A smooth curve C is defined by some vector function R(t) with R = (π, 0, -2) and R '(t)= (2, √5 csc t, 2 cott) for all t = (0, π). πT 2 1. Give a vector equation of the line tangent to C at the point where t = 2. Find the moving trihedral of C for all t€ (0, π). E

Q: Prove that that any Sume with TH Convex Polyhedron has two faces of edges number

A: Let F be the face with greatest number of edges ,suppose n. There will be exactly 'n' other polygons…

Q: Suppose TEL(V) and T² = I and -1 is not an eigenvalue of T. Prove that T = I.

A: We have given that , T ∈ ℒV. Also T2 = I  and -1 is not an eigenvalue of T. We need to prove that ,…

Q: Show that for any x, y ER2 we have doo what conditions on x and y is doo (x, y) d2(x, y) = d₁(x, y)?…

A: Let x,y∈R2 So, x=x1,x2∈R2y=y1,y2∈R2 Now, d1x,y=x1-y1+x2-y2 d2x,y=x1-y12+x2-y22 d∞x,y=maxx1-y1,x2-y2…

Q: f(x) = = 2, 2x² + 2x " X log₂ (x - 1), x<-2 −2 < x < 2, x‡0 x ≥ 2. 1. Sketch the graph of the…

A: Given function f(x)=2x&lt;-22x2+2xx-2&lt;x&lt;2, x≠0log2(x-1)x≥2

Q: Find the solution u(x, y) of u+sin(r) uy = y for z, y ER, u(x = 0, y) = 0.

A:

Q: Let G be the set {a, b, c, d, e, f} with operation ¤ given by the following Cayley table. You may…

A: Look for a cyclic group

Q: Let f (x, y, z) = g (√√x² + y² + 22) where is some nonnegative function of one variable such that…

A:

Q: D = 2 O -1 -2 [0.5 0.5] 0.5 0.5 -2 -1 0 De₂ De 1 2 3 2 - -1 11 -2 -2 22 [0.866 -0.500] 0.500 0.866…

A:

Q: How differential equations and may lab helps in architectural engineering field

A: MATLAB is a computer program that provides the user with a convenient environment for performing…

Q: 38. f(x, y) = ln x + ln y R: |x-1| ≤ 0.2, at Po(1, 1), y - 10.2

A: 38 Given function is fx,y=lnx+lny at P01,1. And R:x−1≤0.2, y−1≤0.2. We have to find the…

Q: Question 5. Apply Laplace Transform to solve the following Differential Equation when x(0) = x'(0) =…

A:

Q: (6) A loan of $20,000 is to be repaid in uniform monthly payments over 3 years. If the interest is…

A:

Q: Call an L-tile to be the following shape Prove that for any nzl, a 2" With a 1 x 1 Corner Sauare…

A: For n = 1 each of the four 2×2 checkerboards with one square removed can be tiled using one right…

Q: Set up an iterated triple integral equal to √√3 S√ SO 3-x² x²+y² 3 2- 4-x²-y² using: a. Cylindrical…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: A = 2 0 T -2 2 c=[12] 0 1 0 -1 [0.5 0.0] 0.0 2.0 -2 -2 -2 -1 Ce₁ -1 Ae₂ Ce₂ 0 0 Ae₁ 1 1 2 2 B = N O…

A: Since you have added many problem in one question, so here are the solutions of first three…

Q: Please go though every step and do not use a texblook solution. Why is the gcd(n-1,n)=1? why is n-1…

A: Why is the gcd(n-1,n)=1? U(n) be the group of units in Zn gcd (n -1 , n ) = 1  Because there is no…

Q: 2. In both parts, full marks will only be obtained if exact answers are given in terms of . √2 etc.…

A:

Q: Consider the following differential equation: d²f df dt² Ignoring the homogeneous solution,…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Question: G be abilian a finite n, he grauß altere (min)el. Defixe G = 19EG = cxcles (9) Im]…

A: It is given that,  G be a finite additive Abelian group of order mn. Then, we have to show the…

Q: Which one of the apportionment methods studied does not violate the quota rule? Group of answer…

A: Let us solve the problem in the next step.

Q: 2. Use f(x) = 2x + 5 and g(x) = x^2 + x - 6 for following combinations. A. (f+g)(x) = B. (g-f)(x) =…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Sketch and identify the graph of z² = x² + You may either sketch the traces onto the xy-, xz- and…

A: The given equation is z2=x2+y24. To Find: The sketch of the given equation. The given equation have…

Q: a. Find whether the following graph is bipartite or not. Explain your answer by your own. 7 187 1146…

A: To find: Whether the given graphs are bipartite or not. A collection of graph vertices—points makes…

Q: 4. Consider the sequence of functions : f₁(x) = 1 n³ [x−²+ +1 (a) the uniform topology (If yes, to…

A: The given sequence of function is ;    fn(x) = 1n3x-1n2+1 We have to answer the following questions…

Q: Verify that the pair x(t) = e 20t, y(t) = e 4t is a solution to the given system below. Sketch the…

A: Given xt=e20t,  yt=e4t   To Verify: xt=e20t,  yt=e4t is a solution to the given system below. Also…

Q: A producer of pedal-powered ice cream makers has determined that the revenue from the production and…

A: Given Data: A producer of pedal-powered ice cream makers has determined that the revenue from the…

Q: Find the general solution to the following system of linear differential equations. The independent…

A:

Q: Use the method of undetermined coefficients to find a general solution to the system x'(t) = Ax(t) +…

A: Introduction: one or more derivatives of a function are included in an equation. Equations involving…

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Let G be the set of all triples of the form (k1, k2,1) or (k1,K2,-1), where the ki, i=1,2 are…

A: Given, G be the set of all triples of the form k1,k2,1 or k1,k2,-1,where k1,k2∈Z. An operation on G…

Q: The area of the region bounded by the 2 curves f(x) = x² + 1 and g(x) = 2x + 1 is best described by:…

A:

Q: 3. Integrate numerically the given function, f(5+ 3sinx) dx using (a) single application of the…

A:

Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives fr and fy at the…

A: Given: fx,y=x-1·y13 We have to determine whether fx,y is differentiable at the point x,y=1,0

Q: Given f''(x) = 3x + 4 and f'(-2) Find f'(x) and find f(1) = = - 1 and f(-2) = 3.

A:

Q: Calculus probelm 2 and 3 please if possible In Problems 1 and 2, transform the given diff. eq or…

A:

Q: A liquor store sells two types of whiskey: Gold and Blue. Gold sells for $3,000/100ml. Every 100ml…

A:

Q: Let ρ be a relation on Z+ such that aρb if there exists an n ∈ Z such that a × 5n = b. i. Give any 3…

A:

Q: y"″ − 3y" − 4y' + 12y = 0 -

A: To find the general solution of the differential equation y'''-3y''-4y'+12y=0

Q: Justify the convergence of numerical series of general term: (Picture 1), where n is natural number.

A: Consider the series ∑n=0∞-1nn2+1 This is an alternating series. Now, consider the general term…

Q: Evaluate (2x+2y)ds if the curve C is given by F(t)=(2t²)ī +(1²)j, 0≤t≤1.

A:

Q: 22. Consider the boundary-value problem a²u əx² a²u + = 0, 0, 0<x< 1, 0 <y< ay² u(0, y) = un cosy,…

A:

Q: Choose the accurate description of the power status in each weighted voting system.  (These are the…

A: Given Data: The accurate description of the power status in each weighted voting system.   1.  [10:…

Q: Solve the following initial-boundary-value problem by using the separation of variables technique:…

A: Given :             utt=uxx                0≤x≤1   ,   t&gt;0 u0 ,t =0  ,u1 ,t =0…

Q: Q21 Let G={xER:x6=-1}. Define A on G by xAy=x+y+xy. (a) Show that gives a binary operation onG. (b)…

A: Introduction: Group is an algebraic structure in modern algebra. When a set along with a binary…

Q: Prove that using the only the form of the given equation (no graphing) that it is a paraboloid.…

A: We need to prove that the the equation: x2+z2-y4=1 is a paraboloid.

Q: Given f(x) = xe¯ = ++ (−1)”x”+1 n! [+0⁰ 'n=0 Solve for the value of f(2022) (0). Solve for the exact…

A:

Q: (a) If f is continuous and | ₁² f(x) dx = 8, show that f takes on the value 4 at least once on the…

A: We will use  the fact  ∫abf(x) dx represent area bounded by curve y=f(x) and x-axis from x=a to x=b

Q: B/ Express f(x) = cos wx, - < x < π, as a Fourier series. Hence prove that 2w 2w 2ω + + π(ω2 – 12)…

A:

Q: ma a) Ro,-90°(A) = b) Ro,-270° (A) =

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Equivalence relations Let ρ ⊆ R × R be a relation such that if cos(a) = cos(b) then (a, b) ∈ ρ. i.…

A: A relation R on a set A is said to be an equivalence relation if and only if the relation R is…