In Example 6 in this section, we were given f(x) = 3x² + 2x + 11 and found f'(x) = 6x + 2. (a) Find the instantaneous rate of change of f(x) at x = 4. (b) Find the slope of the tangent to the graph of y = f(x) at x = 4. (c) Find the point on the graph of y = f(x) at x = 4. (x, y) =

Q: Assignment 9 Section 5.1:4(d) only!!

A: The matrix A is diagonalizable over the real field F = R. To find the eigenvalues and eigenvectors,…

Q: Suppose U and W are finite-dimensional subspaces of an inner product space V. Prove that Pʊ Pw = 0…

A: Assume PUPW=0. We want to show that ⟨u,w⟩=0 for all u∈U and w∈W.Since PU and PW are projections,…

Q: 4. Let S be the subspace of R4 spanned by 2 -2 0 0 and X2 2 2 a. Find orthonormal bases for S and S.…

A: The standard inner product of R4 is defined by<X1,X2>=x1x2+y1y2+z1z2+w1w2For every two vectors…

Q: 5. For each linear operator T on V, find the eigenvalues of T and an ordered basis ẞ for V such that…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: =1 (a) V=R2x2, U = {AEV | sled A = 0}. (b) V=R³, U= {(x, y, z) = V | 2x+y-z = 0}. (c) VR₂[x], U =…

A:

Q: 4. Let A be the following matrix. Find the products A² and A(2) A² (regular matrix multiplication)…

A:

Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

Q: 2. In a market in which the Arbitrage Pricing Theory (APT) model holds, the expected return is given…

A: The Arbitrage Pricing Theory (APT) is used to determine if the expected returns of securities are…

Q: Find the value of k such that the following matrix is singular 1 0 3 B= 2-1 0 4 2 k

A:

Q: The figure shows a telephone wire hanging between two poles at x=-30 and x = 30. The wire hangs in…

A: Here the shape of the wire is a catenary whose equation is y=c+acosh⁡(xa)The arc length of the wire…

Q: show clear and accurate human working out, please.

A:

Q: Find the inverse Laplace transforms of the following functions: s+5 5. (a) F(s) = $² +s-2 4 (b)…

A:

Q: Problem Set B 1. The diagram below shows the function Q (p) drawn to scale. 10 8 6 4 2 4 -3 -2 -1 0…

A: Since Curve is continuous in the interval 2≤p≤5 also given that limit exist at p=3,So, we can choose…

Q: I’m mostly unsure on the notation used and what it means.

A: Step 1:We need to prove,∏d∣n​d=n2τ(n)​Here the left hand side is the product of divisors of n.For…

Q: Solve the initial value problem y' : = 8y² + xy², y(0) = 1 and determine where the solution attains…

A: y=x2+16x−2−2​ minimum at x= -8Explanation:Step 1:Step 2: The double derivative was done to check…

Q: Darden Restaurants, Inc. (DRI) is the largest full-service restaurant company in the world. It…

A: The objective of this question is to calculate the inventory turnover and the number of days’ sales…

Q: A) Find the Eigenvalue and Eigenvector B) Classify the critical point (0,0) and state if it's stable…

A: Given system of differential equation

Q: Derive the conditions of the Kuhn-Tucker theorem for the following problems and find their solution:

A: The actual calculations involve solving a system of non-linear equations, which can be quite…

Q: Show all the work

A: ∙  A=⎣⎢⎡​5−13​217​⎦⎥⎤​∙  T([−26​])=⎣⎢⎡​2836​⎦⎥⎤​Explanation:Given: ∙  T(e1​)=⎣⎢⎡​5−13​⎦⎥⎤​∙…

Q: Which of the following claims are correct: ΟΣ 3 € Θ (3-1) ΟΣ 1 3 € Θ (3) ΟΣ 1 3 € Θ (3+1) 02 € (3")

A:

Q: Find f (t) = L¯¹{F(s)}. a. F(s): = b. F(s): = $3 Se-πs s²+9 c. F(s): 5e-3s = s²(s+5) d. F(s): 2s-1 =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Find 12% of the following function: dx لا xe = Cosh (xy)

A: The given function is: .We need to find .

Q: show all th work with correct ans

A: The answer has been provided.Explanation:

Q: Apply the eigenvalue method to find a general solution of the given system. For the given initial…

A:

Q: (2) Consider the following LPP here a1, maximize subject to У a1x1.. +anxn+y-t = b x1,xn, y, t≥ 0,…

A: subject to We have to find the dual of the problem and solve it.

Q: Please solve and show all work.

A: The answers have been provided.Explanation:

Q: 4. How many triangles can you draw using the dots below as vertices? a. Find an expression for the…

A: This is my final answer. Explanation:Step 1: Part(a) Explanation: The vertices of a triangle are…

Q: Solvo the initial value problems. y1/2 dy dx + y³/2 = 1, y(0) = 4

A: ​y=(7e−23x​+1)2/3​Explanation:Step 1:​y1/2dxdy​+y3/2=1,y(0)=4Substitute y3/2=vUsing the power…

Q: The dead body of a cricket coach was discovered in a prominent hotel at noon on Sunday where the…

A:

Q: A checker is placed in the bottom row of a checker board as shown below. It can move diagonally…

A: This is a counting problem.. we will solve it using the approach of dynamic programming.

Q: Find the flux of the vector field F = xi + ej z k through the surface S given by that portion of the…

A:

Q: The average number of miles driven on a full tank of gas in a certain model car before its low-fuel…

A: Step 1:Step 2:

Q: A sign chart for f" can be used to tell where f is [Select]

A: concave up or concave down" for the first blank:The second derivative test for concavity tells us if…

Q: (2) Consider the following LPP maximize subject to a1x1 + Y +anxn+y-t = b x1, · · ·, xn, Y, t≥ 0,…

A: subject to We have to find the dual of the problem and solve it.

Q: Find the mass, in metric tonnes, of sand in a box that measures 21 mx22 mx 12 m.

A: The mass of the sand is about:M=8881.5metricton  Here, we use the density formula to calculate mass,…

Q: The function f(x) = −2x³ + 30x² − 144x + 9 has one local minimum and one local maximum. This…

A:

Q: Suppose that x is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 23548,…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: e integral;

A:

Q: Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and…

A: First we have to construct a 2x3 matrix of rank 1. then find the vector in the subspace (row space…

Q: Find xₙ and xᵣ

A:

Q: D.( 25 pts) Find the general solution of the ODE y" + 2y + y = ex ln(x), x> 0.

A: The given ordinary differential equation is a non-homogeneous second order linear differential…

Q: If sales N(x) are expressed as a function of the amount a spent on advertising, then the dollar…

A: Detailed explanation: Sales Function, N(x):N(x) represents the total sales as a function of…

Q: Redraw Figure 4.3 for a 3 by 2 matrix of rank r 2. Which subspace is Z (zero vector only)? The…

A:

Q: Determine the order a = 7 modulo n = 24. Type your answer...

A:

Q: For each q € Z+, let B, denote the set of points in [0, 1] whose image under f is at least 1/q: B₁ =…

A: Let's denote the set Bq as defined in the question: \[ B_q = \{x \in [0,1] : f(x) \geq…

Q: 2 2 000 000 3 10 0 0 0 0 0 00 1 - -1 3 0 0 0 0 0 -1 1 0 000 B = 000 0 1 0 0 0 0 0 0 0 0 11 0 0 0 0 0…

A: (.) Given matrix is,        (.) Characteristics polynomial of a block upper triangular matrix  is…

Q: let x and g be elements of a group G. show that x and gxg-1 have the same order. now prove that xy…

A: Hence, proved.Explanation:Step 1:To prove that x and gxg-1  have the same order for any elements x…

Q: If 10 people choose, at random, a letter from the English alphabet of 26 letters, what is the…

A: We find the probability that each of the 10 people chooses a different letter from the English…

Q: e. ƒ (t) = tU(t − 3) f. f(t)=sint U(t − π)

A: We have to find the Laplace transformation of the given function.

Q: Find the maximum and minimum values of x'y', subject to the constraint 2 (()) ((+)+) = 9. At which…

A: Given Information:The objective function is given as .The constraint is given as To find:The maximum…