Problem #2: Given f(x,y) = point (1, 1)? + 4xy, which of the following vectors points in the direction of steepest ascent at the (A) (7,-16) (B) (16,7) (C) (-16, 7) (D) (7,16) (E) (3, 32)
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- Suppose that you are in the garden supply business. Naturally, one of the things that you sell is fertilizer. You have three brands available: Vigoro, Parker's, and Bleyer's. The amount of nitrogen, phosphoric acid, and potash per 100 pounds for each brand is given by the nutrient vectors T(x) = 2 ---A 32 p= b= = 11 Parker's Bleyer's T-¹(y) = V= T-1 7 66 Vigoro Determine the linear transformation T: R³ R³ that takes a vector of brand amounts (in hundreds of pounds) as input and gives the nutrient vector as output. Then find a formula for T-1, and use it to determine the amount of Vigoro, Parker's, and Bleyer's required to produce 44 pounds of nitrogen, 200 pounds of phosphoric acid and 412 pounds of potash. 44 (1)- 412 X 11 2 23 yProblem #2: Given f(x,y) = x³y2 + 4xy2, which of the following vectors points in the direction of steepest ascent at the point (1, 1)? (A) (9, 10) (B) (-10,9) (C) (10,9) (D) (5, 8) (E) (9,-10)Using the inverses of the previous problem, find the solution of Ax = b and Bx = c for the vectors b = (3, 2, 1, 1, 4)^T and c = (1, 2, 1)^T , respectively.
- Graph the two vectors x= (5, 1,3) and y=(-1,3,1The equation r(t) = (3t + 5) i+ (4t - 5) j+ (4t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t=0 as a product of its speed and direction. What is the velocity vector? v(t) = ( 3) i+ ( 8t) j+ (4) k What is the acceleration vector? a(t) = (0) i+ (8) j+ (0) k Write the velocity vector at t= 0 as a product of the speed and direction. 8 v(0) = (/89 i+ V89 j+ V89 V89 (Type exact answers, using radicals as needed.)