Asked by Annonymous
A particle moves along the graph of the function y= 8/3x^(3/2) at the constant
rate of 3 units per minute. The particle starts at the point where x = 1 and travels in the
direction of increasing x. After one hour, what is the x-value, rounded to the nearest
hundredth, of the point of the location of the particle?
rate of 3 units per minute. The particle starts at the point where x = 1 and travels in the
direction of increasing x. After one hour, what is the x-value, rounded to the nearest
hundredth, of the point of the location of the particle?
Answers
Answered by
Steve
y = 8/(3x^(3/2))
y' = -4/x^(5/2)
so, the arc length involved is
∫[1,h] √(1+16/x^5) dx
Hmmm. I suspect you meant
y = 8/3 x^(3/2)
y' = 4√x
∫[1,h] √(1+16x^2) dx
Using the trig substitution 4x = sinhθ, that integral is
s = x/2 √(1+16x^2) + 1/8 sinh(4x)
we want s(x) - s(1) = 180
s(1) = 5.47279
I don't know of any method except graphical or numeric to find when s(x)=185.47279, but wolframalpha says it's when
x = 1.9879
y' = -4/x^(5/2)
so, the arc length involved is
∫[1,h] √(1+16/x^5) dx
Hmmm. I suspect you meant
y = 8/3 x^(3/2)
y' = 4√x
∫[1,h] √(1+16x^2) dx
Using the trig substitution 4x = sinhθ, that integral is
s = x/2 √(1+16x^2) + 1/8 sinh(4x)
we want s(x) - s(1) = 180
s(1) = 5.47279
I don't know of any method except graphical or numeric to find when s(x)=185.47279, but wolframalpha says it's when
x = 1.9879
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.