dx As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation = 1x-0.005x2. dt (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x = 60 when t= 0, how long will it take for an additional 60 g of salt to dissolve?
dx As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation = 1x-0.005x2. dt (a) What is the maximum amount of the salt that will ever dissolve in the methanol? (b) If x = 60 when t= 0, how long will it take for an additional 60 g of salt to dissolve?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![dx
= 1x - 0.005x?.
As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation
(a) What is the maximum amount of the salt that will ever dissolve in the methanol?
(b) If x = 60 when t=0, how long will it take for an additional 60 g of sait to dissolve?
(a) The maximum amount of the salt that will ever dissolve in the methanol is
grams.
(Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F775b1934-3773-4786-a32d-c490024dee34%2Ff4aae56c-1e71-4406-9540-2852e8981ebd%2Fwjldw56_processed.jpeg&w=3840&q=75)
Transcribed Image Text:dx
= 1x - 0.005x?.
As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds satisfies the differential equation
(a) What is the maximum amount of the salt that will ever dissolve in the methanol?
(b) If x = 60 when t=0, how long will it take for an additional 60 g of sait to dissolve?
(a) The maximum amount of the salt that will ever dissolve in the methanol is
grams.
(Simplify your answer.)
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
Properties of derivative
Properties of integration
Second derivative test:
- Determine first derivative
- Find the critical point by equating derivative to zero
- Find the value of second derivative at the critical point then
- If second derivative is negative at the critical point then maxima
- If second derivative is positive at the critical point then minima
- If second derivative is zero then it is point of inflection
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