The demand function for a manufacturer's product is p = f(q) = -0.19q+456, where p is the price (in dollars) per unit when q units are demanded (per day). Find the level of production that maximizes the manufacturer's total revenue and determine this revenue. What quantity will maximize the revenue? q= = units

Q: Are all functions from one vector space to another linear?

A: Let f: V→W is a  map from vector  V to W such that fx=x2 The given example the function from one…

Q: Use a software program or a graphing utility to solve the system of linear equation.

A: There are many software programs and graphing utilities that can solve a system of linear equations.…

Q: The population of bats in a cave can be modeled with the sinusoidal function p=6000cos(π/10t)+51000…

A: Sol:- To find the population in the year 1976, we need to substitute t = 4 into the given equation…

Q: Prove by weak induction on n: i=n Li i=0 n(n + 1)(2n + 1) 6

A:

Q: (a) Prove that for n ≥ 2, 3 > 2n + n². (b) For any n ≥ 1, the factorial function, denoted by n!, is…

A:

Q: Compute A² and A³. Make a prediction for A5 and Aª: 1 b 4 = [] and 4= [²2] A A [33].

A:

Q: 1. (a) Define: invertible linear transformation. (b) T: (7₁,72) → (67₁ - 872,-57₁ +77₂) is a linear…

A:

Q: 4. An investor is considering three types of investments: a high-risk venture into oil leases with a…

A: We have given 3 types of investments: high risk, medium risk, and relatively safe stock.

Q: 2. How much material passes in the time interval [0,1/2] through the points (a) z = 0, (b) z = π/2,…

A: Sol:- To calculate the material passing through a point in the given time interval, we need to…

Q: Let f(x) = xT Ax be a quadratic form with associated n X n symmetric matrix A. Let the eigenvalues…

A: To prove that the minimum value of f(x) is λn, subject to the constraint ||x|| = 1, we first note…

Q: Find the eigenvalues An and eigenfunctions yn(x) for the given boundary-value problem. (Give your…

A: We get eigen functions only when there is non trivial solution. So, we find non trivial solution…

Q: Let 1 √2 1 √2 1 √2 √2 Find, with justification, B2015. (Enter sqrt(n) for √n.) B = J 1

A: Given matrix is B = 12-121212

Q: (m) 2 x+2 + x+3 x² + 2x 12 x³ - 4x

A:

Q: Exercise 3.9.6: Find the general solution to x″ = −6x₁ + 3x2 + cos(t), x″ = 2x₁ − 7x₂ + 3 cos(t), a)…

A:

Q: show that (Important) 8 "Hint x =1₂y = -1" n E K=O (^) (-1) ². =0 VEN

A: We have to prove ∑k=0nkn-1k=0

Q: Given that the matrix A has eigenvalues A₁ = 4 with corresponding eigenvector v1 = and A2=-8 with…

A:

Q: Consider the proposition ((x → (y v z)) → (x → y) v (x → z) a. Is it a tautology or a contradiction?…

A: Given The proposition ((x→(y∨z))→(x→y)∨(x→z) a. The proposition is a Tautology b. To prove that the…

Q: Determine the sum of the series. (-1)n-¹n n³ + 5 n=1 Type a simplified fraction if convergent,…

A:

Q: Let A = 314⁰ 3 2 NO CON 1 -3 OOTO (a) M12 and C12 (b) M23 and C23 0 0 6 2 -1 -4 7 0 0 0 Find the…

A: Since you have posted a question with multiple subparts, we are supposed to answer only the first…

Q: 0.0139 0.0055 0.0028 Let D = 0.0055 0.0111 0.0055 be a flexibility matrix, with flexibility measured…

A:

Q: 3. Let T: R² R2 be a linear transformation such that T H]-[ = -5x1 + 9x2 4x17x2 Find T-¹.

A: T:ℝ2→ℝ2 is a linear transformation  Tx1x2=-5x1+9x24x1-7x2

Q: Find the the characteristics coresponding functions. if there Following for the equation. numbers…

A:

Q: The functions f and g are defined as f(x) = a) Find the domain of f, g, f+g, f-g, fg, ff, b) Find…

A: The function is defined if the value of function is belong to field and finite

Q: Suppose a spring with spring constant 8 N/m is horizontal and has one end attached to a wall the…

A:

Q: If A and B are independent events, P(A) = 0.45, and P(B) = 0.25, find the probabilities below.…

A:

Q: 1) An investor buys a house for £140,000. 2 months later, the investor spends £8,000 to renovate the…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: An unbiased coin is tossed four times. Find the probability of the given event. (Enter your answer…

A:

Q: Use variation of parameters to find a general solution to the differential equation given that the…

A:

Q: A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the…

A:

Q: Find the scalar equation for the plane passing through the points P1(4, -4, 5), P₂(1, 1, 10), and…

A:

Q: Determine L[f]if S() = f(1) = | sin(t - T)e-dt.

A:

Q: 7. (a) Show that A² = I when A= (b) Use partitioned matrices to show that B² = I where Hint: Choose…

A:

Q: 4. Let (Xn)o be a Markov chain with state space S - P = .8.20 .5 .5 O 0 0 1 {1,2,3} and transition…

A: if the eigenvectors of PT are known, then so are the stationary distributions of the Markov chain…

Q: A 50 L tank initially contains 2 L of salt water at a concentration of 5 g/L. Salt water at a…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: ✓2.21 Represent the derivative map on Pn with respect to B, B where B is the natural basis (1,…

A:

Q: Consider the boundary value problem y" + 4y = 0, 0≤x≤ b, Find choices for b and B so that the…

A:

Q: (a) Use the Integral Test to show that the series Σ=1 (b) Find the value of the approximation s5 =…

A:

Q: The population of a community is known to increase at a rate proportional to the number of people…

A:

Q: 3.30 The need to take linear combinations of rows and columns in tables of numbers arises often in…

A:

Q: . Can a square matrix with two identical columns be invertible? Prove it clearly.

A:

Q: I can't understand the red circle I write.Please explain it in detail.

A: As per the question we are given the characteristic polynomial of a n×n square matrix A as f(t) and…

Q: Σ=1(*) (2) Use the Integral Test to show that the series E- converges. Hint: use integration by…

A: Since you have posted multiple questions, we will solve first question for you. If you want any…

Q: A car is given a push down a roller coaster. If it travels a distance of s feet in t seconds, where…

A: Given equation is s(t) = 4t + 3t2

Q: Let A be the point with coordinates (4, 4, 1), let B be the point with coordinates (0, 0, 3), let C…

A: Solution:

Q: 1. Use the definition of the Laplace transform to find C{f} for the following functions: (a) f(t) -1…

A:

Q: erify the Cayley-Hamilton Theorem for a general 2 x 2 matrix A, a b -[1]. For a nonsingular n x n…

A:

Q: Consider the matrix below for items 4.1 to 5: =1/1₁ B = 0 4.1 B is a/an 4.2 Calculate the…

A:

Q: A lamp has 3 light bulbs. Each lightbulb has a life span that corresponds to a random variable X,…

A:

Q: In a sweepstakes sponsored by Gemini Paper Products, 150,000 entries have been received. If 1 grand…

A:

Q: Consider the initial value problem (a) Find the eigenvalues and eigenvectors for the coefficient…

A: