4. A pipeline is to be run to a resort community which is on an island 10 miles from the closest point on the shoreline. The water source for the pipe is 20 miles down the shore. If it costs $500/mile to lay pipe through water and $300/mile to lay pipe on land, at what point on the shoreline should the pipe turn into the water to minimize cost? What is the total cost? (see diagram) Island Pipeline Shoreline Water Source

Q: Suppose f : (a, b) → R is continuous at every point in the open Question 3 interval (a, b), and that...

A:

Q: Find the linear approximation of the function at the given point: f(x, y) = 2 sin x – 3 cos y at (0,...

A:

Q: 8) Janice needs to read her book by Friday. On Monday, she read of it On Tuesday, she read of the bo...

A:

Q: 1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduce...

A:

Q: c) Find a subset of S that is a basis for W. d) Express v= as a linear combination of the basis obta...

A:

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at th...

A: Note: The directional derivative of a function is the rate at which the function changes at a specif...

Q: The results of a certain medical test are normally distributed with a mean of 130 and a standard dev...

A:

Q: .Which of the following ordered pair is a solution to the given inequality? O A. (0,0) O B. (0,-6) O...

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not men...

Q: On the decibel scale, the loudness of a sound, D, in decibels, is given by D= 10 log (1/1,), where l...

A: D=10(logI-logI0)=10logII0 Where I= intensity of the sound in watts per square meters I0=intensity of...

Q: Determine the values of k such that the system of linear equations does not have a unique solution. ...

A: Given x + y + kz = 3 x + ky + z = 6 kx + y + z = 6

Q: en two sets: A and B. A has 8 elements. B has 9 elements. A and B share 4 elements. How many ele...

A: Given two sets: A and B A has 8 elements. B has 9 elements. A and B share 4 elements.

Q: ,A large cube of ice melts such that it maintains its shape. The surface area is decreasing at the r...

A:

Q: This function has vertical asymptotes. X = -5 (Smallest valued vertical asymptote.) (Largest valued ...

A: This is a problem of application of differentiation.

Q: Determine the quadratic equation that best fits the given set of data: (1, 2), (2, 3), (4, 3), (6, 4...

A:

Q: L{ e¬at sinh wt} =

A:

Q: 1. Consider the matrix -3 1. -2 3 1 -1 6 1 (a) Find a basis for Im(A). Be sure to show your work. (b...

A: Given- Consider the matrix A = 2-31-23-1168011 To find-  Find a basis for ImA.  Fill in the blanks ...

Q: Prove that any vector U,U-(U-ei)e,+(U-eeJez +(U.e;)e [Hint:corite u in COmpollent From)

A:

Q: c) Find a subset of S that is a basis for W.

A: A linearly independent set of vectors is a basis of a subspace W if it spans W. Now since S spans W,...

Q: Augmented form and solve using LU decomposition: a + 2b +c + d = 1 a - b + c + 3d = -1 2a +4b + 3c +...

A:

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and indica...

A: Solution:-

Q: IfT: R? → R³ is a linear transformation such that 13 16 (:) - T 26 and T then the standard matrix of...

A: Standard basis for R² is given by {(1,0),(0,1)}.

Q: Vx E R, Jy E R, x + y = 0 %3D

A:

Q: car travels 180 miles in 3 hours. At this rate, how many miles does the car travel in 1 hour? Practi...

A: We have to find how many miles does the car travel in a hour.

Q: From 6 Algebra books and 8 Trigonometry books, in how many ways can Shiela selects 3 Algebra and 3 T...

A:

Q: Sketch the line that you think best approximates the data in the scatter plot. Then find an equation...

A:

Q: f the exponential generating function is (ex-1)3, find a formula for a

A: To find the sequence an for the below exponential generating function. fx=ex−13

Q: Solution Bessel's Function Tutorial sheet 1. a Soll J ş CX) = J +I CX). J를 (x) Jt (x). LJ Cx) - I t ...

A:

Q: Problem 1.27. Find the in-degree and out-degree of each vertex of the following directed graphs a V3...

A:

Q: The differential equation (x +3y²)y'-y 0 is a first order linear differential equation in standard f...

A:

Q: 9. Explain why four vectors is R³ are always linearly dependent.

A:

Q: ) Given Xn+1 = X+ 2X + 3Xn, shown below (also shown is Xn+1 = Xn), and Xs = 0.1, %3D what is AX5? a)...

A:

Q: L{t³}

A:

Q: a 3. In R, let W be the subset of all vectors v = az that satisfy a, -az = a, - a,. az as a) Show th...

A:

Q: 9.19. Exercise. Let P, Q, P' and Q' be points in the Euclidean plane. Assume P' and Q' are inversion...

A:

Q: The differential equation y+ 3y = (y + 4x) y can be written in differential form: M(x, y) dx + N(x, ...

A: The given differential equation is y+3y5=y3+4xy' We have to write the given differential equation in...

Q: ive example to show that a quotient space of a second countable space need not be second countabl

A: This is a problem of topology.

Q: Let p and q be propositions. Then p →1 19 A(p → q)] is a

A: we find this by using truth table.

Q: 1 Let f(x, y) 2 5æ + y - 3y. Зу. 2 Our goal is to find the location and value of the absolute maximu...

A:

Q: 2. Consider the following system of four equations. You are given two solutions X1 and X2. Generate ...

A: Given a system of four equations :                  x1 - x2 + x3 + 2x4 = 03x1 - 2x2 + x3 + 3x4 = 05x...

Q: a, az B. In R*, let W be the subset of all vectors v = that satisfy a, -a, = a, –a,. az a) Show that...

A:

Q: Evaluate : 12C5

A:

Q: 2 Let f(x,y,z) = 4x + 2y +z +7 and P be the point (x,y,z) = (1,1,1). (i) Find a unit vector n in the...

A:

Q: Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the regi...

A: To use the cylindrical shell method to find the volume of the solid obtained by rotating the region ...

Q: À 90% confidence interval for p is given as (0.26,0.54). H

A: Given, a 90% confidence interval for p is given as (0.26, 0.54).

Q: (3) You are an accountant for a manufacturer of radios. The demand function for the tablets is p=40-...

A: Given:Demand  P = 40-4x2Here x = number of tablets produced in millions.  

Q: Show is a contour plot for a function z = 3 В A (a) Is fy positive, negative, or zero at A? (b) Is f...

A:

Q: Which among the following statements is true? * Every conditional statement is logically equivalent ...

A: The 1st two statement is not correct since we know that A conditional statement is logically equival...

Q: Consider the divisibility partial order on N. Find a, b E N so that the interval poset a, b| has hei...

A: To find- Consider the divisibility partial order | on ℕ. Find a, b ∈ ℕ so that the interval poset a,...

Q: 2. Use projections or transposes to determine the least squares quadratic that best fits the points ...

A: Curve fitting: quadratic equation

Q: e of mwl

A: