The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their angle of intersection, 0, 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: 48. x = e' – t, y= 4e"², 0<t<2

A:

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: Find the equation of the tangent plane to the graph of G(u, w) = sin (uw) at the point (r, ).

A:

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

A:

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

A:

Q: Given the xーxy+y? %3D 9 2. Curve 6. Find the coordinates of the POTnts on the Curve where the…

A:

Q: Consider the parametric curve x = Vt , y= 3t –1, for t20. Find the slope of the tangent line to this…

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

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

A:

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

A:

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: (B) The length of the curve r(t)=(1+1i+(1-nj+rV2k from the point t= to the point t=; is 2. - 112

A:

Q: Find an equation for the line tangent to the curve x= 2sin(t), y= 4cos(t) at the point defined by…

A:

Q: Find the lengths of the curves r(t) = (2 cos t)i + (2 sin t)j + t2k, 0 ≤ t ≤ π&gt;4

A: Given r(t)=2costi+2sintj+2tk We need to find the length of the curvature . The length of the curve…

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

A:

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.…

A:

Q: For the function z = = f(x, y) = x² − xy² + y³, find the equations of the tangent lines in both the…

A:

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

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…

A:

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: 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…

A:

Q: Find an equation of the plane tangent to the following surface at the given point. V3 A,1, sin (xyz)…

A:

Q: y = e*, 0<z<1.

A:

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: 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: 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: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

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

A:

Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

A:

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

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

A: Introduction :

Q: Find the lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

A:

Q: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

A:

Q: Find the length of the arcc of the curve x=t2, y=t3 from t=0 to t=4.

A:

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

A:

Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

A:

Q: Use the formula below to find the length of the curve defined by the equation x= cos^2 t , y = sin^2…

A:

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

A:

Q: x = 6 sin t, y = t +t at t = 0.

A: Let's find.

Q: Find an equation for the tangent plane to the graph of f(x, y) V3+ r2 – 3y2 at the point P(2, 1,…

A:

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

A:

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

A:

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A:

Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

A:

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

A: