Question 1 (a)A container holds V cm3 of a liquid where V = x2 + 3x and the height of the liquid in the container is x cm. More liquid is added such that the height of liquid increases at a constant rate of 0.02cm s-1. If the initial height of the liquid is 9.4 cm, find (i) the height of the liquid after 30s. (ii) the rate of increase of the volume at this instant. (b)Find the stationary points of the cubic equation, y = 2x3 – 3x2 – 12x + 7 and determine their nature.
Question 1 (a)A container holds V cm3 of a liquid where V = x2 + 3x and the height of the liquid in the container is x cm. More liquid is added such that the height of liquid increases at a constant rate of 0.02cm s-1. If the initial height of the liquid is 9.4 cm, find (i) the height of the liquid after 30s. (ii) the rate of increase of the volume at this instant. (b)Find the stationary points of the cubic equation, y = 2x3 – 3x2 – 12x + 7 and determine their nature.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 1
(a)A container holds V cm3 of a liquid where V = x2 + 3x and the height of the liquid in the container is x cm. More liquid is added such that the height of liquid increases at a constant rate of 0.02cm s-1. If the initial height of the liquid is 9.4 cm, find
(i) the height of the liquid after 30s.
(ii) the rate of increase of the volume at this instant.
(b)Find the stationary points of the cubic equation, y = 2x3 – 3x2 – 12x + 7 and determine their nature.
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