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9. Find the component form of the vector that starts at (3,-2) and ends at (-1,9). 10. If the terminal point of vis (4.7) and v = Ti - 13), find the initial point of v. 11. Find a imit vector in the same direction as 211 - 7. 12. Determine whether V and w are parallel. orthogonal, or neither. B. v= -2i+3j, w = -6i+9j A. V = 3i-57. w = 6i - 103 18 C. v = 3i...
5.3.6. Sum the following: (a) 2 + 3 + À +...+ , (b) 1 x 1!+2 x 2! +3 3! + ... + nxn!,
Let a × b = ⟨2, −1, 5⟩ and a × c = ⟨1, 4, 2⟩. (a) Find a × (a + b − c). (b) Find a · ⟨2, −1, 5⟩ and a · ⟨1, 4, 2⟩. (c) Find a unit vector parallel to a.
(6 points) Are the following statements true or false? 1. fi (a, b) is parallel to u 2.If iü is a unit vector, then fila, b) is a vector ? 3. Suppose f(a, b) and f(a, b) both exist. Then there is always a direction in which the rate of change of f at (a, b) is zero ?4.I f(x, y) has f. (a, b) 0 and f,(a, b) 0at the point (a, b), then f is constant everywhere |...
consider the linear system A^Tx =b where A^-1=[2,-1;3,4], b=[3;-1].then the solution vector x is 8. Consider the linear system ATX = b, where 4= 6'), =(-1) Then the solution vector x is (A) (15/11)
5. Find the vector 5 that is parallel to vector a = 27 -7 and has the length of 5. 6. Find the distance between two points (-1,-3,6) and (0,3,0). 7. Find the distance from the point (-5,3,-2) to a. the origin b. the x-axis c. the xz-plane 8. Let P; be the midpoint of the line segment between P.(-3,4,1) and P2(-5,8,3). Find the coordinate of the midpoint between P, and P3. 9. Knowing = (2,-3,1), 7 = (-2,0,5), and...
Skin color in frogs is determined by two alleles of gene B (BB and Bb=brown, bb=green). After a drought, 20 frogs remain in the pond. Their genotypes are: 9 BB, 10 Bb, 1 bb. If Hardy-Weinberg equilibrium is established in this new population, what would be the frequency of green frogs in the next generation? A. 0.04 B. 0.09 C. 0.3
Solve in MATLAB Problem 3: Given the vector x- [2 1 0 6 2 3 5 3 4 1 3 2 10 12 4 2 7 9 2 4 51 use a for loop to (a) Add up the values of all elements in x (b) Compute the cumulative sum, y, of elements in x You can check your results using the built-in functions sum and cumsum. Q.5 What is the value of the sum of elements in vector x?...
Exercise 5 Let us consider a market where 4 firms compete à la Bertrand. The demand function is given by q() = 250 - 7p. The cost function is the same for both firms and it is C(q) = 100; for all i E {1,2,3,4} • Write explicitly the demand and profit functions of 1, 2, 3, and 4. • Derive best reply functions and the Nash equilibrium of the game. (9) = 591, what • If firm 1 find...
Question 3 1 pts The color of chickens is determined by gene B, such that BB=black, Bb = gray, and bb = white. A second gene R controls comb shape, with dominant rose and recessive single comb. If a white single-combed chicken is mated with a gray chicken that is heterozygous for rose comb, what fraction of the offspring will be gray with rose comb? 1/4 9/16 1/8 O 3/8 1/16