Consider the cost function C(x) = 182 +56x and the revenue function R(x) = 256x50x², where x ≥ 0. Disregard the units of the cost and revenue functions. 1. Find the formula for the profit. P(x)= 2. Find the maximum profit: 3. Give the value of a where this maximum profit occurs. Type your answer here

Q: If f(a) and g(2) are monic polynomials of minimal degree for which A is a root then f(x) = g(a).…

A: This type of polynomials ( which is monic polynomials of minimal degree of which A is root) is…

Q: Consider the linear transformation T: RR whose matrix A relative to the standard basis is given. A =…

A:

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A: Let V be a finite dimensional vector space of dimension n and B={α1,α2,…,αn} be its basis. Dual…

Q: 3 Consider the Euclidean inner product space R³ with a basis B={(1, 1, 1), (0, 1, 1), (0,0,1)}.

A:

Q: The boat travels downstream in 2/3 of the time as it does going upstream. If the velocity of the…

A: We know that: D=R+CT, when the boat moves up downstream. D=R-CT, when the boat moves up upstream.

Q: Let A, B, and C be subsets of a universal set U. (a) Draw a Venn diagram with A G B and B ≤ C. Does…

A:

Q: Which of the following statements hold for the minimal polynomials of matrices? (i) Nonsimilar…

A:

Q: EVALUATION Find the domain and the range of the relation. 1. AN 2. X Y -2 -1 3. {(x,y)/y=x²,2<x<5}…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let V O The line x+y=2 O The line x+y=1 O The line x+y=0 O The line x+y=-1 O The line x+y=-2 = R²…

A:

Q: 2. Is the following statement true or false? why? 2 It D 1 a1 \n € N, 3|(n³ + 2n)

A:

Q: A) Use Green's theorem to compute the area inside the = 1. 2² y² ellipse + 19² 14² Use the fact that…

A: (A). Given,                            x2192+y2142=1,      use the fact that the area can be written…

Q: In the Euclidean inner product space R4 with an orthonormal basis B={(1.1.1.1.1.1.-1.-1.…

A:

Q: If  n(A) = 106, n(A ∪ B) = 152, and n(A ∩ B) = 48, find n(B).

A: Introduction: We carry out specific operations in mathematics, such as addition, subtraction,…

Q: Slove: √x12 - X=0 it there there are multiple solutions. list them separated by a 2. Comma . X= eg.…

A: We need to solve the equation: x+2-x=0. An extraneous root is one that is derived by solving an…

Q: 3. A line in the xy-plane passes through the point 늘 following points lies on the line? (1,-2) and…

A:

Q: Let A = -32 -21 and B={b₁,b₂}, for b₁ = a. Compute Ab₁. Ab₁ = and b₂ = 1 2 Define T: R² R2 by T(x) =…

A:

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A:

Q: b. Let M2x2 consist of all the 2 x 2 matrices. M2x2 with the matrix addition and scalar multiple…

A:

Q: Consider the function ƒ : Z × Z → R defined as 1. What is the domain of f? 2. Find ƒ(2, −1) 3. Is f…

A:

Q: (foh) is a 4x3 matrix, M (f) is a 2x3 matrix and M(h) 4x2 matrix (h) is a 4x2 matrix, M(f) is a 2x3…

A:

Q: Proposition 6: Let F/k be an extension field. Let E = {α = F α is algebraic over k}. Then E is a…

A:

Q: A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of…

A: The linear function that needs to be optimized is called the objective function. The objective…

Q: A) Find all y such that the distance between the points (-1, 5) and (9, y) is 11. y= B) Find ALL x…

A: To find  A) Find all y such that the distance between the points (-1, 5) and (9, y) is 11.   y=   B)…

Q: Given the power series expansion 8 In(1+x): Σ(-1)"-12" N = n=1 determine how many terms N of the sum…

A:

Q: Let V be a vector space over a field F with zero vector 0 and let S, T be subspaces of V. Then which…

A:

Q: oan calculator, change the interest rate to 4.22%. Loan period 60 months. What would your monthly…

A:

Q: Which of the following maps from R2 to R³ are R-linear? f(x, y) = (x, x-2, x+y+z) f(x, y) = (x, 2x +…

A:

Q: Multiple-Choice Tests   Professor Easy's final examination has 11 true-false questions followed by 2…

A: Given, Number of true false questions = 11 Number of multiple-choice questions = 2 Each of the…

Q: Consider a function f given by А f(x, y) u(x) + iv(y). Determine all possible functions f of the…

A:

Q: 6 7 A) y=e+e B) y=e" C) y=e+e D) y = ex By using a suitable substitution, the non-separable ODE…

A:

Q: Barahan Plus Chemicals, Inc. produces two products that are sold as raw materials to companies…

A: Let x gallon of product A and y gallon of product B are produce Given production cast is ₱80 per…

Q: ryzdS if S is the part of plane z = x + y that lies over the triangular region 32. Evaluate in the…

A:

Q: Consider the following integral. Sketch its region of integration in the xy- plane. X [[ In(x) (a)…

A:

Q: Let V be an inner product space over R and x, y, z E V. Let U, W be the subspaces of V, if U is…

A: To Check whether the following statement is true or false: If U is orthogonal to W then, U⊥ is…

Q: 11. If 4x-9-11, then x = ? . A. 5 B. 6 C. 6.5 D. 9 E. 16 2. Consider the following 2 logical…

A:

Q: What is the order and degree of the following differential equation: y(y")4 + 2x(y')5 = 8xy2? A. 1,5…

A:

Q: The following vectors are linearly independent in R4 u1 = (0,0,-7,1) u2 = (1,-2,0,5) u3=(0,0,0,-4)…

A:

Q: Which of these relations on the set {0, 1, 2, 3} are equivalence relations? Determine the…

A:

Q: Show that fee-2 dz is independent of the path C joining the points 1 - mi and 2 + 3 mi and determine…

A:

Q: Eliminate the arbitrary constant A in the equation y sin x = A cos x.

A:

Q: 1 2 3 4 5 6 7 Which of the following is a second-order linear nonhomogenous ODE? A) sin(x)y" + y = 0…

A:

Q: In the vector space P, of polynomials of degree at most two, then the first column f the matrix of…

A:

Q: The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes…

A:

Q: Question 10 m*n = m+n+mn The Binary operation is associative on Z. True False

A:

Q: Identify the function represented by the following power series. co Σ(-1)k *k k=0 44

A:

Q: Consider the basis B = {(2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A: Given Data: Let us consider the given basis B =2,1,3,1 for V=R2 A=2311 is a matrix of basis is…

Q: Consider the basis B = {{2, 1), (3, 1}} for V = R2 and let {x1, x2} be the dual basis of B. Then for…

A:

Q: Let a be algebraic over a field k, with deg o being odd. Show that Does this hold true if deg α is…

A:

Q: The third column of the change of basis matrix from the basis B={u= (1,1,1); v= (1,0,1); w= (0,1,1))…

A: Given the basis             B=u=1, 1, 1, v=1, 0, 1, w=(0, 1, 1), to the basis,            B'=r=(3,…