7. (12pts) Solve a right triangle ABC, if side a = 7, and hypotenuse c = 7/2.
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
1. (12pts) Solve the triangle AABC. a. Given A = 45°,b= V8, and c = 2 b. Given a = 10, A = 30°, and b = 24
7. Suppose U(X., X) = X.-X, (12pts) a. Solve for the marshallian demands for x, and X, as functions of p1, p2, and m. b. Is this an interior or corner solution? C. Is the budget exhausted here? Yes/no d. Assume that the above prices and income have all doubled. How does this change your solution in a?
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find bases for the four fundamental subspaces of the matrix A. Basis for n(A) = nullspace of A: Basis for N(4")= nullspace of A": Basis for col(A) = column space of A: Basis for col(A) = column space of A': () Give a vector space that is isomorphic to col (A) N(A).
4167%, 5 of 12pts 0 of 1 p P6-26 (similar to) 0
Solve the differential equations ?
Problems: Solve the following differential equations, 1) V1+x?.y?-3xV/y2 -1=0.
1) Solve the following exponential equations: a) 5+ (7).(34x-1) = 40 b) 2 + (4). (e2x+1) = 14 2) Solve the following logarithmic equations: a) log (4x + 1) = log,143 – log (4x - 1) b) 5+ (3). In(2x – 1) = 17 3) Solve the following non-linear system: x + y = 6 x2 + 5x - y = 10 4) y = f(x) = x2 – 4x – 12 is given. a) Find the Vertex b) Find...
1 (8+7 15 pts) Linear equations Consider the system of equations 1 -1 0 0 0 0 1 2-1 03 - 0 0 1 2 3 4 4 (a) Determine all values of a and b such that this system is 1 inconsistent (ii) consistent (b) Find the set of solutions for 1 a b 2.
Solve the following equations: (a) 5x + 2 = 7 (b) 6x + 5 = 3x + 11 (c) 2x - (1-3x) = 8x - 2(3x - 4)