Expert: Paul Klarreich - 3/30/2008

Question
QUESTION: hi,

A circular oil slick is expanding on the water such that its area is increasing at a rate of 500m^2/min.

a)express the area as a function of time
b) express the radius, r, as a function of it's radius
c) determine a formula for r follows A (roA) and explain what it means
d) what is the radius after 1h

Im just having troubles on a and b. thanks

ANSWER: Questioner:   khakeel
Category:  Advanced Math
Private:  No
 
Subject:  composite functions
Question:  hi,

A circular oil slick is expanding on the water such that its area is increasing at a rate of 500m^2/min.

a) express the area as a function of time
b) express the radius, r, as a function of it's radius
c) determine a formula for r follows A (roA) and explain what it means
d) what is the radius after 1h

Im just having troubles on a and b. thanks
.................................
Hi, Khakeel,

This is a Related Rates example. [Look them up in the Archives.]

a) IF dA/dt = 500, then  A = 500t + A(0).
Presumably, at t = 0, A = 0, so that's it -- A = 500t

b) If you meant what you said, then   r = r  is the answer.

NEXT TIME, PROOFREAD YOUR QUESTION.


---------- FOLLOW-UP ----------

QUESTION: sorry I meant

b) express the radius as a function of its Area

Answer
Questioner:  khaleel
Private: no
Subject:   

 
Question:  
QUESTION: hi,

A circular oil slick is expanding on the water such that its area is increasing at a rate of 500m^2/min.

a)express the area as a function of time
b) express the radius, r, as a function of it's radius
c) determine a formula for r follows A (roA) and explain what it means
d) what is the radius after 1h

Im just having troubles on a and b. thanks

ANSWER: Questioner:   khakeel
Category:  Advanced Math
Private:  No

Subject:  composite functions
Question:  hi,

A circular oil slick is expanding on the water such that its area is increasing at a rate of 500m^2/min.

a) express the area as a function of time
b) express the radius, r, as a function of it's radius
c) determine a formula for r follows A (roA) and explain what it means
d) what is the radius after 1h

Im just having troubles on a and b. thanks
.................................
Hi, Khaleel,

This is a Related Rates example. [Look them up in the Archives.]

a) IF dA/dt = 500, then  A = 500t + A(0).
Presumably, at t = 0, A = 0, so that's it -- A = 500t

b) If you meant what you said, then   r = r  is the answer.

NEXT TIME, PROOFREAD YOUR QUESTION.


---------- FOLLOW-UP ----------

QUESTION: sorry I meant

b) express the radius as a function of its Area

................................
Well, if that's all you need, since  A = pi r^2,

r = sqrt(A/pi)