Solve the following equations. Be sure to check the potential solution(s) in the original equation, to see whether it (they) are in the domain. (a) log, (r² – x– 2) = 2
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- given the following equation x2 = 16 O a. (+4,-2) O b. (+2,-4) O c. No Solution O d. (+4,-4)A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution with 1/5 pound of salt per gallon is added to the tank at 10 gal/min, and the resulting mixture is drained out at 5 gal/min. Let Q(t) denote the quantity (lbs) of salt at time t (min). (a) Write a differential equation for Q(t) which is valid up until the point at which the tank overflows. Q' (t) = = (b) Find the quantity of salt in the tank as it's about to overflow. esc C ✓ % 1 1 a 2 W S # 3 e d $ 4 f 5 rt 99 6 y & 7 h O u * 00 8 O 1 9 1 OFor an object of mass m=3 kg to slide without friction up the rise of height h=1 m shown, it must have a minimum initial kinetic energy (in J) of: h O a. 40 O b. 20 O c. 30 O d. 10
- Q4: Write the parametric equation of revolution surface in matrix form only which generated by rotate a Bezier curve defined by the coefficient parameter in one plane only, for the x-axis [0,5, 10,4], y-axis [1,4,2,2] respectively, for u-0.5 and 0 = 45° Note: [the rotation about y-axis].• Suppose that we want to find a solution of the equation sin² (2) + 1-2x = 0, on the interval [0, π/2]. Is there a solution of the equation in this interval? How do you know?Problem 3 In class, we solved for the vorticity distribution for a "real" line vortex diffusing in a viscous fluid. Integrate this vorticity distribution to find the tangential velocity as a function of radius. Plot the velocity distributions for a a line vortex of circulation 0.5 mls in 20 °C air for times of 1, 10, and 100 seconds.
- please answer 1(a) and 1(d) also, please show workVerify that each function is an "eigenfunction" for the given linear operator, and determine it's eigenvalue. (a) First derivative; f(x) = e³x (b) Second derivative; g(x) = sin(2x)2. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):