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**Question 1** *(7 minutes)* Given: \[ a^2 + b^3 + c^4 = 47 \] Find \(\frac{db}{dt}\) when \(a = 2\), \(c = 2\), \(\frac{da}{dt} = \frac{9}{2}\), \(\frac{dc}{dt} = \frac{9}{16}\). Options: - \(\frac{4}{3}\) - \(0\) - Not enough information to answer the question. - \(\frac{7}{2}\) - \(\frac{1}{2}\) **Note:** Moving to the next question prevents changes to this answer.

**Question 1** *(7 minutes)* Given: \[ a^2 + b^3 + c^4 = 47 \] Find \(\frac{db}{dt}\) when \(a = 2\), \(c = 2\), \(\frac{da}{dt} = \frac{9}{2}\), \(\frac{dc}{dt} = \frac{9}{16}\). Options: - \(\frac{4}{3}\) - \(0\) - Not enough information to answer the question. - \(\frac{7}{2}\) - \(\frac{1}{2}\) **Note:** Moving to the next question prevents changes to this answer.

Advanced Engineering Mathematics
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** *(7 minutes)* Given: \[ a^2 + b^3 + c^4 = 47 \] Find \(\frac{db}{dt}\) when \(a = 2\), \(c = 2\), \(\frac{da}{dt} = \frac{9}{2}\), \(\frac{dc}{dt} = \frac{9}{16}\). Options: - \(\frac{4}{3}\) - \(0\) - Not enough information to answer the question. - \(\frac{7}{2}\) - \(\frac{1}{2}\) **Note:** Moving to the next question prevents changes to this answer.
Transcribed Image Text:**Question 1** *(7 minutes)* Given: \[ a^2 + b^3 + c^4 = 47 \] Find \(\frac{db}{dt}\) when \(a = 2\), \(c = 2\), \(\frac{da}{dt} = \frac{9}{2}\), \(\frac{dc}{dt} = \frac{9}{16}\). Options: - \(\frac{4}{3}\) - \(0\) - Not enough information to answer the question. - \(\frac{7}{2}\) - \(\frac{1}{2}\) **Note:** Moving to the next question prevents changes to this answer.
Expert Solution
Step 1

Consider the information.

a2+b3+c4=47 and a=0,c=2,dadt=92,dcdt=916

Substitute the value of a and c in the given equation to find the value of b.

a2+b3+c4=4722+b3+24=47b3=47-16-4b3=27b=3

Thus, the value of b is 3.

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