The rate at which the remainder of a substance dissolves in a small quantity of water is inversely proportional to the weight, w grams of the substance already dissolvod. Initially, there are 20 grams of the undissolved substance. Show that after Lime t scoonds, the eitestirn can be modelled by the difforential cquation (a) (20-w)= dt where k is a positive constant. Afler I second, 6 grams of the substance have disolved. Show that w- 36t Hence , find (0) (1) the weight of the substance remaining undissolved after 4 seconds. (ii) the time taken for 18 grams of the substance lo be dissolved.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Topic Video
Question

Show all working explaining detailly each step

Answer must be typewritten with a computer keyboard!

Answer Q3a

The rate at which the remainder of a substance dissolves in a small quantity of water is inversely
proportional to the weight, w grams of the substance already dissolved. Initially, there arc 20 grams
of the undissolved substance. Show that after lime t scoonds, the sinetinn can be modelled by the
differential equation
3.
(a)
-k
(20- w)=
dt
where k is a positive constant.
Afler I second, 6 grams of the substance have dissolved.
Show (hat w-36t
Hence, find
(1)
the weight of the substance remaining undissolved after 4 seconds.
(i)
the time taken for 18 grams of the substance to be dissolved.
(L)
A prarticle performs simple harmonic motion btween two points A and B which are 10 metres apart
on a horizontal straight line. Whcn the particle is 3 metres away from the centre, O, of the line AB,
its spced is 8ms'.
Find
(1)
the periodie time of the motion.
(ii)
the least timo required for the particle to move from B to the midpoint of OA.
Transcribed Image Text:The rate at which the remainder of a substance dissolves in a small quantity of water is inversely proportional to the weight, w grams of the substance already dissolved. Initially, there arc 20 grams of the undissolved substance. Show that after lime t scoonds, the sinetinn can be modelled by the differential equation 3. (a) -k (20- w)= dt where k is a positive constant. Afler I second, 6 grams of the substance have dissolved. Show (hat w-36t Hence, find (1) the weight of the substance remaining undissolved after 4 seconds. (i) the time taken for 18 grams of the substance to be dissolved. (L) A prarticle performs simple harmonic motion btween two points A and B which are 10 metres apart on a horizontal straight line. Whcn the particle is 3 metres away from the centre, O, of the line AB, its spced is 8ms'. Find (1) the periodie time of the motion. (ii) the least timo required for the particle to move from B to the midpoint of OA.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Propositional Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,