Assume that Achilles' speed as 100 times as fast as the tortoise's and that this animal has been given a head start 1000 meters. Suppose also that Achilles runs 200 m in 1 minute. a) Use the theory of limits to compute the distance that Achilles will travel to catch the tortoise. b) Use the formula for a geometric series to compute the distance that the tortoise will have advanced when Achilles reaches the tortoise. c) How long will it take for Achilles to reach the tortoise?

Q: 5.8. Let R = C[t]. Show that S = R[x]/((x)^(x, t)²) is not flat over R.

A: please find the attached answer

Q: P is a point and PM and PN are the perpendiculars from P to z-x and x-y planes. If OP mak angles 0,…

A:

Q: Question 4. A circle centered at (0,0) with radius one is revolved about the line x=3. The solid of…

A: The equation of the circle is x2+y2=1 Now consider a horizontal strip of width dy…

Q: Let X = C[0,4], with the usual notation and suppose X is endowed with the norm, ||f||2 Consider the…

A: Let X=C0, 4, with the usual notation and suppose X is endowed with the norm,…

Q: the base of an objec cross sections (perper nd your answer to at

A: Here, in the question, the graph shows the base of an object. We have to compute the value of the…

Q: (d) Show that Z under addition is a subgroup of under addition

A: Given : ℤ is a set of integer. To prove : ℤ is subgroup of Q under addition.

Q: Find the shortest distance between the times y-2 3 2-1 २ and X-2 3 2-3 ។ y-4 4 ५-८ 5 and also obtain…

A:

Q: Solve the matrix equation AX = B for X. 1-2-3 HH - 1 4 6 B= 6 1 -1 -2 A = 3 7

A: First convert given system of equation in augmented matrix then solve by Gaussian Elimination…

Q: Define f: [1,00)→ R by f(x) = (-1)"/n for all z € [n, n+1). Prove that (a) f exists; (b) f is not…

A: Please find the attached solution

Q: For the given​ functions, find ​(f◦​g)(x) and ​(g◦​f)(x) and the domain of each. ​f(x)= 2x + 1​,…

A:

Q: value 1. Let K be the subgroup of positive real numbers. Determine whether or not he canonical map H…

A:

Q: ACTIVITY: Problem Solving (show your solution) 1. Determine which Simpson's Rule you are going to…

A: Given : Time (min) 0 5 10 15 20 25 30 Velocity(m/s) 25 28 32 30 29 26 23 To find :(a)…

Q: EXERCISE 57 Prove that f(x) = x cannot be written as a finite sum Σ b, sin(nx) A

A:

Q: ixed points and stability Slope field Phase line

A:

Q: 24. Using the CAD drawing below, calculate the measures of angles C and E in degrees and minutes if…

A:

Q: (a) Check as to whether ordinary multiplication is a binary operation on Z or not

A:

Q: Suppose b is changed to b' . How large relative change can this change produce in the solution to Ax…

A: The given matrix is, A=1112501-12,  and b=123. To Find: The maximum change in the solution of the…

Q: 5 Questions 5 and 6 refer to the following information. Dakota and Alex work as babysitters. For…

A: Dakota charges   $10  per hour  and  $5  for travel expenses.  Alex charges  $8 per hour  and  $4…

Q: a. What is the trapezoid approximation with n subintervals? T(4)= (Round to six decimal places as…

A: Let the given integral  I=∫1e6xdx   Take y=fx =…

Q: Consider the following initial value problem. y" + 6y' + 25y = 8(t) + 6(t5a), y(0) = 1, y'(0) = 0…

A: Formula of Laplace transformation…

Q: Determine a CRS modulo 17 whose elements satisfy both of the following properties: i) congruent to 3…

A:

Q: What is the inverse matrix of. SE S FOR SE Pemb CEPURE AGRE PAPERS SPORT TELE P PRECES CHEAPES…

A:

Q: Find the sum of the areas of the shaded rectangles under the graph. Round to two decimal places.…

A: Area of rectangle= Base × Height Base if every rectangle us 1.  Height is 3x1/2

Q: smallest such k is called the index of nilpotency of N. (a) Show that if a matrix N is nilpotent,…

A: A matrix N is said to be nilpotent if Nk =0 for some integer k.

Q: Given a matrix 2x 1 Choose all values of x and y for which the given matrix A has a row echelon form…

A: Reduced echelon form and row reduced echelon form of the matrix

Q: f(r,0) = e-to Find the regions where f is the analytic function Consider the function

A: Given that     f(r,θ) = e-iθr Since  fr,θ = ur,θ + i vr,θ  and  e-iθ = cos(θ) - i sin(θ)…

Q: 2. Solve the general cubic equation x³ + ba + bx + c = 0 with the trick of Cardan's Ars Magna.

A: The general cubic equation x3+ba+bx+c=0. We have to solve this equation using Cardan's Ars Magna.

Q: 2. y+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e* (4+sin x) b. y=4e¹ cos x c. y=e*(1+3 cos x) d.…

A:

Q: Solve the modified Laplace equation with a source term (Poisson's equation!): Uxx = —Q(x), for Q= =…

A: Please find the attached image

Q: 0 0/5 Graph the parabola. y =−x²+3 Plot five points on the parabola: the vertex, two points to the…

A: Given equation of parabola,  y=-x2+3

Q: Question 2 ! problem dy dx Consider the initial-value =1+2x−y, y(0) = 1. (a) Use the Euler's method…

A:

Q: . During the class, we derived in detail the first order Richardson extrapolated derivative, by…

A: Note: As you asked only subparts (a) and (b) so, i answered here only (a) and (b).

Q: Prove that there is an even integer x which is the sum of the cubes of 4 odd integers. Recall that…

A: We have 4 odd integers and and even integer x , and we need to prove the sum of cubes of 4 odd…

Q: Find the following matrix product, if it exists. 100 0 1 0 0 0 1 -2-5-9 8 4 100 OA. 010 001 -6 0 2-8…

A:

Q: Determine whether the table could represent a function that is linear, exponential, or neither. If…

A:

Q: Let n, m € Z. If n+m is odd, then n and m are not both odd.

A:

Q: Prove that 3" +4" ≤5" for all integers n ≥ 2.

A:

Q: Problem No. 1. Three products are made by the Wright Company. The contribution of each of these is…

A: Max Z=2x1+4x2+3x3 subjected to 3x1+4x2+2x3≤602x1+x2+2x3≤40x1+3x2+2x3≤80 The problem is converted to…

Q: The following statements are made about (right) cosets of a subgroup H of a group G. Say whether…

A:

Q: n=1 TL (4- π)¹² 2

A:

Q: Given the differential equation y" + xy = 0 and assume a solution of the form y = Choose All Correct…

A: Given differential equation is y''+xy=0 The solution is determined as shown in the next step.

Q: c. 6-3

A:

Q: the equation to the plane in the new position is ax + by ±z √√a²+ b² tan α = 0.

A:

Q: 2. Complete each of the following. a) Let [x] € Z/nZ. What is the additive inverse of [x]? b) Show…

A:

Q: Prove that 3" +4" ≤5" for all integers n ≥ 2.

A: The given problem is to prove the following inequality 3n+4n< 5n for all the integers n>2.

Q: Determine the pivot element in the simplex tableau. (If there is more than one correct pivot…

A: Given,

Q: K Perform the indicated operation, if possible. H + 2 9 8-8 7 -1 13 0 80-14 1 -27 1 -8 11 O A. The…

A:

Q: 32. 4+ 3+ 2+ 7-6-5-4-3-2-1 1 2 3 -3- Show Transcribed Text 567 Write an equation for the function…

A: Let fx=A(x)-∞<x<-2B(x)-2<x≤2C(x)2≤x<4D(x)4<x<∞

Q: K Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the…

A:

Q: 1. 2. Quantity A 0.01410 pitzon ¹410 adiant Quantity B 0.0141 Quantity A The average price of the…

A: