Group 4: Alex, Problem G - LaPlace's Equation Lucas, du¸ du =0. əx əy Nicolas Determine if the function u(x, y) = e-2* sin(-4y) satisfies the equation. Problem H - Partial Derivatives Your monthly car payment in dollars is P = f(Po,t,r) where P, is the dollar amount you borrowed, t, is the number of months it takes to pay off the loan, and r percent is the interest rate. What is the sign of? What are the units? ar
Group 4: Alex, Problem G - LaPlace's Equation Lucas, du¸ du =0. əx əy Nicolas Determine if the function u(x, y) = e-2* sin(-4y) satisfies the equation. Problem H - Partial Derivatives Your monthly car payment in dollars is P = f(Po,t,r) where P, is the dollar amount you borrowed, t, is the number of months it takes to pay off the loan, and r percent is the interest rate. What is the sign of? What are the units? ar
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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![**Group 4: Alex, Lucas, Nicolas**
**Problem G - LaPlace's Equation**
\[
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0
\]
Determine if the function \( u(x, y) = e^{-2x} \sin(-4y) \) satisfies the equation.
---
**Problem H - Partial Derivatives**
Your monthly car payment in dollars is \( P = f(P_0, t, r) \) where \( P_0 \) is the dollar amount you borrowed, \( t \) is the number of months it takes to pay off the loan, and \( r \) percent is the interest rate.
What is the sign of \( \frac{\partial P}{\partial r} \)? What are the units?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddb72669-0680-48fe-8aa6-56d86c073f3c%2F24761042-5da6-4507-b0b9-9de9c089f919%2Fqa3369rfz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Group 4: Alex, Lucas, Nicolas**
**Problem G - LaPlace's Equation**
\[
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0
\]
Determine if the function \( u(x, y) = e^{-2x} \sin(-4y) \) satisfies the equation.
---
**Problem H - Partial Derivatives**
Your monthly car payment in dollars is \( P = f(P_0, t, r) \) where \( P_0 \) is the dollar amount you borrowed, \( t \) is the number of months it takes to pay off the loan, and \( r \) percent is the interest rate.
What is the sign of \( \frac{\partial P}{\partial r} \)? What are the units?
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