Question Detail

MTH 102 Differentiation Objective Question
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Question

A soap bubble volume decreases at 6 cm^3/sec. Formula \( V = (p - qt)^2 \). At \( t=1, V=9 \). Find \( p \) and \( q \).
Options
A p=4, q=1
Correct Answer
B p=3, q=2
C p=5, q=1
D p=2, q=3
Correct Answer

Option A is the correct answer.

Detailed Explanation

( V(1)=9 \implies (p-q)^2 = 9 \implies p-q = 3 ) or ( -3 ). ( dV/dt = 2(p-qt)(-q) ). At ( t=1, -6 = 2(p-q)(-q) ). If ( p-q=3 ), then ( -6 = 2(3)(-q) \implies q=1 ). Then ( p=4 ).

Hint

Differentiate with respect to time and solve the system of equations.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 188 of 930
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