cost- sint sint+ cos t i+ - cost- sint cost- sint i+ Find the binormal vector B and torsion t for this space curve. For the space curve below, T = N = i, and K = 5e'V2 r(t) = (5 e' cos t)i + (5 e' sint)j+2k Find B B = (Di+ (Di+ (Ok (Simplify your answers.)
Q: set D: Problem #G Find the eauation OF the Iine tangent to F Cx) = cos? x - Sin? (x) at X 3r %3D 4
A: To find the equation of the tangent line at x=3pi/4.
Q: Part 2. Use the integration techniques to solve for the anti-derivative of each fur I. S3p? tan p dp…
A: According to the company rule we can answer only the first question and rest can be reposted.
Q: plz
A:
Q: Solve the initial value problem for r as a vector function of t. Differential equation: = - 22k 2 dt…
A: On solving this we will get:-
Q: A particle is moving along a horizontal path which starts at a distance of 5 ft to the right of a…
A: We have to check of the objects collide.
Q: It is estimated that x months from now, the population of a certain town will be changing at a rate…
A:
Q: c2 1 dx x² +1 4. e* + 0.
A:
Q: sec(2) tan(2) – 1 dz 3.
A:
Q: 4. Consider the curve with equation y = x* as shown in the diagram. A tangent line meets the curve…
A:
Q: Question 1 Determine the inverse Laplace transforms of: 2s2-5s-1 (a) (s+3)(s²+9) (b) 3s2+5s+1 (d) 3…
A:
Q: a²z B. For each of the following functions z, find a² z and ду? a² z дх? дудх" дхду" 1. z = 2x2 –…
A:
Q: dx Vx²-4x-7
A: According to the company rule, we can answer the first question and rest can be reposted.
Q: The approximate value of -31.8 using linear approximation, O -1.0075 O -2.0025 O -1.9975 O (E) None…
A:
Q: dz az and ду Suppose z is a function of x and y, and tan Vy? + x2 = ze6y. Solve for
A:
Q: a²z B. For each of the following functions z, find z ²z əxəy and əx²' @yəx'axây' 1. z = 2x2 – 5xy +…
A:
Q: A supermarket sells two brands of coffee: brand A at $p per pound and brand B at $q per pound. The…
A: Revenue = price per unit × number of units.
Q: Evaluate each limit: x +x-30 a) lim x-3 x-6x+5 3-1-4x b) lim X-2 x+2 x+3 c) lim x→-3 Vx-5+2
A: Limit
Q: y = e-x" and the x – axis is revolved about the y - axis.
A:
Q: What is the first term of the Maclaurin expansion of y = 8 e -0.5t cos t?
A:
Q: ) Eliminate the arbitrary umstants of y= C, + C2 e ** + C3 e 3x
A: The given equation is y=c1+c2e2x+c3e-3x. We have to eliminate arbitrary constants c1, c2, c3. Since…
Q: X=34-3 X=2-2y (-3,0) 12,07 y = 2X-4 -4 49-3
A:
Q: To-42 5-2X-3 (6z) odz dy oe aly de
A:
Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about
A:
Q: EXERCISES 1.1 Answers to selected odd-numbered problems begin on page ANS-2. 1. Evaluate the…
A: Since you have posted multiple questions with multiparts. As per guidelines we"ll solve only first…
Q: 1 е. (s²+1)(s²+4s+8)
A:
Q: 4. A car costs Php 800,000. Find its value after 4 years if it depreciates 20% of its cost per year.
A:
Q: y" + 4y= cos'x
A: Given: y"+4y=cos2x
Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…
A:
Q: dx Evaluate the integral 7+6x – x²
A:
Q: y =, x = 1, x = 4, and y = 0 is revolved about the y – axis.
A: Let's find.
Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…
A:
Q: Use trigonometric substitution to find or evaluate the integral. (Use C for the constant of…
A:
Q: 2. Evaluate the given line integral, (x – y, y) · dR, where C is the line segment from (0, 1) to…
A:
Q: III. GRAPH ANALYSIS: The graph of f is shown below. Use it to answer A, B, and C. -7 -$ -4 -3 -2 1 2…
A:
Q: dx 2. S Vx2-4x-7
A:
Q: Determine the absolute maximum and minimum values of the function f(x) =+x the interval -2sxs2. x…
A:
Q: 3s + 2 4s2 + 12s + 9 3 5 4 + Stezt 2 5 4 3 Option 1 Option 2 3 2 4 +te -tet 4 5 3 e O Option 3 O…
A: Find inverse Laplace
Q: The following question is about the rational function (x + 1)(x - 2) rex) = (x + 2)(x – 6) The…
A:
Q: sin 2t sin 5t 20 s4 + 58s² + 441 None of the choices Option 3 10 1 s4 – 58s² + 441 2 s2 + 32 s2 + 7?…
A:
Q: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface…
A: We have to solve above problem.
Q: Line 1: 3 1 — у - = Z – 8 2 - 4 Line 2: X=-2t y=2+2t z=6+2t 1.If the given lines intersect at a…
A:
Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…
A: To find out the characteristic equation.
Q: 2) w = 2yTan(2x + y) – 3xSec(x²y³) %3D
A:
Q: 2. (D² + 4)y = 5e* - 4x
A:
Q: Suppose z is a function of x and y, and z^xe^6y=y2+x2. Solve for ∂z/∂x and ∂z/∂y. [b]
A:
Q: LEARNING TASK 1: Determine the antiderivatives of the following functions: 1. f(x) = (x+1) 100
A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…
Q: dr 21. (1+x²)/16 – (tan-l r)² dx e2x+2+2 22. 8. dx x2 - 6x + 25 23. 6. 24. dr J (2 - r)V - 4x +3 dr…
A:
Q: 12г3 — 9г? + 2 dr
A: LetI=∫1612x3-9x2+2dxApply the Sum RuleI=∫1612x3dx-∫169x2dx+∫162dxTake constant…
Q: 4 2 6e"*+2dydx =? (a) 2 (e* – e?) (b) 2 (e10 – e°) (c) 2 (e16 – e?) (d) 2 (e2 – e?) (e) 2 (e64 – e?)
A:
Q: dx 8. Evaluate the integral / zlnrV(In x)² – 8 x In a V(In a)2 – 8 |
A:
Step by step
Solved in 2 steps with 2 images
- Torsion of a helix Compute the torsion of the helixr(t) = ⟨a cos t, a sin t, bt⟩, for t ≥ 0, a > 0, and b > 0.Angular speed Consider the rotational velocity field v = ⟨0, 10z, -10y⟩ . If a paddle wheel is placed in the plane x + y + z = 1 with its axis normal to this plane, how fast does the paddle wheel spin (in revolutions per unit time)?Parametrize the sine curve y = sinx using the parametrization r(t)=(t,sint), t ∈ R. (a) show that this curve is smooth. (b) Compute the curvature, and find all points where the curvature is zero. What geometric property do all those points share? (c) Without doing any computations, explain why the torsion of this curve must be identically zero. (d) Rotating the plane 30◦ is an isometry, which transforms the original sine curve into the curve parametrized by r(t) = √3t −sint 2 , t + √3 sint 2 , t ∈ R. Compute the speed, curvature, and torsion of this curve, and compare them to those of the original curve. (e) By graphing the curve, decide if it is the graph of some function y = f(x). (f) In single-variable calculus, you studied the qualitative properties of the graphs of functions y = f(x). In particular, you characterized the maxima, minima, and inflection points in terms of the vanishing of certain derivatives of the function f(x). Using the earlier parts of this problem to supply…
- a parametric position vector is defined as pictured - the final condition makes sure of a positive radius plots show space curves for the pos. vector alpha = 3, beta = 1, k = 2, h = 4, and w = 1. cylindrical vector definitions x = p cos(phi), y = psin(phi), z = z , p = sqrt(x^2+y^2), phi = arctan(y/x) a) find when the velocity vector r'(t) is perpendicular to the position vector (pictured) b) simplify the answer to a) for the parameter values used to construct the space curve in thefigure. Is the result consistent with the space curve?Let f(x,y) = xe^(xy). Find parametric equations of the indicated (directional) tangent lineor normal line to z = f(x, y) at the point (1,1, e).a. Find the tangent line in the x direction, l_x(t).b. Find the directional tangent line, l_u(?), where vector u is a unit vector in the direction ofvector v = < squr(3), 1 >.c. Find the equation of the normal line.Dierentiable curves with zero torsion lie in planes That a sufficiently di¡erentiable curve with zero torsion lies in a plane is a special case of the fact that a particle whose velocity remains perpendicular to a fixed vector C moves in a plane perpendicular to C. This, in turn, can be viewed as the following result. Suppose r(t) = ƒ(t)i + g(t)j + h(t)k is twice di¡erentiable for all t in an interval 3a, b4 , that r = 0 when t = a, and that v # k = 0 for all t in 3a, b4 . Show that h(t) = 0 for all t in 3a, b4 . (Hint: Start with a = d2r/dt2 and apply the initial conditions in reverse order.)
- A particle travels along the curve r(t) = (cos t, sin t, In(cos t)). a) Find the distance the particle travels along this path between times t = 0 and t = pi/3 b) Find the unit tangent, unit normal, and unit bi-normal vectors along this curve at (1,0,0)A particle is traveling along a circualr path defined by x^2 + y^2 = 4, where x and y are measured in centimeters. If the particle starts at the point (2,0) and moves in a counterclockwise direction at a speed of 6cm/sec, what will be the coodeinate fo the particle's position after 10 seconds? (show detailed diagrams)parametric 1 Determine the parametric equations of the path of a particle that travels the circle: (x−1)2 + (y−1)2=81 on a time interval of 0 ≤ t ≤ 2π: if the particle makes one full circle starting at the point ( 10 , 1 ) traveling counterclockwisex( t ) = y( t ) = if the particle makes one full circle starting at the point ( 1 , 10 ) traveling clockwise x( t ) = y( t ) = if the particle makes one half of a circle starting at the point ( 10 , 1 ) traveling clockwise x( t ) = y( t ) =
- A particle at (1, 0, 0) starts moving in space in such a way that its position vector at any time t ≥ 0 is R~ (t) = (cost + tsin t)ˆi + (sin t − t cost)ˆj + t²ˆk, t ≥ 0. (a) Find parametric equations for the line tangent to the trajectory of the particle at the point where t = π/2. (b) Calculate the acceleration of the particle at time t = π/2. (c) Calculate the total distance traveled by the particle in the time interval 0 ≤ t ≤ π/2Given:Vector-valued function R(t) = <4cos2t, -3, -4sin2t>Reference Point P(4, -3, 0) a. Reparametrize R using arc length s from reference point in direction increasing tb. If a particle moved along the graph from P. What is the position of the particle if it has travelled π units.A car travels over the hill having the shape of a parabola. When the car is at point A, it is traveling at 9 m/sec and increasing its speed at 3 m/sec2 . Determine the tangential and normal components of acceleration of the car at point A labeled below