A company manufactures z units of one item and y units of another. The total cost in dollars, C, of producing these two items is approximated by the C = 7x² + 4xy + 4y² + 1000. (a) If the production quota for the total number of items (both types combined) is 98, find the minimum production cost. cost = (b) Estimate the additional production cost or savings if the production quota is raised to 99 or lowered to 97. production cost or savings =

Q: Discuss De Moivre's Theorem. Using an example, explain how the square root of a complex number can…

A: De Moivre's Theorem: The De Moivre's Theorem states that for any real number x, we have,…

Q: Find A and B so that f(x, y) = x² + Ax + y² + B has a local minimum at the point (8,0), with…

A: We know that a function of two variables x & y is given by z=fx, y. We have fx, y=x2+Ax+y2+B.…

Q: 8. Write an equivalent statement that does not use the if... then connective. Use the fact that p→q…

A: We know that, p → q is equivalent to ~p v q.  The given statement is        "If the sun comes out…

Q: . Let f(x) be the function with McLaurin series xn n². n=0 (1) Find the McLaurin Series of f'(x).…

A:

Q: Derive the general solution form for the following recurrence equation:  t(base n) = 4t(base n-1) +…

A:

Q: Rewrite the quadratic function ƒ(x) = x2 – 4x + 6 in standard form and identify the vertex of its…

A:

Q: 26. Use the the lattice method, Egyptian algorithm or the Russian Peasant method to find the product…

A: Question can be solved using Lattice method of Multiplication.  Write both numbers outside…

Q: Given the inflation model C(t) = Co(1 + r)' and given that a boat that currently sells for $290,160…

A:

Q: For the matrix A below, find a nonzero vector in Nul A and a nonzero vector in Col A. A = 3 2 - 12…

A:

Q: Use the savings plan formula to answer the following question. Your goal is to create a college fund…

A:

Q: Using Simplex Method, Calculate: Maximize: Z = 3x + 2y Subjected to: 2x + 3y ≤ 12 2x + y ≤ 8 x ≥ 0,…

A:

Q: 7) For which values of the parameters 'a' and 'b' the system does have either i-unique solution or…

A:

Q: A vertical dam has a semicircular gate as shown in the figure. The total depth d of the figure is 42…

A:

Q: 7. (FE) Let A = a b C de f and B = 2a 26 a+d b+e 9 h 2c c+f i (a.) By using permutation approach,…

A:

Q: all, separated by commas.

A:

Q: Find the following for the vectors u = 7i+10j + √√7k and v= -7i-10j-√7k. a. v.u. Ivl, and lul b. the…

A:

Q: Compute the line integral of the vector field F = (3y, -3x) over the circle x² + y² clockwise JcF.…

A:

Q: In what follows, the Function f is given by Fox) = 3x+1 (a)i Use Taylor's Theorem to derive a…

A: Given : fx=3x+1 To approximate the integral ∫01fxdx using Romberg integration technique with initial…

Q: (1 point) Consider the function z = x7y + 7x6 – 1y. Find and classify all critical points of the…

A: To find critical points and classify them for a two variable function we need to use following…

Q: Design a rectangular milk carton box of width w, length I, and height h which holds 494 cm³ of milk.…

A:

Q: Find the absolute maximum and minimum of the function f(x, y) = y√x - y² − x + 3y on the domain 0 ≤…

A:

Q: A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $8 the…

A:

Q: In 2010, an oil explosion spilled millions of gallons of oil in an area. The oil slick took the…

A: Given; At=0.26πt2 So the area function depend on time t So the area functionA is dependent and  time…

Q: What is the future value if $6,000.00 is invested for 2 years at 6% compounded quarterly?

A:

Q: Find the critical points for the function f(x, y) = x² − 2xy + 3y² – 4y and classify each as a local…

A:

Q: What are the coordinates of the vertex of the graph or table? Is it a maximum or minimum? -8 0 0 0 0…

A: Maximum of a function is a value where the function has maximum value no other value is greater than…

Q: cost- sint √2 r(t) = (5e¹ cos t)i + (5e¹ sint)j +5k For the space curve below, T = Find B B=i+j+k…

A:

Q: A box with a square base and open top must have a volume of 296352 cm³. X X Y We wish to find the…

A:

Q: 5) Fourier transform of the triangular pulse in the following figure is given as G(f) = 1 (2) [ej²nf…

A:

Q: A survey of athletes revealed that for their minor aches and pains, 28 used aspirin, 52 used…

A: Let A represent asprin, I represent ibuprofen. The number of athletes who used aspirin are 28, the…

Q: In each of Problems 13 through 16, determine the critical point x = xº, and then classify its type…

A: Given,         dxdt=-211-2x+-21.

Q: Prove or disprove the following: (a) If X and Y are path-connected, (b) If A CX is path-connected,…

A: Let X and Y be topological spaces. We need to prove or disprove the following: If X and Y are…

Q: Write the compound statement in symbols. et r= "The food is good" ll exercise if I don't eat too…

A: Symbolic form of the compound statements

Q: Give bases for row(A), col(A), and null(A). 1 1 -8 0 2 1 1 -1 -9 row(A) col (A) null(A) A = ↓ 1

A: Row Space: Non zero rows in the row reduced form is the basis of row space. Column Space: Since the…

Q: -10 + -5 y 5 В A В -5 5 с 10 X С'

A: The given figure is,  (1) To Find: Transformation that maps triangle ABC to A'B'C'. (2) To Explain:…

Q: What are credit​ scores?

A:

Q: Use Newton's Method to estimate a root of the function f(x)=6x+4−e^x Use the initial estimate…

A: The given function fx=6x+4-ex We have to find the root of the function using Newton's method with…

Q: Let B be a square matrix  (True or False): 1)The eigenvalues of 10B, are 10 times the eigenvalues of…

A:

Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: Consider the following. Write the above using cylindrical coordinates. (Choose 0 < A. Choose 0 < B.)…

A:

Q: Are the sets (AUB) - (ANB) and (A-B) U (B-A) equal? Draw Venn diagrams to illustrate why or why not.…

A:

Q: Find the general solution to the system: dx =x-4y dt dy dt = x + y

A:

Q: Chapter 5, problem 8b Consider a cyclic group G and two positive integers A and B with the…

A:

Q: V = ¾¼R³

A:

Q: In step2 , ur answer  says g o f is bijective then states its injective. Which one is it

A:

Q: (1 point) If log, 2 = x and log, 3 = y, evaluate the following in terms of x and y: (a) log, 324 =…

A:

Q: Σ(1-4). 2 (a) Compute 5 Express your answer as a simplified fraction. 1 1 Σ(-A) 2 (c) Use induction…

A:

Q: Evaluate (x + y −52) dV where E = {(x, y, z) | − 2 ≤ y ≤ 0, 0 ≤ x ≤ y, 0 < z<x+y²} . E Round your…

A: We have to set limit of integral and then evaluate it

Q: Evaluate the integral. x/2 [2 cos 5t i- sin 5t j+ sin² 7t k] dt x/2 [2 cos 5t i sin 5t j + sin² 7t…

A:

Q: Find and classify all critical points of the function. If there are more blanks than critical…

A: Introduction: Let us suppose that a function is f(x,y) and it partial derivatives are fx, fy, fxx,…