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.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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.
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning