At time to, a moving particle has the velocity vector v = 5i and the acceleration vector a = 3i + 4k. Determine the curvature k(tg) of the particle's path at time fo. (Use symbolic notation and fractions where needed.)

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

A:

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

A:

Q: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Suppose that a particle following the path (e' cos(t). sin(), ) flies off on a tangent at lo = 2.…

A:

Q: Suppose that a particle following the path c(t) = (t,t – 5t,0) flies off on a tangent at to = 3.…

A: Given:c(t) = (t2 , t3-5t , 0)

Q: Find the time required by the particle in passing between points which are at distances 4 and 2…

A:

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: A hang glider is spiraling upward along the curve r(t) = (5 sin t, -5cos t, 4t2-3t +1) Find the…

A:

Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

A:

Q: Determine the parametric equation for a line that is tangent (intersection) of the two fields below:…

A: We have to find out parametric equation for a line that is tangent (intersection)of the two fields…

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

A:

Q: Find the curvature of the function y=ln(3x)y=ln(3x) at x=3x=3. Find the radius of curvature at…

A:

Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: Solve the problem by using Laplace Trons form +y= Sin 2€ %3D yo) = 0

A:

Q: Find the unit tangent vector to the curve defined by 7 r(t) = (5 cos(t), 5 sin(t), 2 sin² (t)) at t…

A: To find the unit tangent vector to the curve defined by r→t=5 cost, 5 sint, 2 sin2t

Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

A:

Q: Find the unit vector towards the tangent of the curve y = x at x =1

A:

Q: Compute the principal unit tangent vector at t = T/2. F(t) = sin(2t) î + 2 cos(t) ĵ + tk COS 2 2 - -…

A: unit tangent vector

Q: For time 1 > 0, the position of a particle moving in the xy-plane is given by the parametric…

A: Velocity==rate of change of distance per unit time=displacementtime=dsdt. Given that: x=4t+t2  and…

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as <1,m> vector. And point= (a,b)

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: Find an equation of the tangent plane to: 3x +y = z at P(-1,1,-2) %3D

A:

Q: Find the equation of the plane tangent Z = (x+2)*- (y-1)²-5 at (2,3,3) to

A:

Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

A:

Q: For time t > 0, the position of a particle moving in the xy-plane is given by the vector (, et).…

A: Position of particle = (1/t, e3t) Velocity = derivative of position of particle = (-1/t2 , 3e3t)

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

A:

Q: Find the tangent plane to the equation z 2y cos(5x – 4y) at the point (4,5, 10)

A: Given; z=2ycos(5x-4y) at the point (4,5,10)

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

Q: Please solve

A: Parametrization of tangent lines is given by

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

A:

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Let r(t) = (sin 2t ,3t, cos 2t), -n SIST, a) Is speed always constant? b) Show that the velocity and…

A:

Q: Find the vector equation of the tangent line to 7(t) = 2 (e1 %3D

A:

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j +…

A:

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

A:

Q: Find the equation for the principal curvatures, the differential equation of the lines of curvature,…

A:

Q: Find the acceleration of a particle having position function r(t) 6 sin ti+ 9t j+ 2 cos t k

A:

Q: The Normal component of the acceleration of a moving object in space at time t is given by aN + 1 If…

A: Explained below

Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

A:

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: he position x(t) of an object moving in 1-D on the a - aris in an inverse-square force held (such as…

A: As given by the question There are given that the equation of inverse-square force field is:…

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: The position vector of the particle is 1 R = î cos(t) + ĝ sin(t) + k log (0 <t < T/2). sin t' (a)…

A: Differentiate the position vector R→=costi^+sintj^+log1sintk^ with respect to t, to obtain the…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.