A manufacturer supplies refrigerators to two stores, A and B. The manager esti- mates that if x refrigerators are delivered to store A and y units to store B each month, the monthly profit will be P(x, y) pesos, where P(x, y) = 2x² – 3xy - 2y² + 20x + 40y - 300. Each month, the company can produce exactly 700 refrigerators. How many refrig- erators should be supplied to store A and how many to store B in order to maximize monthly profit?

Q: 4. Students in a film class have volunteered to form groups and create several short films. The…

A: Given- Students in a film class have volunteered to form groups and create several short films. The…

Q: The area of the region enclosed by the x-axis, the curve y = f(x) > 0, and the lines x = b and x =…

A: Given- The area of the region enclosed by the x-axis, the curve y = fx > 0, and the lines x = b…

Q: g(x) = -6x5 (1+x6)²

A:

Q: inition of determinant of T, prove that det(T-¹) = (det(T))−¹ (Hir erminant of the identity man?)

A:

Q: Find the volume of the solid region in the first octant inside the cylinder x²+y2=4 and between the…

A:

Q: Find the mass, in kilograms, of the portion of the cone x² + y² = z² 1 and z = 3 if the area density…

A: Given the portion of the cone x2+y2=z2 between the planes z=1 and z=3. and density δx,y,z=y2z2

Q: Let V be an F vector space of dimension n. Prove that, for k≤n the vectors V₁, V2,..., Uk are…

A: Hints:   It is given that V be a vector space of F of dimension n. Then we have to prove that  vi's…

Q: Show that for any nonrandom, continuously differentiable function f(t), the following formula of…

A:

Q: Prove that if Xn X and Ync, then (Xn, Yn) → (X, c).

A: Please see the answer innext step

Q: 4. following is correct? A. B. C. Let p = a + jb, b > 0 be the complex root of the denominator of…

A:

Q: Find the distance between the origin and the intersection line of the planes : 2x+y+z=2 and x+2y+z=3…

A:

Q: 6. Find the transition matrix from B to B' and find the coordinate matrix [x] B¹, given the coordi-…

A:

Q: 3 Find the sequence of similarity transformations that maps quadrilateral DONL to quadrilateral…

A: To Find: The sequence that will transform the Quadrilateral DONL to Quadrilateral MCKY.

Q: Let x₁ (n) = 3"u(n − 2). What z-transform property is applicable? A. Linearity B. Time shifting C.…

A: Properties which are applicable

Q: Consider the following matrix A 2 -5 4 -1 2.6 2 5 -3 9 Select possible error magnification factors…

A: Given the matrix A=2-54-12.625-39

Q: 5. Find (a) a basis for the row space, (b) a basis for the column space, (c) the nullspace, and (d)…

A:

Q: Complex Numbers. 1. Evaluate the following. Express all final answers in rectangular form. a. A =…

A: Solution 1(a): Given A=cosln(-π)3⇒A=cosln((π)(-1))3⇒A=cosln(π)+ln(-1)3⇒A=cosln(π)+πj3…

Q: Three cards are drawn from a deck without replacement. What is the probability that they are not all…

A:

Q: Which of the following statements is(are) true if

A: Introduction: Only zero and one are the eigenvalues of the identity matrix and the zero matrices,…

Q: Obtain the Lagrange interpolating polynomial using all the data points below: 0.5 1.0 1.5 2.0 2.5…

A: Introduction: The Lagrange interpolating polynomial is a basic interpolating polynomial that fits…

Q: 2. H(s) = 3. Determine Laplace 13s² + 46s + 133 (s + 1)² (s² + 6s + 25) the value of h(0) using the…

A:

Q: Prove that T: V→ W is a linear transformation if and only if T(au + bv) = aT(u) + bT(v) for all…

A:

Q: 2 Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A:

Q: 3. Determine whether each of the following sets are subspaces of R³ with the standard operations. Be…

A:

Q: QUESTION 1 a. An invoice of RM 10,000 including service charges RM 500 dated 26 June 2020 was…

A: Solution:

Q: B) Given the set S = {(3k, -2k): k ER}. Which of the following is wrong? Select one: O (-2, 3) is…

A:

Q: There is a vector field F(x, y, z) = (M (x, y, z), N (x, y, z), R (x, y, z)) , such that divF (x, y,…

A: We need to determine the validity of the statement: divF=div(curlF) for a vector field of the form:…

Q: Let A be an 8 x 8 matrix with det (A) = -2. Let B be the matrix that can be obtained by applying the…

A:

Q: Let V, W be vector spaces over F and let T:V → W be a linear map. Prove that if T is injective, then…

A:

Q: 2. The graph of a function and its derivative are shown y y y=h(x) Determine, where applicable, the…

A: Since you have asked a question with multiple sub parts here, we will solve the first three sub…

Q: a)! Find the limit or show it does not exist: xy³ lim x,y) →(0,0) x² + y²

A: Note: Since you have posted multiple questions. As per our guidelines we are supposed to solve one…

Q: Show that the following differential equation is perfect or not, then find its general solution:…

A: Introduction: Any equation with one or more terms is a differential equation. It includes taking the…

Q: 34 12 25 13 5 30 22 a.) Pivot variables of matrix A? 0 1 1 1 -2 1 1 Let A = b.) Free variables of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: The number of students at a school increases at a rate proportional to its current size. In 2005,…

A: An equation which consists of the independent variable, dependent variable and their derivatives is…

Q: [* [V²*³ ƒ(z,y) dz dy = "ƒ(x, LS 3. Change the order of integration. y) dr dy = '"* ftal") ƒ(x, y)…

A: Introduction: Changing the order of integration in double integrals is the process of going from…

Q: Construct the truth table for the statement (q + p)^~q.

A:

Q: V(x, y) = 80-20xe ²+₁²

A: Note the following facts about a function f(x, y):   (i) The maximum rate of change is ∇f  (ii) The…

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: The set of all polynomials of the form ax³ bx² cx + 2, where a,b and can real numbers is a subspace…

A:

Q: Find the characteristic polynomial of the 3 x 3 matrix, A, where

A: A matrix is a mathematical object containing numbers arranged in rows and columns. If the number of…

Q: A dance class will be conducted in Bloomingdale Dance School. A group of eight students will be…

A: Graph Coloring : It is a simple way of coloring graph components such as vertices, edges and…

Q: Use the transformation u = y - x, v = y, to evaluate the integrals on the parallelogram R which has…

A: We need to evaluate the integral: ∬Ry-xdA using the transformations: u=y-x, v=y. Here, R is a…

Q: Use variation of parameters to find the general solution of the differential x²y" - 5xy + 5y = 4x6…

A:

Q: QUESTION 5. Use the fourth order Runge-Kutta method with h = 0.25 to approximate (to 6 decimal…

A: Given : y'=-2xy      y0=1              0≤x≤1            y0=1    x0=1    h=0.25 TO Find : Approximate…

Q: Let x₁(n) = 3¹u(n − 2). What z-transform property is applicable? A. Linearity B. Time shifting C.…

A: Hints: The z transform of the function anu(n) is zz-a. The given function is 3nu(n-2).

Q: 3. Find the equilibrium points of the following nonlinear system. Find its linearization at each…

A: Given:          x'=yy'+6x+y=-3x2x0 =-2.1  y0 =0.1 To Find : Solution of given system Note: In case…

Q: Let CR" be an open set on which f is locally integrable. Tony is computing the improper integral…

A: Hints: It is given that ∫Ωf dV is improper.

Q: For example, starting with 5 and 8 th 5, 8, 13, 12, 7, 10, .. The calculations for this example are…

A: (c) find with explanation , a diginacci sequence that has no term equal to 11? solution it is known…

Q: Determine the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown. x…

A: Using the cylindrical coordinates

Q: - Sketch, evaluate, and reverse the integral: lí dy dx/

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.