Lesson 6.1 (10 points) • Solve each proportion for x. Show your work and mark your...
Solve the following problems. Show your work clearly. Q1. (10+10+5=25 points) a) Find the gradient of the function f(x, y) = 3x2 – 2xy + 2y and calculate it at (-1,1). b) Calculate the directional derivative of f(x,y) = 3x2 - 2xy + 2y at the point (-1,1) in the direction of the vector v =< -2,2> c) After solving part (a), if the vector in part (b) was given as v =< 1,0 > could you find the derivative...
Clearly show work and explain each step needed to solve 10. If Vs = 30 V, and is = 4 A, determine the power associated with the current source. OSレ Answer: The current source is supplying 120 Watts.
just problem number 4 please! thank you! There are ten problems totaling 10 points. Show all your work! 1-4 For each system below, (a) solve the initial v stability of the critical point at (0,0) 1. alue problem, and (b) determine the type and x' =-4x1 + 5x2 X2,--5x1 + 4x2 x1(0) -16, x2(0) 25. x'= 6x1 + x2 x1(0) 6, X2(0) = 4 2. xi(12345e) 55, X2(12345e)--729 3 xi-43x Xi(-101) = 9, x2(-101) 5 4 x' = 2x1-x2 x2,=...
Solve for x Show your work 7 = 4 10
questions 9-12 Solve each proportion. Round your answers to the nearest hundredth. 9) 7.7 3.6=2.3b 10) v 4.9=5.4 6.1 11) 6.3x -2.56 9.3 12) 3.4x 2.17 7.7
6. Choose one problem, mark it, and solve it. (10 points) Find the closest point to y in the subspace W spanned by v, and v2. (8 points) Is the set of following vectors an orthogonal set of vectors? Justify your answer.
Solve the following problems. Show your work clearly. Question 1 (25 points): Let f(x) = x5: (A)Determine whether fis one-to-one by using a geometric method. (B)“The inverse function of f(x) = xs is equal to the inverse function of f(x) = x5 +6" Is this statement true or false? Justify your solution steps. (C) Solve the equation ex®+6 = 7. Determine whether the solution changes or not when ex* = 7. Compare your solution steps by using the properties of...
how to solve this?! Section III Longer Problems (4 points each - 68 points total). Show your work. 1. Consider Mary's utility function u(x1, +2) = [min{2x1, x2}]} (a) Draw Mary's indifference curve that yields u = 1 and u = 2. Mark the kink clearly. (b) Derive Mary's optimal demand function for each of the goods, i.e., find ai (P. P. m) and (P1, P2, m). (C) If Pi = 1, P2 = 1 and m 6, what is...
1. Choose one problem, mark it, and solve it. (10 points) A scientist solves a nonhomogeneous system of ten linear equations in twelve unknowns and finds that three of the unknowns are free variables. Can the scientist be certain that, if the right sides of the equations are changed, the new nonhomogeneous system will have a solution? Justify your answer. (8 points) If a 6 x 4 matrix A has rank 2, find dim NulĄ and dim RowA.
QUESTION 10 Evaluate the follow integral on notebook paper: ſsin(x) cos-2(x) dx Show all work for full credit. Clearly mark your answer.