Find the speed of the object whose position function is given by 7(t) = (4t – 7, 5t – 3, t° + 2t) at t = 3 Speed =

Q: m Find the equation of the tang ent to the curve ym =1 at the point (x1.y1). m

A: Topic:- application of derivatives

Q: Find the points on the curve a = t – 16t + 1, y = t² + 12t – 8 that have: %3D A. a horizontal…

A:

Q: Find the Cartesian equation of a curve defined parametrically by 5t and y = 10t for all real values…

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

Q: Find the equation for the line tangent to the parametric curve: t3 – 4t 4t2 – t4 - at the points…

A:

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

A:

Q: Find a direction in the xy-plane in which f(x, y) = e¹-xy has zero change at the point P(1.0. e).

A: We know directional derivative formula Du→fa, b, c=∇fa, b, c.u^ Lets say u→=cosθ, sinθ be the…

Q: Find the equation of the line tangent to the parametric curve 2t r(t) %3D t2 +1 - 0 <t<0 12 -1 y(t)…

A:

Q: Find the points on the parametric curve c(t) = (3t2 − 2t, t3 − 6t) where the tangent line has slope…

A: Given curve: So,

Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: Sz(t) = - 2t2 ly(t)…

A: The objective is to to eliminate the parameter t to find a cartesian equation

Q: A particle follows the trajectory x(t) = t3 + 2t, y(t) = 20t – t2 with t measured in seconds and…

A:

Q: Find the points on the curve a = ť² – 14t – 9, y =t² + 14t + 1 that have: | A. a horizontal tangent…

A:

Q: Find the speed of the object whose position function is given by F(t) = (7t – 1, 7t – 2, t + 5t) at…

A: Find speed

Q: The surface of a mountain is modeled by the equation h(x, y) = 5000 − 0.001x2 − 0.004y2. A mountain…

A: Hints:  The given equation is h(x,y)=5000-0.001x2-0.004y2 and the given point is (500,500,3750). To…

Q: Find the Cartesian equation of a curve defined parametrically by 5t and y =10t for all real values…

A:

Q: Find the points on the parametric curve c(t) (3t2 - 5t, t3 - 10t) where the tangent line has slope…

A: Given curve is Firstly, we find dy/dx

Q: The function y=f(x) is given in parametric form by the equationsx=t3,y=t2+1,where t&gt;0. Find…

A: Given:

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

A:

Q: Find . F dR such that F(x, y) = (2y, xy – 2x) And I is the curve in the 3rd quadrant from the point…

A:

Q: A curve is described parametrically by x(t)=1/(t+1), y(t) =1/(t-1). Find the equation of the line…

A: Consider the curve Find the equation of the line tangent to the curve at t=2

Q: nd the length of the given curve. 3y2/3 = 3y43 32 X = -216 < y < 125 -

A:

Q: Given the data points, determine the y at x = 0 using Lagrange method. -1.2 0.3 1.1 y -5.76 -5.61…

A: Suppose we have three points x1,y1,x2,y2 and x3,y3 then by Lagrange approximation  quadratic…

Q: Find the points on the curve a = t? – 4t + 1, y = t² + 8t – 8 that have: A. a horizontal tangent…

A: Let's find.

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Write the equation of the line tangent to the curve x In y+7xy = 28 at the point (4, 1). 32 y-7x 60…

A:

Q: I need a 3d sketch of the equation  Z=x+xsiny+xy

A: z=x+xsiny+xy

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Find the orthogonal trajectory of the curve a2 + y² = 2ln cx

A: The given family of curve is                                           x2+y2=2 ln(cx)

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

Q: Find the length of the curve. r(t) = 8i + t2j + t³ k, 0sts 1

A:

Q: Q4: Find the angle between the tangents to the curve R(t) = t²i+ 2tj – t³k at the points t = F1

A:

Q: Calculate | F.dr, where F(x, y) = (x²–3y)i+(ye")j and the curve and curve C is the parabola æ = y² +…

A: We have to calculate ∫CF.dr, where Fx,y=x2-3yi+yeyj and the curve C is the parabola x=y2+1 from A1,0…

Q: V 25t* – 1 dt with 4 < x < 6. Find the length of the curve y = 1 - Length is

A:

Q: A curve C is defined by the parametric equations x(t) y(t) = 8t³ – 2t² + 4. Write the equation of…

A:

Q: Find the coordinates of the point(s) on the curve 2y = 10 – a² that are closest to the origin. а) О…

A: Given that

Q: Find the equation of the osculating plane of the helix: r(t) = sin(3t), y(t) = 2t, 2(t) = cos(3t)…

A: Given the equation of the helix:     x(t)=sin(3t), y(t)=2t, z(t)=cos(3t) So, rt=sin3t,2t,cos3t. Find…

Q: Find the tangent plane to the equation z 5x? – 2y? – 5y at the point (3, 0, 45).

A: We need to find the tangent plane equation at (3,0,45)

Q: Find the point at which the line F (t) = +t intersects the yz plane.

A: Given: An equation of a line in the parametric form is, r→t=&lt;2,-7,7&gt;+t&lt;-5,-6,6&gt; The…

Q: Find Dy 2 y of the following parame equations: x = t2 - 2t +1 y= 2t2 - 4t3

A:

Q: Find the equation of the plane that passes through the point (2, 1, 1) and is tangent to the surface…

A: We have to find the equation of the tangent plane.

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: Ex (50) / Find the distance from the line = 2 +t, y = 1 +t, z = -1- 2t to the plane x + 2y + 6z = 10

A: Using. Distance formula form line to plane,

Q: 1. Find the equation of the tangent lines to the ellipse x² + 4y = 8 perpendicular to the line x +…

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

A: The line x(t)=2+4t, y(t)=-6-8t, z(t)=6-7t intersect yz plane Note:    Multiple questions are given,…

Q: Find the points on the curve x = t – 16t + 4, y = t + 16t + 5 that have: A. a horizontal tangent…

A:

Q: trace the path of the curve f(t) = (3e', 4e24)

A:

Q: Given the position function, s(t)=÷r' -3r² +5, describe the motion of the particle at t= 2

A: Calculate the first and second derivative to get the velocity and acceleration of the particle…

Q: 3. If the position function of a particle is x(t)=t^3+8t^2-2t+4, t>0 Find when the particle is…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.