A manufacturer of machinery parts determines that q units of a partic- ular piece will be sold when the price is p = 110 -q dollars per unit. The total cost of producing those q units is C(q) dollars, where C(q) = q° – 25q² + 2q + 3000. %3D - (a) Express the profit derived from the sale of the machinery parts in terms of q. Determine the domain of the profit function. (b) For what value of q is profit maximized? (c) Find the consumer's surplus for the level of production qo that corresponds to maximum profit.

Q: 4. Three vectors are so related that A +C = 5 + j15 and A + 2B = 0. Where B is the conjugate of C,…

A:

Q: f(t) = 3e " cosh (In 21)

A:

Q: 3. If the radius of the circle were 2, would that change the value of the sin, cos, tangent for each…

A: Let us write the reasons of the circle based problem in the next step.

Q: Let u, = 5" cos" xcos nx dx. It turns out that u,u, u,. form a GP. Find %3D (a) the ratio of the GP.…

A: We need to find value of un fir different values of n and then find series representing u1 , u2 , u3…

Q: ulie works no more than 40 hours per week during the school year. She is paid $16 an hour for…

A: The LPP is as follows maximize Z=16m+14t+12pm≥10m≤15p≥8p≤12m+t+p≤40m,t,p≥0 use the simplex to solve…

Q: a) Let q(t) = 4t2 + 2t + 9 be an element of P2. Write the coorfinate vector of q(t) relative to…

A: We have to find the followings ; (a) We have to find the coordinate vector of  q(t) = 4t2+2t+9 with…

Q: Please write the solution...

A:

Q: Prove that L(f) ≤ 0 ≤ U(f). Given that the bounded function f : [a, b] → R has the property that…

A: Given that the bounded function f : [a, b] → R has the property that f(x) = 0 for all x ∈ [a, b] ∩…

Q: 3. The general form of a linear, homogeneous, second-order equation with constant coefficients is dy…

A:

Q: you know f(t) = L¯'{F(s)}, how would you find {F(s)/s²j? %3D

A: Inverse Laplace transform

Q: 9. The segments are tangent to the circle. Solve for x. 7. Solve for x. Assume any segment that…

A:

Q: 10. (. A is the relation defined on Z as follows: for all x, y € Z, x Ay = x=y (mod 3). Describe the…

A: Given : A is the relation defined on ℤ as-               xAy ⇔ x=y mod 3  for all x, y ∈ ℤ. To find…

Q: A = (1 3 - 2), B= a) b) A = B = (3 -7) 2 8 A = 3 B: 011 c) -1 2 4 1, -3 d) A = -2 0 - 2) A = 2 3 -3…

A:

Q: 1. Find the determinant of the following: [2 0 1. 1 2 4 l4 4 2 0 41 -2 3 1 4. 4 5 -2 -3 4 5 2 61 2.…

A:

Q: Construct a graph from this map where the vertices are the cities and are connected by an edge if…

A: Given the map of some cities. To construct a graph where the cities are represented by vertices and…

Q: -7 -12 x' = x(t)+ u(t) 1 y(t)=[1 2]x(1)

A: As per the policy we are allowed to answer only 1 question at a time, I am providing the same.…

Q: . Use the Euler , improved Euler and Runge-kulta. methools to solve the fellowing ODES: d. ý <…

A: We can solve this by using given information

Q: t1 = 1 t2 = 2 t3 = 3 t4 = 4 C1 = 11 C2 = 29 C3 = 65 C4 = 125 1 1 1 1 11 1 2 4 8 29 65 1 3 9 27 1 4…

A:

Q: Let a +b = 4, where a 0 for all x, prove that g(x) dr + g(x) dx increases as (b- a) increases.

A:

Q: Is the following function harmonic? If your answer is yes, then reproduce corresponding analytic…

A:

Q: a linear system in matrix form. 2. Rewrite the specified linear system in component form. dx dr = 2x…

A:

Q: Find the values of w, x, y, z and Dx x + y + z + w = 13 2x + 3y - w = -1 -3x + 4y + z + 2w = 10…

A:

Q: Assume that the number of barbeque dinners that can be sold, x can be related to the price charged,…

A: Introduction: When there are some outputs that are produced, the total cost to produce these outputs…

Q: Estimate f(7) from the given data using Lagrange's Polyn

A: Given, x -3 1 5 5.3 9 F(x) -9 -3 0 7 15

Q: Let U={a,b,c,d,e,f.g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A U B…

A:

Q: a) Identify three non-zero vectors in span{v1,v2}. b) Show that {v1,v2} is linearly independent.…

A:

Q: August eats a mix of Food X and Food ? Y for lunch. The amount of protein, calories,and sodium per…

A: We will form a linear programming from given data and then solve it by  graphical corner point…

Q: Raul has a wall 4 units long and 2 units wide in the Cartesian plane centered on the origin. On this…

A: Given equations: f(x)=(x+12)(x+1)(x-1)(2x)g(x)=(2x+2)(2x-2)(x)(-x-12) on simplifying we get,…

Q: Let a, b, c be real numbers. If ax' + bx +c = 0 has two real roots a, B where a 1, then show that…

A:

Q: . Consider the initial-value problem y'= 0.1!y+0.4x², y(2) =4. Use Euler's method to obtain the…

A: Given Initial value problem: y'=0.1y+0.4x2 , y(2) = 4   To Find: Use Euler's method to obtain an…

Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan -リーz=0 a + 2y - z = 6 2x ー=5…

A:

Q: 1. What does the Fundamental Theorem of Arithmetic tell us about natural numbers?

A: Fundamental theorem of arithmetic : Any natural number can be decomposed uniquely into the product…

Q: EXERCISE Show that for a random sample from a normal population, the sample a consistent estimator…

A:

Q: 1) [ x² y" – xy – 8y = 3x – Consider the DE 4 - - satisfy A) Verify that yı = x* and y2 = x the DE:…

A: The given ODE is x2y''-xy'-8y=3x-4x. (A) To verify:  y1(x)=x4, y2(x)=x-2 satisfy x2y''-xy'-8y=0. (B)…

Q: Proposition and Connectives. 1. Let p be "It is cold" and let q be "It is raining". Give a simple…

A: The answers are below.Hope it is useful

Q: A jug of buttermilk is set to cool on a front porch, where the temperature is 0°C. The jug was…

A:

Q: Answer the following question in a less mathematical and more undestandable to a layman 1. What…

A: Introduction: The cardinality of a set is a mathematical measure of the set's "number of elements."…

Q: 9. E is the binary relation defined on Z as follows: For all m, n E Z, mEn m-nis even. Is this an…

A: The given relation is defined as For all m,n, m E n⇔m-n is even. To Prove or disprove:  whether the…

Q: I. In a particular very small region, the consumer price index, C, depends on the current value of…

A:

Q: 21. lim x2 – 2x – 8 = 6 - - x 4 x – 4 -

A:

Q: II. Consider the function g defined by 1 g(x, y) = sin (7 /æy) + log3 (r – 3y) Do as indicated. 1.…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: dY 1. The system in Section 3.2 - Exercise 1 (previous page): dt Y dt -5 2. The system in Section…

A:

Q: 3dx xV4-x²

A:

Q: A line passes through the points P(9,5, – 1) and Q(- 9, – 3, – 8). Find the standard parametric…

A:

Q: Consider the group D4 = (a, b) = {e = (1), a, a², a³, b, ab, a²b, a³b} where a = (1 2 3 4) and b =…

A:

Q: s-3 F(s) = /3)(s+ The inverse Laplace Transform of is O f() = sin 3t – 3 cos 3t O f() = /3 sin 3t-3…

A:

Q: Answer the following using Jacobi Method. Show complete solutions. The iteration should have atleast…

A: The Given equations are: 9x1 - 13x2 + 4x3 = 111 4x1 + 22x2 -13x3 = -128 8x1 + 8x2 + 17x3 = 10   To…

Q: Compute for the inverse Laplace transform of Y (s) = (s+2)³ * 3 e-2t+2 e-2tt e-2442

A:

Q: Rotate the region bouNded by X= (y-3)² and x= 16 about the x=-5

A: 1st we will find shaded region bounded by given curve and line

Q: 6. "Find the mserse Laplaie fnanform 10 11 25+3 12

A: