Suppose the cost (in dollars) of removing p% of the pollution in a river is given by the following function. C = f(p) =  53,000p 100 − p     (0 ≤ p < 100) Find the cost of removing 90% of the pollution.

Q: 36. If the second ball is red, what is the probability that the first ball was red?

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 3. Let f(x) [1,00) and = for all x ≥ 1. Show that ƒ is integrable on the interval √ 1₁²01 = 2 = ²³²…

A:

Q: Find the future value of an ordinary annuity of $100/month for 11 years at 3.5% / year compounded…

A: The future value of the annuity formula:              Future Value=P×(1+r)n-1r,    Here,…

Q: 2. ( images. (a) f({0, 1, 2}) Let f: Z→ R, with f(n) = 4-n². Find the following direct and inverse…

A:

Q: I. Find the intercepts, the critical points and point of inflection for each of the following…

A:

Q: Write out careful proofs, or give counterexamples, to the following statements. (a) Show that the…

A: Note: We are allowed to solve 1 question/ 3 subparts at a time, kindly reupload remaining questions…

Q: 21. Given that z is a complex number satisfying |2z - 1|=|z2|, prove that |z| = 1 by: (a) letting z…

A:

Q: Solve the given system of differential equations by systematic elimination. (0²-1)x - y = 0 (0-1)x -…

A:

Q: Suppose f: X→Y, and A, B CY. Prove that (a) f-¹(AUB) = ƒ−¹(A) U ƒ−¹(B). (b) f-¹(ANB) = f¯¹(A) n…

A:

Q: Find an SVD of the indicated matrix.

A: Let A=34 To find singular value decomposition (SVD) of A. The singular value decomposition of a…

Q: A fixed point of a function f is somer where f(x) = x. Suppose that f: [a, b] → R is differentiable…

A:

Q: Let D be a subset of R. (a) point xo in D is said to be an isolated point of D provided that there…

A:

Q: Evaluate the integral R2 exp(-x² – xy − 3y² + x)dxdy -

A:

Q: If vectors b, c and d are not coplanar then prove that vector

A:

Q: Solution: Next, solve the system , or max 2² +² subject to: a² + xy + y² = 3 L(x, y, A) = (x² + y²)…

A: The system of equations can be solved graphically or algebraically. The method of substitution and…

Q: 1. Chapter 14 Review 43: Let g(u,v) = f(u³ - v3, v³ - u3). Prove that g д + u2 ди ди 2 = = 0.

A:

Q: Solve the given system of differential equations by systematic elimination. (x(e), y(t)) =( Need…

A:

Q: Solve the following equations for .x. 19. e²x = 5 21. In(4-x) = 23. In x² = 9 25. 6e-0.00012x = 3…

A: Given some equations. The objective is to solve it for x

Q: Let A and B be n×n matrices.Let v be an eigenvector of A corresponding to λ1 and let v also be an…

A: Given: A and B are two n×n matrices. Let v be an eigenvector of A corresponding to  λ1 and let v…

Q: In the following functions, iterate up to 7 times regardless whether the result is less than or…

A:

Q: The ratio of hot dogs to hamburgers at the picnic is 35:21. If there are 63 hamburgers, how many…

A:

Q: Prove that if A2 = O, then 0 is the only eigenvalue of A.Getting Started: You need to show that if…

A: To show that if A2=O then 0 is the only eigenvalue of A. We need to show that if there exists a non…

Q: 11. Determine whether each of these statements is true or false. a) 0 € Ø c) {0}c Ø e) {0} = {0} g)…

A:

Q: of the vertices 4. and Cofa tetrahedron ABCD are i+j+k, and 31, respectively. The altitude from…

A:

Q: Find the Jacobian of the transformation: x = = 1.es+t y = 5. es t Jacobian (in equation form) =…

A:

Q: Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no…

A:

Q: Find the equation of the parabola by using three points (4,0), (2,8), and (6,0).

A:

Q: 5. In this question, we will prove that all non-empty subsets of Z>o has a smallest element. Start…

A:

Q: 3 Show that 2 is irrational.

A:

Q: Say a set A is countable if there is an injective map f: A → N. Show that the product of countable…

A:

Q: For any two vectors u and v, prove that . (u.v)² +\ux vf=|uf|vf and ↑

A:

Q: Let n = Your-Reg-ID (7 digits number) and let 2₁, 22, 23,..., Zn be the (distinct) n-th roots of 1.…

A: Given: Let n=Your-Reg-ID (7 digits number) i.e., n=2205275. Let z1,z2,z3, . . . ,zn be the distinct…

Q: largoths of two a md by the shortest distance between there edges is d, and the angle between the is…

A:

Q: 2) A firm is a monopoly for the good it produces. Its average variable cost function is AVC = q ²+4…

A:

Q: If a, b, c are three given non-coplanar vectors and any arbitrary vector F in space, where à ba ca a…

A:

Q: Test each of the following conjectures by choosing sets of numerical values for the variables a, b,…

A:

Q: Problem 8. Let the "Tribonacci sequence" be defined by T₁ = T₂ = T3 = 1 and Tn = Tn-1 + Tn-2 + Tn-3…

A:

Q: Q-1)Find the optimal solution for the Lpp below by using the graphical method ? Max z=X1+X2 S.TO…

A:

Q: If vectors b, c and d are not coplanc then prove that vector

A:

Q: Determine the next pattern. ۸ ہیں سعد سعد

A: Sequence of patterns are given, we have to find the next pattern of the sequence.

Q: (b) Prove the Principle of Mathematical Induction (Theorem 17) using the Least Number Principle.

A:

Q: Sketch the solution sets of the following systems of linear inequalities. 15x + 3y 4y + 2x >4 3x -…

A:

Q: Use a motrin method to determine the value of e for which the system of equations x + 3y = 2 2 = -2…

A:

Q: Using the method of the Determination of Integrating Factors, what will be the function M(x,y) when…

A: The given equation is    [3x^2e^(y)-2]dx + [e^(y)+2x]dy = 0 . . . . . . . (1)  Comparing with the…

Q: Apply the Gram-Schmidt Process to the basis B to obtain an orthogonal basis for the inner product…

A: The given basis are B=1, 1+x, 1+x+x2 on the vector space V=P2ℝ. We have to find the orthogonal basis…

Q: I. Find the intercepts, the critical points and point of inflection for each of the following…

A: Critical point: Critical points are the points where the real valued function is zero or undefined.…

Q: Circle below has center O, and its radius is 7 ft. Given that m<AOB = 30°, find the length of the…

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

Q: An office building is installing eight Wi-Fi transmitting stations.  Any stations within 200 feet of…

A: Consider that an office building is installing eight Wi-Fi transmitting stations. Any stations…

Q: Mapping 7 ()-(-4) () :) 25 -7 maps the plane onto itself. Show that the mapping is a reflection and…

A:

Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

A: