The profit function of a certain firm is f(x) = −2x² + 396x - 400, where x denotes units of product produced, and f(x) is in Rands. PART A: a) If the firm produces 10 units of the product, its profit will be R b) If the firm produces 210 units of the product, its profit will be c) The production level that will maximize the firm's profit is d) The maximum profit the firm can make is R

Q: 2) ∞ και 2- N n=0 α 2-' Σ δ(t - n)dt 1-0 3) | 2-1 Σ δ( - nat n=-

A: A delta function is defined as δ(t-a)=0       for t≠a ∞    for t=a    . The fundamental property of…

Q: 64. The Perimeter of an Ellipse: P = 2 = 2√2 The perimeter of an ellipse can be approximated the…

A: Note: As company policy, we solve first question only. Please resubmit those questions in case you…

Q: DETAILS ZILLDIFFEQMODAP11 1.2.013. MY NOTES ASK YOUR TEAC his problem, y c₁ex + c₂ex is a…

A:

Q: Suppose P, Q and R are statements. Complete the truth table for the statement (P⇒ Q) or (P and (not…

A: To determine: The Truth table for the statement P⇒Q or P and not R.

Q: Find the critical points of the function. Then use the second derivative test to classify the nature…

A: Introduction: If the critical point of the function fx,y is a,b. then fx,y has local minima at a,b…

Q: 1. Let A = a. 1 1 -3 -5 V -8 and b= 3 4 -7 9 4 V V Solve Ax=b by hand and write your solution in…

A:

Q: If P(a, ß), the point of intersection of the y² a² (1-e²) X ellipse2 x² 2 + y² 1 a² (E²-1) 4 (C) E=-…

A: Given equation of ellipse is x2a2+y2a21-e2=1 and equation of hyperbola is…

Q: V Consider the quadratic form Q(x₁, x2, x3) = 2x² + 2x² + 2x² + 2x1x2 + 2x1x3 + 2x₂x3 a) Determine…

A:

Q: 1. (e)(1-e²y)¹/² dx = dy 2. cos x cos y dy-sin x siny dx = x² cos x sin y dx

A:

Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A: Sol:- A second order linear, homogeneous ODE has the form of   y''+py'+qy=0y'' -6y' +9y=0Here…

Q: To prove that the limit of f(x)=x^2+4x as x approaches 2 is 12, given any ε>0, choose 8>0 such that…

A: Definition: Epsilon-Delta of Limit : Here is the limit limx→af(x)=L is given as : While ∀ε>0…

Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

A:

Q: Use mathematical induction to prove the inequality n < 2n

A: Put n = 1 1 &lt; 2 It is true. Let it is true for n.  That is.      n &lt; 2n  We will show it is…

Q: c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real…

A: A be a matrix 5 * 5  We have to find the matrix A and also find the geometric description of A and…

Q: 5. Determine whether or not matrix A shown below is orthogonal and justify your answer. 1 0 A = 0 1…

A:

Q: Give the Particular Solution of the following Differential Equation d²y dx² IBC: y(0) = 1 y'(0) = -3…

A:

Q: f(t) = 0≤t≤1 1≤t≤2 1 t²-3 t>2

A: The function f(t) is a rule that associates or fixes a number to the particular point t. The Laplace…

Q: 2 2 n(n-1)x", n²-n 37

A:

Q: s absorbed into the body, 14% is eliminated from the body each hour. Assume a person drinks an 8-oz…

A:

Q: Note: you can enter pin) by writing pi in the boxes provided. Let R be the finite region enclosed by…

A: We have to find the volume of the region enclosed by the curve y= 11(X)^(1÷2) , the X axis and the…

Q: Let f(x,y,z) = g(√√x² - 4y² +₂²)√√x² +16₂² +₂², + 16y² + z², where g is some nonnegative function of…

A:

Q: Consider the function f(x) = 6 x4 +62² in the interval I = [1,3]. Let KR be such that K = max |…

A: Let us solve the given numerical analysis problem in the next steps.

Q: Show that the differential equation x²y³ + x(1+y²)y' = 0_ is not exact, but becomes exact when…

A:

Q: the mean and standard deviation of the measurements. If the mean is 75°C and the standard deviation…

A:

Q: A TUN f: {1,2,3,4} is defined by f(1) = 6, ƒ(2) = 7, f(3) = 8, Drag the answers into the right place…

A: Given function is f:1, 2, 3, 4 → 5, 6, 7, 8 defined by f(1) = 6, f(2) = 7, f(3) = 8, f(4) = 6

Q: Let W be a space with an orthogonal basis given by for each vector given below. 1) y = 3 ایک دیک که…

A: Given : An orthogonal basis 1-10211 , 11-20-11 ,20000-2                y=y^ + z             and…

Q: (X- At which value does the function g(x)= 3x^4 - 4x^3 attain a the minimum value? Type answer as…

A:

Q: 2 [(3x² + 1)(x³ + x)² dx [(3x + 8) ¹¹ dx 11

A:

Q: 1. Graph the function over the specified interval. Then use simple area formula from geometry to…

A: a) The given function is f(x)=6-x. To Sketch: Graph of this function over [-2,x]. To Find: A formula…

Q: which representation would be the most useful for presenting a concept for a new statue outside an…

A: The solution is given below

Q: a) Explain what it means, by definition, that a polynomial m(r) € P(R) is the minimal poly- nomial…

A: Given That : minimal polynomial for a matrix A∈ Mn×n(R) We have to explain  that the polynomial…

Q: In each of Problems 25 through 31: (a) Find an integrating factor and solve the given equation. (b)…

A: Given equation is y'=e2x+y-1   (a) To Find: An integrating factor and solve the given equation. (b)…

Q: a) Prove that for an NxN-dimensional orthogonal matrix A, the determinant |A| = ±1. matrix A for…

A: For an n×n matrix A, a number λ is an eigenvalue if there exists a non-zero vector x such that we…

Q: (1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a…

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Solve the initial value problem y" + 4y - 32y = 0, y(0) = a, y'(0) = -80. Find a so that the…

A:

Q: Evaluate the integral (6x +12y)dx + (6æ — y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: Let us evaluate the given integral in the next steps.

Q: dy Write down a differential equation of the form dt 11 12 solutions all approach y = y' = as t→∞. =…

A:

Q: Find the inverse Laplace transform of the function. where y(0) = 1, y(0) = 0 and y" + 4y = f(t).…

A: Sol:- Since f(t) function is defined in the range t≥4 , so it can also be written as 3H(t-4)(where…

Q: Given: F(s) = Evaluate: f(2) S-3 Use 2 decimal places.

A:

Q: To prove that the limit of f(x)=x^2+4x as x approaches 2 is 12, given any ε>0, c that 6-min{4,k).…

A: Epsilon-Delta Definition of Limit : A limit limx→af(x)=L is defined as : If ∀ ε&gt;0 there exists a…

Q: Question 13 Indicate if the following statement is TRUE or FALSE. Briefly justify your response with…

A: Solution: Given statement is TRUE

Q: ✓ Your answer is correct. y = 5+t-y, y(0) = 1 (a) Find approximate values of the solution of the…

A:

Q: Choose the letter of the correct answer. If (x_n) is a bounded sequence in R then there is a…

A: True,

Q: Solve the following dynamics equation using the Laplace transform with the initial conditions x(0) =…

A:

Q: 2. Simplify completely: (a) √1+i√3

A:

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (t + 1)³ L{f(t)} =

A: L{t^n}=(n!)/(s^(n+1) ).

Q: 41. If you apply the following rotation matrix, what direction are you rotating the matrix? 270…

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

Q: For an NxN-dimensional matrix A, prove that a) the product of the eigenvalues is equal to the…

A:

Q: y' : 320 -1 1 0 004 у

A: