3. Given function f(x, y, z) = √x²+y² + z², find the direction in which ƒ decreases most rapidly at point (2, -3, 6). What is the directional derivative in this direction?

Q: Exercise 2.9 A company manufactures two products X and Y. The profit contribution of X and Y are…

A:

Q: Museli has put $10 into a savings account. This savings account pays 6.25% interest each year. X 0 1…

A:

Q: 5. Given the function f(x)=1/(x-2), the linear approximation of f(x) around f(x)=-1 is most nearly:…

A:

Q: rating of at least 10 and contain at most %1 sulfur. The crude oil blended to form gas 2 must have…

A: Suppose, xij=barrels of crude oil i used daily to produce gas j. bi=dollars spent on advertising…

Q: View Policies Current Attempt in Progress What is the period of the earth's revolution around the…

A:

Q: Let A = 3 -1 0 0 2 -2 3 2 2 0 Find the solution of the following intial value problem: 1 () 0 1 y' =…

A: Given that the initial condition y→'=A.y→    ,  y→0=101 Here  A=3-102002-23    .

Q: In the market for a good, the equilibrium point occurs when 6095 units are produced at a price of…

A:

Q: The equations in Exercises 1-8 have distinct, real, characteris- tic roots. Find the general…

A:

Q: Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the…

A:

Q: (a) Determine the exact time, tr, at which the rock hits the river by solving the equation h(t) = 0…

A: According to guidelines i solve first 3 subparts. So kindly request you to repost the remaining…

Q: Find the general solution for the following differential equation: ty' + 2y = 5t² + 5t - 7 Then find…

A: The given differential equation is ty'+2y=5t2+5t-7, y1=-9.3. We have to find  (a) General solution…

Q: A collector of toy vehicles has 12 hot rod cars, 10 pickup trucks, 9 classic cars, and 1 big rig…

A:

Q: Find the vectors T, N, and B at the given point. 16 (t) = (2, 룰,t), (4,-1, -2) T= N = B = 481 9'9'9…

A:

Q: 5. Solve the following equations (a) Log(2²-1) = (b) e²= + e² + 1 = 0; (c) z+1-i = 0 (here z denotes…

A:

Q: So λ (1-ey) o λ + (2-2) e-y Ө 0+ ℗ + (2 − 0) e¯½ dy

A:

Q: Is b in (a, a, a)? How many vectors are in (a,. a2. a3}? Is b in W? How many vectors are in W? Show…

A:

Q: sing the integer root theorem, list out all possible and candidate integer roots of…

A: The given equation is  fx = 3x4 - 3x3 - 26x2 + 19x + 20 Integer root theorem  :   Let  fx =…

Q: The domain of the function is the set of all real numbers with two exceptions. The smaller exception…

A:

Q: Let f(x) = e-* - 9 and g(x) = eª. Consider the following actions: (a) reflecting the graph of g(x)…

A: The given functions fx=e-x-9 and gx=ex. We have to find the transformation of fx from gx and find…

Q: Use Green's Theorem to find the area under one arch of the cycloid generated from the circle of…

A:

Q: Let ƒ : [0, 1] → R be defined as ƒ(x) = { = { 8 0 Prove that f is not Riemann integrable. x² x € X E…

A:

Q: 2. The distance x, measured in metres, of a downhill skier from a fixed point is measured at…

A:

Q: If H and K are subgroups of G, show that H > K is a subgroup of G.(Can you see that the same…

A: Given: H and K are subgroups of G.We need to prove that H∩K is a subgroup of G and ∩i∈IHi is a…

Q: Find the inverse function. NOTE: Enter the exact answer. f(t) = 17+ Int f-¹(t) =

A:

Q: Let A = 10-3 02-2 and b = -44 2 -2 . Denote the columns of A by a₁, a2, a3, and let W = Span 6 a. Is…

A:

Q: Solve the following equation, checking that your solution is correct: 16 6 56 x+3

A:

Q: find laplace inverse uch that the poles are real and distinct) num(s) den (s) G(s)=- 25+.6 + -7s²…

A:

Q: Check the following function for continuity at x=2 6 5x 8 3√6x²-32 - a. X +1 if x 2 The function is…

A:

Q: An investor was afraid that he would become like King Lear in his retirement and beg hospitality…

A: 1st part

Q: Find the projection of v onto u. 1 -AHD V = 1 proj (v) = U = Draw a sketch. O -4 8

A:

Q: 33. Use the vectors u = (U₁,..., Un), V = w = (w₁,..., wn) to verify the following algebraic proper-…

A:

Q: A tank has initially 10 lb of salt dissolved in 100 gal of water. A solution containing a variable…

A:

Q: Calculate an explicit general solution for the ODE: dy dx = = 3y2e +1

A:

Q: Find the eigenvalues and eigenvectors of the matrix A = 2₁ = ₁: = and 22= 1/₂ = and 23 = √3 = - 0 10…

A:

Q: Find a branch cut for √z(z-1) that is analytic in C\[0, 1] and takes value (a) √2 at z = 2; (b) -√2…

A: Answer given below.

Q: Let g(t) = 9t² + 4. (a) Find g'(8). 580 x (b) Find g'(a). 9 Additional Materials eBook 2. [-/2…

A:

Q: Give the vector equation of the line passing through P and Q. P= (3, 1), Q = (2, 0) X = + t

A:

Q: Find a conformal mapping from the following set onto the upper half plane S' = {(u, v) | v>

A: Answer given below.

Q: Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region…

A:

Q: Find the Fourier series of f(x)=e^(-x) in (0,1)

A: Given: fx=e-x. To Find: The Fourier series of fx=e-x in 0, 1.

Q: In Exercises 25-36, find the solution of the given initial value problem. y" - 2y' +17y = 0,

A: Given differential equation y''-2y'+17y=0 D2y-2Dy+17y=0D2-2D+17y=0     .

Q: (6) -y=0 d³y dx³ 3

A:

Q: Let X₁ and X2 be metric spaces. Consider X₁ × X2 with the metric from the previous homework. Let Uį…

A:

Q: 3. Show that the initial value problem * = |x|¹/² x(0) = 0 has four different solutions through the…

A: Given: Let us consider the given IVP, x˙=x12x0=0 To determine: Graph these solutions in the t, x…

Q: 5. (a) Using Laplace Transforms and the Bromwich integral method for the inverse, solve the…

A: The given differential equation is  y''+2y'+y=ft where ft=δt-1+δt-2 with y0=y'0=0

Q: Let G=(V,E) with V={a,b,c,d}. For which sets E is G a graph as per definition of the lecture? O…

A:

Q: 3. Let y(t) be the solution to the differential equation y = (y-1)y(y + 2) satisfying the initial…

A:

Q: R = {(x, y) ERXR = x +2y=1} S = {(x, y) ERXRx_y=1} لذا كانت أوحد RS, (RUS) ROS, RUS

A:

Q: Consider the equation Find an approximation class. Answer: 4 cos(4x) sin(5x) = 3. of it's root in…

A: 6. Given that the equation is                              4cos(4x)sin(5x)=3.

Q: d²r 1 dn dz² n dr n(r) =< - While in general any profile is possible, for simplicity we will choose…

A: