle is moving along the curve $y=2sqrt{5x+11}$. 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 got $frac{298}{13}$ which is incorrect. I think what I am having the most trouble with is finding the $frac{dy}{dt}$ value.
calculus
calculus
edited Jan 25 at 2:51
NolantheNerd
134
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
edited Jan 25 at 2:51
NolantheNerd
134
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
edited Jan 25 at 2:51
NolantheNerd
134
edited Jan 25 at 2:51
NolantheNerd
134
edited Jan 25 at 2:51
NolantheNerd
134
134
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
asked Jan 25 at 2:18
Caroline ArnsCaroline Arns
6
6
3
$begingroup$
try to include your attempt so that we can point out your mistake?
$endgroup$
– Siong Thye Goh
Jan 25 at 2:20
add a comment |
3
$begingroup$
try to include your attempt so that we can point out your mistake?
$endgroup$
– Siong Thye Goh
Jan 25 at 2:20
3
3
$begingroup$
try to include your attempt so that we can point out your mistake?
$endgroup$
– Siong Thye Goh
Jan 25 at 2:20
$begingroup$
try to include your attempt so that we can point out your mistake?
$endgroup$
– Siong Thye Goh
Jan 25 at 2:20
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Find r, the rate of change for the y axis and calculate the magnitude of the sum of those two vectors, $sqrt{r^2 + 2^2}$.
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
$endgroup$
add a comment |
$begingroup$
You are given $frac{dx}{dt}$. You need $frac{dsqrt{x^2+y^2}}{dt}=frac{1}{sqrt{x^2+y^2}}left(xfrac{dx}{dt}+yfrac{dy}{dt}right)$ You want $frac{dy}{dt}$ to be able to continue. You can compute $frac{dy}{dx}$ and you know $frac{dx}{dt}$. Can you put this together?
answered Jan 25 at 7:58
orionorion
13.7k11837
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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active
oldest
votes
$begingroup$
Find r, the rate of change for the y axis and calculate the magnitude of the sum of those two vectors, $sqrt{r^2 + 2^2}$.
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
$endgroup$
add a comment |
$begingroup$
Find r, the rate of change for the y axis and calculate the magnitude of the sum of those two vectors, $sqrt{r^2 + 2^2}$.
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
$endgroup$
add a comment |
$begingroup$
Find r, the rate of change for the y axis and calculate the magnitude of the sum of those two vectors, $sqrt{r^2 + 2^2}$.
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
$endgroup$
Find r, the rate of change for the y axis and calculate the magnitude of the sum of those two vectors, $sqrt{r^2 + 2^2}$.
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
edited Jan 25 at 5:54
Lord Shark the Unknown
106k1161133
106k1161133
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
answered Jan 25 at 4:53
William ElliotWilliam Elliot
8,6222720
8,6222720
add a comment |
add a comment |
$begingroup$
You are given $frac{dx}{dt}$. You need $frac{dsqrt{x^2+y^2}}{dt}=frac{1}{sqrt{x^2+y^2}}left(xfrac{dx}{dt}+yfrac{dy}{dt}right)$ You want $frac{dy}{dt}$ to be able to continue. You can compute $frac{dy}{dx}$ and you know $frac{dx}{dt}$. Can you put this together?
answered Jan 25 at 7:58
orionorion
13.7k11837
$endgroup$
add a comment |
$begingroup$
You are given $frac{dx}{dt}$. You need $frac{dsqrt{x^2+y^2}}{dt}=frac{1}{sqrt{x^2+y^2}}left(xfrac{dx}{dt}+yfrac{dy}{dt}right)$ You want $frac{dy}{dt}$ to be able to continue. You can compute $frac{dy}{dx}$ and you know $frac{dx}{dt}$. Can you put this together?
answered Jan 25 at 7:58
orionorion
13.7k11837
$endgroup$
add a comment |
$begingroup$
You are given $frac{dx}{dt}$. You need $frac{dsqrt{x^2+y^2}}{dt}=frac{1}{sqrt{x^2+y^2}}left(xfrac{dx}{dt}+yfrac{dy}{dt}right)$ You want $frac{dy}{dt}$ to be able to continue. You can compute $frac{dy}{dx}$ and you know $frac{dx}{dt}$. Can you put this together?
answered Jan 25 at 7:58
orionorion
13.7k11837
$endgroup$
You are given $frac{dx}{dt}$. You need $frac{dsqrt{x^2+y^2}}{dt}=frac{1}{sqrt{x^2+y^2}}left(xfrac{dx}{dt}+yfrac{dy}{dt}right)$ You want $frac{dy}{dt}$ to be able to continue. You can compute $frac{dy}{dx}$ and you know $frac{dx}{dt}$. Can you put this together?
answered Jan 25 at 7:58
orionorion
13.7k11837
answered Jan 25 at 7:58
orionorion
13.7k11837
answered Jan 25 at 7:58
orionorion
13.7k11837
answered Jan 25 at 7:58
orionorion
13.7k11837
13.7k11837
add a comment |
add a comment |
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try to include your attempt so that we can point out your mistake?
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– Siong Thye Goh
Jan 25 at 2:20