Problem 4. Solve the equation utt=c2uxx+sinx For 0≤x≤π and t>0, with the boundary conditions u(0,t)=1,ut(π,t)=2, and the initial conditions u(x,0)=f(x),ut(x,0)=g(x).Hint: Make the change of coordinates u(x,t)=y(x)+v(x,t), where y(x) satisfiesc2y′′+sinx=0, y(0)=1, and y(π)=2. Find y.What will be the PDE for 0≤x≤π0 ?What are the (boundary and initial) conditions for 0≤x≤π0 ? Get tutor helpf(x)=(x−2)(x+4)(x+5)(x−1)(x−9) has zeros at x=−5,x=−4,x=1,x=2, and x=9.What is the sign of f on the interval −4<x<1 ?Choose 1 answer:(A) f is always positive on the interval.(B) f is always negative on the interval.(C) f is sometimes positive and sometimes negative on the interval. Get tutor helpSection 8.4−8.6: Area Btwn Two Curves Worksheet**NON-CALC QUESTIONS**For questions 1−3, sketch the region bounded by the graphs of the given functions and find the area 0 the region.1. f(x)=−x2+4x+2,g(x)=x+22. g(x)=2−x4,y=4,x=03. y=x21,y=0,x=1,x=54. Find the area bounded by the given functions (as shown in the graph below) with respect to y.x=4−y2,x=y−2 Get tutor helpThis question: 1 point(s) possibleSolve the system of equations. If the system has no solution, say that it is inconsistent.\begin{cases}3x-4y=-4\5x+y=24\end{cases}Select the correct choice below and, if necessary, fill in any answer boxes within your choice.A. The solution of the system is x=□ and y=□.(Type an integers or simplified fractions.)B. There are infinitely many solutions. Using ordered pairs, the solution can be written as {(x,y)∣x=□,y any real number }. (Simplify your answer. Type an expression using y as the variable as needed.)C. The system is inconsistent. Get tutor help