The curves r1(t) = <4t, t2, t4> and r2(t) = intersect at the origin. Find their angle of intersection, θ, correct to the nearest degree.

Q: For which values of t is the curve x = ln t, y = et concave up?

A: given curve x=lnt  , y=et

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: 2.) Find the acute angle between the given curves y² = 2x and 4x²+ 4y² +5y=0

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Q: (11) At what point do the curves ri(t) = (t, 2-t, t²) and r3(s) = (1-s, s+1, s²+1) intersect? Find…

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Q: For what value of t will the slope of a line tangent to x = 6 sin t, y = t² + t be 0?

A: We have to find t

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

Q: Q3/ Find the acute angle between the two curves at their points of intersection: r = 2si n 0, r =…

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Q: The curves r1(t) = (5t, tº, – 4t³) and T2(t) = (sin(t), sin(3t), t – n) intersect at the origin.…

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Q: If C = {(x, y): 1 ≤ x ≤ 2, y = ln(x + √x² − 1)}, find the length of the curve. -

A: C=x,y: 1≤x≤2, y=lnx+x2-1

Q: The curves r¡(t) = (2t, t², t³) and r2(t) = (sin(t), sin(3t), 2t) intersect at the origin. Find…

A: If there are two curves y=f1(x) and y=f2(x) which intersect each other at point (x0, y0).  The angle…

Q: Find the length of the following curves. a.) x= 2t , y= cos 4t , 0 ≤ t ≤ π/2

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Q: Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y =…

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Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

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Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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Q: Find dy/dx and (d^2)y/dx^2, and find the slope and concavity (if possible) at the given value of the…

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Q: Find the condition that the line x cos a + y ain a =p may touch the curve yh =1. am bm

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Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: At what point do the curves r¡(t) = (t, 1 – t, 3 + t²) and r2(s) = (3 – s, s – 2, s²) intersect?…

A: Given Data: Curve 1: r1t=t, 1-t, 3+t2 Curve 2: r2s=3-s, s-2, s2   For the intersection point,…

Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: Find f (x-y3)d a + xy dy if the contour C looks as follows: It consists of two arcs of radius 1 and…

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Q: A particle P moves on the curve r= 3i + 4t²j. The distance of P from the origin when t =1 is

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Q: The curves r1(t) = (4t, t³, – 5t°) and i2(t) = (sin( – 2t), sin( – 5t), t – T) intersect at the…

A: Solve the following

Q: Given the function z = = f(x,y) = 2y³ -5xy-3x²+2, find the equation of the tangent plane at (1,-1),…

A: Given problem:- Given the function z  = f(x, y) = 2y³ −5xy-3x²+2, find the equation of the tangent…

Q: 3. For the 2 curves xy = 9 and x = 81y, find angle between the two tangent lines at the point of…

A: NOTE: Refresh your page if you can't see any equations. . the first curve is  . the second curve…

Q: find an equation of the tangent plane at the given point. G(u,w) = sin(uw), ( π/6 , 1)

A: Given that: G(u,w)=sin(uw) Now, Find the partial derivatives of Gu(u,w)  and  Gw(u,w) at point π6,1.…

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Find the exact length of the following curve y = Vx – x² + sin-'(/T).

A:

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/4 %3D

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Q: xy = -4 and y² = 2х

A:

Q: The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their…

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Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0stsa/4

A: In this question we have to find the length of the curve.

Q: Find the length of the curve r = 4 – 4 sin 0

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Q: I. Find I = ždz where C is the line segment from 3 +i to 3 - 2i.

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: 3x + xy? 2y + x?y dy dx

A:

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

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Q: 4.For the 2 curves xy = 8 and x2 = 64y, find the angle between the two tangent lines at the !! %3D…

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Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

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Q: Consider the two graphs y= 2x and x2 - xy + 2y = 28. The absolute value of the tangent of the angle…

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Q: Find the length of the curve. x- 5 sin t+ 5t, y= 5 cos t, 0 st< O A. 5T O B. 20 O C. 10 O D. 30

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Q: Find the tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

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Q: 3. Draw the following curves on the grid provided y=-2 sin (x+30°) - 1 -90 90 180 270 360 -1 -2 -3

A: (x+30) represents a horizontal shift of30° to the left.(1 unit on the graph !!)-2 represents…

Q: find equations for the lines that are tangent andnormal to the level curve ƒ(x, y) = c at the point…

A: given: ƒ(x, y) = c at the point P0 y - sin x = 1, P0(π, 1)

Q: where c is a constant, then prove that the foot of perpendicular from the origin upon the straight…

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.