Two vertical poles, 8 ft and 16 ft high, stand 18 ft apart on a flat field. A worker wants to support both poles by running the rope from the ground to the top of each post. If the worker wants to stake both ropes in the ground at the same point, where should the stake be placed to use the least amount of rope?

Q: Determine if the matrix below is invertible. Use as few calculations as possible. Justify your answe...

A:

Q: Given that lim n²(x- 5)" converges by the Ratio test. If xEZ then the numerical n- 00 value of x is ...

A: Using Ratio test we have to find the value of X.

Q: Use implicit differentiation to find the specified derivative at the given point. Find at the point ...

A: Find the implicit  derivative at point.

Q: Prove or disprove: If > an is a convergent series with positive terms, then nan → 0.

A:

Q: Prove that for any vectors u, v E C", and scalar z € C, a) u· v = v•u b) zu v = z(u · v)

A:

Q: 2. Express the region between y = e* and y = 4 – e-* as both a type I region and a type IlI region. ...

A: Given, y=ex    and   y=4-e-x Intersection points are- ln(2+3,2+3 ) and  -ln(2+3,12+3 ) =(1.317, 3.73...

Q: 2. Rectangle ABCD has vertices A (3,5), B (5,5), C (5,1) and D (3,1). Determine the coordinates of t...

A: Introduction: There is a linear transformation that rotates a point about the origin in a counter-cl...

Q: Let {a,},{b,} be sequences of real numbers satisfying Ja,|s[b,| for all n 21. Then (a) Za, converges...

A:

Q: We consider a thin plate having the shape of the surface S parametrized by Ř(u, v) = v cos(u)i + v s...

A: The equation of the thin plate is as given below. Ru,v=vcosui+vsinuj+uvk  and 0≤u≤4π 0≤v≤3

Q: We are interested in determining whether or not the following linear matrix equation is ill-conditio...

A:

Q: Let f and g be continuous functions on [a, b], and suppose that f(a) g(b). Prove that f(c) = alc) f...

A:

Q: a) The manager of a certain office supply store plans to increase the stock of calculators by a cert...

A: Introduction: Suppose, there is an initial quantity that is given. Also, the quantity is increased a...

Q: 2. (Sets) Given the universal set U= {n € N |1SnS 10), and the sets A= {n €U |n is the square of an ...

A: U=n∈ℕ| 1≤n≤10 List of all universal set U=1,2,3,4,5,6,7,8,9,10    

Q: 1 (a) Find a power series representation of 3+ 2x 1 (b) Find a power series representation of [Hint:...

A:

Q: 00 6" + 5 To test for convergence you could compare it to S (3)" and use the limit comparison test. ...

A:

Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D...

A:

Q: Find equations for the tangent plane and the normal line at point Po (X0,Yo,Zo)(1,5,0) on the surfac...

A: As per our guidelines we are supposed to solve only one question. For the solution of the first prob...

Q: Please help me with this one question (has multiple parts): Which of the following sets form a linea...

A:

Q: The terms of the Maclaurin series of the function f (x) = are 1-x OA. 4-2x +-x 2 4 3 OB. O B. 1+-x+ ...

A: Given f(x) = 41-x

Q: Given the Euler equation 2a?y" + ry' – y = 0. i. Find the initial value problem with y(1) = 1, y (1)...

A:

Q: For a natural number n, let C, = {(a¡j) E M„(R): aij = aki for all i, j,k,l such that j– i=,l- k}. (...

A: Given that,  Cn={aij∈MnR:ai,j=akl where,  j-i ≡nl-k

Q: 5. (Induction) We will prove the formula 1.1.1, 1 248 valid for n-1,2,3,.., using induction. (a) Ver...

A:

Q: Ais an n x n matrix Check the true statements below. DA. To find the eigenvalues of A, reduce Ato ec...

A:

Q: 6. Prove that the matrix A = -1 2 is diagonalizable, and find the corresponding diagonal matrix D an...

A:

Q: Evauate, el4/135°) O 0.11e-2v2i O 0.059e?v2i O 0.59e-2v2i O 0.11e?v2i Not saved

A:

Q: Let B, D be the following two bases of R°: 2 -1 B = 2 4 D = -3 -3 a) Find the change of coordinates ...

A: Given: B=222, -122, -320 and D=4-3-1, 0-3-4, 1-2-2  To find: Change of coordinate matrix PD←B from b...

Q: The regular price of a color TV is $529.43. During a sale, Hill TV is selling the TV for $425.79. De...

A:

Q: If A(3,-1,2), B(2, 1, –1) and C(1,-2,2) then A x (B x C) is. (15, 15, -15) O (15, -15, 15) O None of...

A: As per our company guidelines we are supposed to answer only the first question. Kindly re send the ...

Q: nd the linearization L(x.y) of the function f(x,y) = e X (5y) at the points (0,0) and 0,5 CoS

A: In this question, the concept of Linearization of function is applied. Linearization The Linearizati...

Q: The pawnbroker charged Elisa a simple interest rate of % (Round to the nearest whole number as neede...

A: We have to find the simple interest  rate.

Q: 7. Let V be a vector space and l: V → R be a linear map. If z E V is not in the nullspace of l, show...

A: Given: 7) V is a vector space and l:V→ℝ is a linear map. To show: If z∈V is not in the null space of...

Q: Let φdenote the Euler phi-function. Answer a and b (a) If n = 2a3b, for natural numbers a, b, show ...

A:

Q: Evaluate, in spherical coordinates, the triple integral of f(p,0, ¢) = sin ø, over the region 0 < 0 ...

A: Volume by using special coordinates.

Q: Question 1. Consider the second order partial differential equation = c2 (1) for an unknown real-val...

A:

Q: Given: A = 8 – 2i B = 4e-i C = 5260 1. ABC in POLAR FORM А-С 2. * in EXPONENTIAL FORM B (): 3. C in ...

A:

Q: r+1 Q5. Graph the function y = by applying the first and second derivative tests. Also discuss the a...

A:

Q: Draw the Venn diagrams for each of the sets. a) AN (BUC) b) (AU B) – C

A:

Q: (tx)3 -dr is equal to (x++t)² 00 The numerical value of the improper integral ...... 00

A: For a function g(x) and its derivatives f(x) such that; d(g(x))dx=f(x) Then; ∫f(x)dx=g(x)+C where C ...

Q: H. WAK 36 EXERCISE 3 Sketch the graphs of the following linear functions. Determine and indicate the...

A: Please specify which question is to be solved. As per policy solving only Question 1.  We will draw ...

Q: Find the linearization L(x,y) of the function f(x,y) = x - 5xy + 2 at Po(5,2). Then find an upper bo...

A:

Q: D. lhustrate using Venn diagram. 1. Not Prime Number Prime Number Odd Number Card Not Odd Number Car...

A: Given are three parts where in each part there are given sets and we have to write them in Venn- dia...

Q: Evaluate the triple integral of f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball æ? + y² +...

A:

Q: Hpply the eigenvalue method to find the general Solution of the given systim. Then solve the ini tic...

A: The given problem is to solve the given system of differential equations with given initial conditio...

Q: (3xe" + 2y) dx + (x*e" + x) dy = 0

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want...

Q: How do you graph: -x^2+4x-5<0?  I believe the solution is negative infinity to positive infinity?

A: Given is an inequality  We have to graph the inequality. First we solve the given inequality to find...

Q: Question 1 Let D be the region of the plane bounded by the curve C parameterized by 7(t) = [3 cos(t)...

A: It is given that, r→(t)=[3cos(t)-cos(3t)]i^+[sin(3t)-3sin(t)]j^, 0≤t≤2π   It can be written as, r→(t...

Q: Find the general solution of the following equations: 3) y" + y = tan x

A:

Q: Activity 5 Real Life Appllcation Using Arithmetic Sequence and Geometric Sequence Directions; Make a...

A: according to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: Define a recurrence relation and all necessary initial conditions for the following problem: A strin...

A: As per the question we have to find a recurrence relation with necessary initial conditions for the ...

Q: ne-third th

A: Introduction   When the Earth is assumed to be spherical, the circumference varies as the cosine of ...