Use induction to show that for any n ≥ 0, then (n/e)" ≤n! where e is base of the natural log and it equals, 2.7183. Hint: use the inequality, (1+1/n)" ≤e.

Q: Let R be an n × n plane rotation. What is the value of det(R)? Show that R is not an elementary…

A: R is a n×n plane rotation.

Q: 2. Using Romberg Integration to sixth order accurate a obtain of fevet de X

A: Using the trapezoidal rule for first step in each value of h, step size.

Q: (f) Jocelyn is walking along the same path. Selected values of her velocity and positions on the…

A: From given table in part (f): m(10)=20, m(2)=55 We know, m'(t)=dm(t)dt∫m'(t)dt=m(t)+c

Q: Suppose p = 22 +1 is prime, with m > 1. Show that the order of 3 mod p is p-1, so 3 is a primitive…

A: Results used in this problem will be 1) Euler's Theorem 2) Law of Quadratic Reciprocity 3) Eulers…

Q: 11. Use the divergence theorem to compute B (f, nn) dvols for f(x) = |x|x over the surface S given…

A: Given integral and divergence theorem:

Q: The image shows the graph of a degree 7 polynomial with leading coefficient -1 whose roots are -1,…

A: The given graph shows the graph of a degree 7 polynomial say px. Leading coefficient :-1 Roots: -1,…

Q: Find the 5 number summary for the data shown X 2 7.5 8.7 9.6 10.1 10.8 10.9 24.4 30 5 number…

A: The question is about 5 no. summary. We have to find the 5 numbers summary .. The procedure is given…

Q: Question #4 (2p). Evaluate the following integrals using the integral properties of odd and en…

A:

Q: Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your…

A:

Q: Q.13 The upward velocity of a rocket can be computed by the following formula: v=uln- mo mo + qt -gt…

A: The upward velocity formula is given as follows: v=u·lnm0m0+qt-gt Where, u=2000 m/sv=750…

Q: Brain weight B as a function of body weight W in fish has been modeled by the power function B =…

A: given B=0.007 W23W=0.12L2..53t=10,000,000 years∆L=23 cm -16 cm=7 cmL=18 cmnow we have to find out…

Q: The projected year-end assets in a certain country's government trust funds, in trillions of…

A:

Q: Use proof by contradiction to show that √3 is irrational.

A: We will use contradiction method

Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A:

Q: Sketch the graph satisfying all the given conditions: (Show all in one graph) lim g(x) = 5 x-3 lim…

A:

Q: anx ; and an [a, b] ⇒ flan) → f(x) ;ant an[a,b]

A: The given statement is related to sequence.

Q: At a large company picnic attended by 2,545 people, two of the food items served are bratwurst and…

A: A)  We have to construct a Venn diagram B)We have to express each given set by set notation symbols…

Q: Suppose that f: [a, b] → R is a continuous function, and f f = 0 for every rational number a in the…

A: Let us Suppose, for the sake of contradiction, that there exists a point c in [a, b] such that f(c)…

Q: 11. Calculate F.ds where F = (3xy, xe², z³) and S is the surface of the solid bounded by the…

A:

Q: Use a graphing utility with matrix capabilities to find the following, where u = (1, -3, 1, 2), v =…

A:

Q: In Exercises 37-42, set up the iterated integral for evaluating ƒ ƒ(r, 0, z) r dz dr de over the…

A: Clarification of your query:

Q: Suppose p = 22 +1 is prime, with m > 1. Show that the order of 3 mod p is a power of 2.

A: p=22m+1 is prime, with m≥1.

Q: Solve the given initial value problem. y' + 2y' + 17y=0; y(0) = 4, y'(0) = -3 y(t) =

A: Note :- '' As per guidelines we will solve first question. If you want any specific question to be…

Q: a. Find all the intersection points of the following curves. b. Find the area of the entire region…

A: Plotting the curve:

Q: 4. A salesperson must visit 5 stops within the same city, each connected by travel routes taking…

A: Note: According to the guidelines we are allowed solve one question at a time. Please post question…

Q: 3. The value in pounds of a fund at time t = 0 is Vo= 50, 000. After one year (at t = 1) it has…

A: V0=50,000V1=51,500V2=50,800Withdrawn amount after 1 year=£1,500

Q: Let V be set of all vectors (x, y) in R² such that xy ≥ 0. Addition and scalar multiplication are…

A:

Q: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for…

A: x1=1-301x2=3-6-51

Q: Using the graph, find the missing values of x and f(x). Ax) g(x) 3 2 + -2 -3 3 4 1. f(-1) 2. f(1) 3.…

A:

Q: B: Solve the following differential equation by using general method. a²u อน = +2 u(0,y) = 0,…

A: Given a differential equation; ∂2u∂x∂y=∂u∂x+2 Subjected to boundary conditions u0, y=0uxx, 0=x2

Q: Prove that the groups A and DXZ are not isomorphic. 5

A: The given in the question is the two groups A5 and D6×Z5, and the objective is to prove that these…

Q: y" +13y' +26y=5446e cos 14t solution is y, (t) = CL

A:

Q: Use variation of parameters to find a general solution of the system, x' (t) = Ax(t) + f(t), where A…

A:

Q: Find the orthogonal projection of ✓ = projw(u) = 61 90 904 45 281 30 52 45 8-60 onto the subspace W…

A:

Q: Which of the following sets form a basis for the vector space P₂(R) = {ax² + bx + c : a, b, c = R}…

A: According to guidelines first three subparts can be solved.

Q: the center and foci of the followin 4x^(2)+8y^(2)-16x+32y+32=0

A: Given,              4x2+8y2-16x+32y+32=0. To find the center and foci of the given equation.

Q: If R and S are rings, define the direct sum of R and S, ROS by RS = {(r, s) : r € R, s € S} where…

A:

Q: | The graph of y = √3x - x 2 is given. Use ansformations to create a function whose graph is as s…

A: The graph of y=3x-x2 as below After some transformations we have the following graph We have to…

Q: In this exercise use the transformation rules given in the updated Lecture 4 slides, slides 61 to 70…

A: Quantified relational logic is a type of logical system that deals with the relationships between…

Q: 1. (Section 17.7) Use Stokes' Theorem to calculate the work done by F(x, y, z) = î+ (x + yz)j + (2xy…

A: From the given information:

Q: Please give me the answers for the fourth and fifth questions. And Is V a vector space?

A:

Q: Frank borrowed $8000 at a rate of 16.5%, compounded quarterly. Assuming he makes no payments, how…

A: Principal, P=$8000Rate, r=16.5%=0.165n=4 (since interest is compounded quarterly)Time, t=10 years

Q: 9. Find the least nonnegative residue of (a) 148! (mod 149) (b) 70! (mod 5183)

A: The given problem is to find the non negative residue for the given congruence problems. Given  a)…

Q: The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for…

A: The given set 10-109, -515-9 is a basis for a subspace W. Using the Gram Schmidt process to produce…

Q: dentify and sketch the surface (S) of equation z your work). -²+ 4 16 (Show all the details of

A: The given equation z=x29+y216. We have to sketch the graph of the equation.

Q: Sarah negotiated a price of $24,520.00 for a new Toyota Camry Hybrid Sedan. She is prepared to give…

A: We have to find the. How much money will be paid in interest? What will the monthly payment be? How…

Q: Start by converting to get the dimensions in the same units. 20.5 ft ramp 1 021.6 in. 4. a) The code…

A: The code for wheelchair ramps states that they must not have a slope greater than 112. We have to…

Q: Graph the hyperbola using the transverse axis, vertices, and co-vertices: 2²-22=1 25 Use the green…

A: Given equation of the hyperbola is y2-x225=1 Or (y-0)212-(x-0)252=1, Which is of the form…

Q: With f(x)=2x^5+3x^4 in [0,1] , we now use Simpson's rule. In order to achieve an error ≤1×10−6 , how…

A: We find the number of points when the error is 1x10-6

Q: 5, determine which sets of vectors are orthogonal. 5 DOD 4 2 -4 -3 1 -7 3

A: A set S is said to be orthogonal if for all u,v inS 《u v》=0 .  Given set contains  vectors so the…