Suppose surface #1 is defined by =45°,0

Q: Find the exact arca of the surface obtained by rotating the curve: 3 24 = 5 sin Tr, 0 <I<1 about the…

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Q: 7. Identify the surface for each of the following equations. (a) z = r² (b) r² + z² = rl (c) p = 4…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 1. Let S be the surface generated by the curve +y+4= 0 when it is revolved about the z-axis. (a)…

A: y = x2 - 4 (a) we choose x, θ as perameter = (x, - (x2 + 4) cos θ, -(x2 +4) sin θ)   (b) dr→dx= (1,…

Q: ne if the curve (In t. t In t. 1) is tangent to the surface rz- uz? + cos Tu =1 at (0.0. 1).

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Q: 13. Find the length (units) of the arc of the curve 8y = x* +; from x = 1 to x = 2. 35 а. 16 33 33…

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Q: 1 + 2)7 fromy = 0 to y = 5. Find the exact arc length of the curve x = Enter the exact answer. L =

A: Given:- x=(1/3)(y2+2)(3/2) To find:- Find the Exact arc length of curve from y=0 and y=5

Q: Find the following (hint: The FTC and Green's Theorem might be helpful on this problem) (a) If f(x,…

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Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…

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Q: to The diagiam Shous The Cauve Cosx and k g where KT a Constant, for 0Lx S T. he curves touch et…

A: In order to find the solution of the given question, we will use the concept that the gradient of…

Q: The given curve is rotated about the y-axis. Find thearea of the resulting surface.   y = 1 -x2…

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Q: 10) The line x = -1+t,y = 2 +t,z 2t + 7 intersects the surface z = x2 + y?. Find the cosine of the…

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Q: draw and identify the graph of the following surfaces a. x² + y² = sin²z, z = [0, π]

A: Any surface in the 3D plane can be represented in the form of f(x,y,z)=0. A graphing utility can be…

Q: 10. For the asteroid given by = 4cos (t), y = 4sin' (t) on 0,2n|, find the slope of the tangent at…

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Q: II. Find the length of the following curves. (a) x = 2t , y = cos 4t, 0 <t <

A: Given:    x = 2t    y = cos4t    0 ≤ t ≤ π/2

Q: What is true about the rose curve r= sin (990)? t has 99 petals and minimal domain D=[0,7) (b) It…

A: Given, the rose curve                              r=sin99θ

Q: Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in…

A: Let's find.

Q: Let C be the curve given by r(t) = (t cos 1, 1 sin 1, 1). (a) Show that C lies on the cone x² + y² =…

A: GivenParametric equation is r(t)=&lt;tcost,tsint,t&gt;To show C lies on cone x2+y2=z2.

Q: (2) Consider the curve given parametrically by 1=1+2/2 cost, y = tant +2/2 sin t, for dy and show…

A: This is the application of derivatives.

Q: 10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: for y^2 - z^2 =1, find the point(s) on surface nearest to origin

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Q: A curve is defined by the parametric equations sin Z dz, cos z dz, t> 1. X= y= Find the length of…

A: Differentiating under the sign of integral.

Q: Given the expression x* – 3x + 7 = y³. on the interval [3,5], determine the surface of revolution if…

A: Given; x4-3x+7=y3 on the interval [3,5]

Q: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

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Q: III. Find the length of the following curves. (a) x = 2t , y = cos 4t, 0 < t <

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Q: s) The given curve is rotated about the x-axis. Find the are √2x +3,0 ≤ x ≤ 6. of the resulting…

A: Introduction: The formula for the surface of revolution of the curve is given by,…

Q: 5. Find the total length of the curve r-4 (1-sin e) from 0-90° to 0-270° and also the total…

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Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cos t î + sint ĵ+ k.

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Q: A curve is defined by the parametric equations cos z dz, sin z dz, t > 1. X= y= Find the length of…

A: Use the formula for the length of curve in parametric form.

Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j + k.…

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Q: Find the length of the following two-dimensional curve (2t + 1)3/2| r(t) = 21 for 0sts4 3 L= (Type…

A: To find the length of the below two dimensional curve. rt=t22,2t+13/23, for 0≤t≤4

Q: Enter the appropriate value to answer the question or solve the problem. 6. Set up, but do not…

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Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: A circle of radius a in the xy plane, centred at the c is described by T = ¢ +acos (t) i +asin (t)…

A: In this question, we need to change the orientation of the path.

Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: 10) Consider the oriented curve C, which is the intersection, in the first octant of the surfaces…

A: Given that Surface 1: y-22=x-2 Surface 2: y+z=4 Fx,y,z=-x, y+z, z2 Find the value of ∫CF·dr

Q: In designing a new gear system for a truck, an engineer needs to determine the smallest positive…

A: By using the bisection method  Hust put y1=y2 and find out the point of intersection of these two…

Q: A polar curve is given by the differentiable function r = † (0) for 0 sos 2n. If the line tangent to…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

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Q: #4

A: Find the tangent plane to the given surface at the specified point

Q: Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the…

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Q: Consider the following. x = sin(6t),  y = −cos(6t),  z = 24t;    (0, 1, 4?) (a) Find the equation…

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Q: 10) Consider the oriented curve C, which is the intersection, in the first octant of the surfaces…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis 1 = (e…

A: Given y=112e6x+e-6x  ,for -2≤x≤2  Area of surface of curve when revolved about x-axis…

Q: Below is a curve C, which is the intersection between the surfaces  S1 : z = 4 − x2 S2 : z + 2x −…

A: Given that,Below is a curve C, which is the intersection between the surfaces   S1 : z=4−x2  S2 :…

Q: 10. Given the expression x* – 3x + 7 = y* on the interval [3,5], determine the surface of revolution…

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Q: Which of the following curves are on the surface z2 = x2 + y² for ever value of t? (You must select…

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Q: Consider the oriented curve C given by the parameterization r(t) = (e', cos(at)) for 0sts2. Circle…

A: The parametric equation is,rt=(et,cos(πt))

Q: Sketch the curves defined by the following equaitons: (a) z = 1– it, 0<t< 2 (b) z = a(cost+ i sin t)…

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