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Problem 5. Find the curvature of the curve R(t)=(t-sinh(t), 4cosh(t/2)), t > 0.
A tank contains 144 gal of water and 48 oz of salt. Water containing a salt...
Prove thatAnis a normal subgroup of Sn. Prove both that it is a subgroup AND that...
Given statement p q, the statement q p is called its converse. Let A be the...
Solve the ODE y"+3y'+2y=(e^-t)(sin2t) when y'(0)=y(0)=0
1.49 Two particular solutions of the equation 4f''(z)+f(z)=4f'(z) are f1(z)=ez/2 and f2(z)=zez/2. a) Show that any...
A young person with no initial capital invests k dollars per year at an annual rate...
Find a function f(x,y,z) such that ∇f is the constant vector 〈8,3,5〉.
Using Lagrange multipliers, prove that the least-cost design of a cylindrical storage tank of any volume...
1a) Prove that the infimum of the set (a, b] is equal to a, where a...
4) For each of the following functions, establish on which subset of its domain it is...
Consider the following set: A = { 1, {2,3}, 3, 4, {3,4}, 5, {5,6,7} } Indicate...
Give examples of the following relationships: a) A transitive and symmetrical relationship, but not reflexive. b)...
Differential Geometry (2) Find the exterior derivative of the 2-form ψ = x2y3 zdx∧dy and evaluate...
A tank, shaped like a cone has height 99 meter and base radius 11 meter. It...
Consider the subspace S = {[x, y, 2x + 3y] | x, y ∈ R} of...
Suppose {xn} is a sequence of real numbers that converges to +infinity, and suppose that {bn}...
Use spherical coordinates. (a) Find the centroid of a solid homogeneous hemisphere of radius 1. (Assume...
What type of proof or argument form is this?: A daughter tells her mother that she...
Plot the point whose spherical coordinates are given. Then find the rectangular coordinates of the point....
When the velocity v of an object is very large, the magnitude of the force due...
Show that RθRφ = RφRθ = Rθ+φ for any two angles θ,φ.
Consider the relation on {1,2,3,4} defined by r = { (a, b) : a > b...
Prove: Let (a,b,c) be a primitive pythagorean triple. then we have the following 1. gcd(c-b, c+b)...
(a) Prove or disprove: if H and K are subgroups of G, then H ∩ K...
Let S = {2, 6, 8, 9} and T = {1, 2, 5}. Explicitly list the...
1. Let ⃗u = −2[4,0,1]+[−1,3,−2] and ⃗v = 3[4,0,1]+5[−1,3,−2]. Let w⃗ = 3⃗u−⃗v. Express w⃗ as...
For each of the following equations, find the general solution (perferably using imaginary numbers): y′′ −2y′...
Estimate the integral of f(x)=x^3+4x^2+x using Gauss quadrature in the interval [1,4] when n=2. Explain the...
Find the Binomial Expansion of (5x +3y)^3, using the Binomial Theorem.
Let x ∈ ℝ. Prove that if x is irrational, then 2 + x is irrational
. Find a basis for Nul A and dim Nul A. ? = [ 2 2...
Find all elements of order 2 in the dihedral group D4.
Let a,b,c be integers with a + b = c. Show that if w is an...
Let X1 and X2 be two right inverses of a matrix A. a) Show that if...
. Prove f(z) = e-xe-iy is entire.
how many sets with 3 numbers in each set can you get out of these numbers....
Compare the monthly payment and total payment for the following pairs of loan options. Assume that...
Show that if f and g are uniformly continuous on some interval I then cf (for...
Verify that the following vectors form an orthogonal list: v1=1, 1, 2 v2= 2,0,-1] v3=1,...
One of your students claims that, unless a function is 1-1 it does not have an...
1. A restaurant maintains an inventory of disposable napkins. They use 45000 of these napkins annually,...
If u(t) = sin(6t), cos(2t), t and v(t) = t, cos(2t), sin(6t) , use Formula 4...
For a ball of mass m > 0 with velocity v in the direction of the...
Solve y''+3y'+2y=Delta(t-1)+t^13*Delta(t-0) y(0)=0,y''(0)=0
How many bijections f : {1, 2, . . . , n} → {1, 2, ....
You have been given the order of the nodes (vertices) as visited by a postorder traversal...
Liquidity refers to: Select one: A. A company’s ability to generate sales from use of its...
Show that the center of an algebra is a subspace of that algebra. If the algebra...
construct a Lyapunov function to show the zero solution of x' = -x + y -...
In topology, how do the intrinsic geometry differ among a Euclidean plane, a flat torus, a...
What happens to the adjacency matrix of a graph if this graph consists of two subgraphs...
Prove that the function f(x,y) is differentiable at (0,0) by using epsilon-delta method. (1) f(x,y) =...
Let f : A → B, and let S, T ⊆ A. Suppose also that f...
Answer b please... Let R be a ring and let Z(R) := {z ∈ R :...
Perform the following matrix multiplications A = [2 5 6] [-3 0 1] B =...
Deegan Industries manufactures two types of roll bars for Porsches. Model DRB is bolted to the...
A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with...
the following EDO: dx/dt= x4 −µx2 where µ is a parameter in R. (i) Identify the...
Given the following: Number purchased Cost per unit Total January 1 inventory 36 $ 5 $...
Find the general solution to the following equation t^2y''+4ty'+2y=1 need answer in 10 minutes
Subject: discrete mathematics - sets and logic. Determine whether the following argument is valid: Some computers...
Prove every element of An is a product of 3-cycles.
Find the minimum perimeter of a triangle with one vertex at (7,1), one on the x-axis...
Consider the following two-player game. Each player takes turns placing a penny on the surface of...
A two-dimensional, square region has two specified-temperature sides and two adiabatic sides. The model is: txx...
Find closed form expression for the generating function of the sequence: Sk + Sk-1 – 42Sk-2...
What is the sequence corresponding to the generating function : (6-3z) / (1-Z-6Z^2) ?
Second derivatives For the following sets of variables, find all the relevant second derivatives. In all...
Consider the following two ordered bases of R^2: B={〈1,−1〉,〈2,−1〉} C={〈1,1〉,〈1,2〉}. Find the change of coordinates matrix...
A sphere of radius R has total mass M and density function given by ρ =...
Can you please prove this Gordan's Theorem using Duality? Show that exactly one of the systems...
Donna De Paul is raising money for the homeless. She discovers that each church group requires...
Let x1, x2, x3 be real numbers. The mean, x of these three numbers is defined...
Find T(t) and find a set of parametric equations for the line tangent to the space...
How many different black-white colorings of the 8times 8 grid have exactly 34 black squares and...
The base o a solid is the region in the xy plane bounded by y =...
If the Classroom Building catches fire the amount of heat the structural support beams will be...
(1 point) Find an efficient formula in terms of mm and nn for the following sum...
How many different onto functions f:S→Tf:S→T can be defined that map the domain S={1,2,3,…,10}S={1,2,3,…,10} to the...
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