Consider curve C which is the intersection of the surfaces shown in the attached figure. image 1 the approximate value of ∫C (x - y - 2z) ds is: image 2

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: Eliminate the parameter 0 and obtain the standard form of the rectangular equation. circle: x = h +…

A: We know the trigonometric identities Sin2θ + cos2θ = 1

Q: In  the given equation as  follows , find the area of the surface generated by revolving the curve…

A: Given: x=t ; y=4-2t; 0≤t≤2To find the area of the surface generated by revolving the curve about…

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes A units apart.…

A: To show: That the surface area of the band is 2πRh. Given: The shaded band is cut from a surface pf…

Q: et C be the curve of the intersection of the two surfaces a² +} = z and 4x2 +y} +? =9. nd let L be…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y =x2 4 In(x),…

A: Given curve is y=14x2-12ln(x) Differentiate with respect to x. dydx=x2-12x

Q: 1. Given to the right is the graph of a portion of four curves: x = 0, y = 1, x – V3y = 0 and a? +…

A: Given: slope of line,m values.... Let us solve step by step

Q: Use the center and radius to answer the next two questions. 16 1 point Center: (4, 1) Write the…

A: Ans : given the centre and radius of the circle = (4,1) and 2 So we want to choose the equation of…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 1sy& 4

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Q: sketch the given curves together in the appropriatecoordinate plane, and label each curve with its…

A: Draw graphs of y=ex and y=1ex

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

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Q: In the figure below, VY and VW are tangent to the circle centered at O. The segment YW passes…

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Q: | (4x – y? + 6z)ds

A: We have to find the line integral of the function : 4x - y2 + 6x Along the curve C , which is the…

Q: Find the length of the following parametric curve. x = 6 + 916, y = 5 + 6t°, 0<t < 2.

A: solution is given below

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: If C is a circle of radius 8 centered at the point ( 0, 5 ), then evaluate pain(2dr + (11æ sin(y*…

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Q: Use the graphs of x = f(t) and y = g(t) to sketch the parametric curve x = f(t), y = g(t). Indicate…

A: We can solve this problem by plotting some points on the curve of y vs x by taking some specific…

Q: The speed (mph) and the stopping distance (ft) of a travelling car are given as follows. Speed…

A: Use the Excel and Perform the Regression. Followings are the Steps to perform the Regression 1) Open…

Q: Figure 1 illustrates two surfaces which are summarized by the following equations: S1:z = x2 S2:Z =…

A: The angle between two surface at a point is given below.

Q: The base of a solid is the region in the first quadrant between the graph of y and the raxis for 0<…

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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: Consider the curve C shown in the attached figure, which is the intersection between surfaces S, and…

A: To parameterize the curve which is the intersection of the below curves in the first octant.…

Q: Evaluate where C is the portion of the circle centered at the origin with radius 2 in the 1st…

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Q: Find the DE of the family of plane curves described and sketch some of its members. Straight lines…

A: In the figure the blue straight lines are members of some of family which are tangents to the given…

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

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Q: T 9. TO = PO nrre CHOICE 10.Sector of a circle is the region bounded by two radii and their…

A: We have to identify true or false.

Q: Find the exact length of the portion of the curve shown in b r = 0+ 2 2 (i)

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Q: Use the graphs of x=f(t) and y=g(t) to sketch the parametric curve x= f(t), y=g(t). Indicate with…

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Q: Consider the parametric curve defned by r=3+5t and y=1+ Over which values of y does t curve has a…

A: Given problem:- Consider the parametric curve defect by   x = 3 + 5t and y = 1 + 3t   Over which…

Q: If C is a circle of radius 7 centered at the point ( 4, -2 ), then evaluate $ (7y – esin (2) ) dæ +…

A: Given:  C is a circle of radius 7 centered at the point (4,-2).

Q: Given that the line y =r- b is an asymptote to the ar curve y a,b €R,r = 1, then b = I-1 -1-a B 1-a…

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Q: If C is a circle of radius 9 centered at the point ( -5, 5 ), then evaluate $ (2y – esin ( x ) ) dæ…

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Q: Question 13: Fill in the circle next to the plot that shows the level curves for the plane z = f(r,…

A: Given, z=fx,y=3+2x+2y Given options are,

Q: Consider the region left half-plane (that is, æ < 0), inside the circle x² + y? : and y = -6x .…

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Q: BE f : C+ C GIVEN BY AND C IS THE CIRCLE OF CENTER IN z0 = a + br AND RADIUS r f(z) = z = + yr b 20…

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Q: Consider curve C which is the intersection of the surfaces shown in the attached figure. x = y² +3…

A: Given is the curve. The object is to approximate the given integral.

Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes h units apart.…

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Q: Find the equation of the osculating, normal, and rectifying planes for a (t) ( cos t, – sin t, cos…

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Q: A curve called the folium of Descartes is defined by the parametric equations 3t 3t2 x(t) = y(t) 1+…

A: solution is given below...

Q: : The area of the surface obtained by rotating the curve y = 2 In a, for 1 < a <e, about the a-axis,…

A: We have to find the integral that given the surface area.

Q: Consider the curve described parametrically by X = 3cos(t) , y = 3sin(t) , 0<t< 57/4 tch the curve,…

A: Given parametric Curve x= 3cos(t), y=3 sin(t), 0≤t≤5π4

Q: KS is tangent to the circle at T. secant KR contains P, the center of the circle. PR and PT are…

A: Consider the given information. Let's draw the graph step by step given as KS is tangent to the…

Q: The shaded band shown to the right is cut from a sphere of radius R by parallel planes h units…

A: Given data:  The radius of the circle is "R". The equation of circle with radius "R" is given by…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. = Vx, 1sys 5

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Q: -y° dr + x* dy where C is the union of the circles of radii 1 and 2 (centered at the origin).

A: Let I=∮C−y3dx+x3dy According to green theorem ∮CLdx+Mdy=∬D∂M∂x−∂L∂ydxdy Where, D is the region…

Q: Evaluate S,lz| dz for the curves C1 and C2, both of which begin at a = 1 and end at b = -1. The…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 2 < y<…

A: Given: The given curve is, y=x3=x1/3,  2≤x≤4   To determine: The area of the resulting surface.…

Q: The accompanying figure shows a spherical cap of height h cut from a sphere of radius r. Show that…

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Q: Sketch the curve r = 3 sin 20. a b Show that its Cartesian equation is (x² + y² )° =36x²y²,«

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