2-By revolving the semicircle: X= r cos t, Y=r sin t, (0

Q: Find the surface area of the part of a sphere having radius 2 centered at origin for 1 <z < 2. 8pi O…

A: Given  Radius of the sphere R=2 and 1&lt;z&lt;2

Q: a The curvature of the helix r(t) = (a cos t) i + (a sin t) j + bt k (a,bz 0) is K=- What is the…

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Q: Eualuate Je m Cz -i) dz (z-i)dz from Z =1+2i to to contour 2=

A:

Q: 3. Find the surface area of the surface created when the cylinder y + 2- intersects the cylinder 1²…

A: surface area of the surface given by equation z=f(x,y) A=∫∫Dfx2+fy2+1dA D is the region on xy plane

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

A:

Q: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: e surface generated by y=x^3 on [0,1], about the x-axis. Final Answer is A(s)=3.563 sq. units, Show…

A: Solution:- y=x3       0,1 y'=3x2 y'2=3x22y'2=9x4 Now find surface area S= ∫012πy1+y'2dx…

Q: Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir…

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Q: The area of a cylinder sector with radius r and central angle of radian measure 0 is A = r20, and…

A: If the area of the sector is 1 sq. unit, then A=112r2θ=1θ=2r2          ...(1)

Q: Find the area of the surface generated by revolving the curve y = cos(r), 0<aS5 about the r- axis.

A: The solution is given below in the next step:

Q: 18. Find the surface area of the sphere with radlus 5 by dou- bling the surface area of (x, y)…

A: Given: f(x,y)=25-x2-y2 is the surface bounded by the circle x2+y2=25 where radius, r=5

Q: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis. Find the area of…

A: Given: The arc of the parabola y = x^2 from (1, 1) to (2, 4) is rotated about the y- axis.

Q: The radii of the bases of two right circular solid cones of same height are r1 and r2 respectively.…

A: Given, the radii of the bases of two right circular solid cones of the same height are r1 and r2…

Q: 1.a)Find the area of the surface generated by revolving the curve y=√(121-x^2), −1 ≤ x ≤ 1 about the…

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Q: (1) Find the area of the surface of the portion of the cone 2 +y² between the cylinder y? = x and…

A: To find the surface area of cone between given cylinder and plane, use the surface area formula as…

Q: H use spherical Cingidinates to find the velumi of the oliet inside xtty42²=9 and outside z=ty" and…

A: Given sphere, x2+y2+z2=9 outside z=x2+y2   and above xy plane. We use spherical coordinates to find…

Q: Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central…

A: If a cylinder of radius b is cut from a sphere of radius a, then the volume of sphere depends on the…

Q: Use Stoker Cur theorem to evaluate. IF - ds S Where F= of radius I with x ] +ya³k ands is the +yx³k…

A: Given That  ∬Curl F →·dS→ F→=yi-xj+yx3k To Find: evaluate  ∬Curl F →·dS→  using strokes theorem

Q: 2. The portion of a cylinder of radius 3 centered along the y-axis that lies between the planes y =…

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Q: 35. Find the area of the surface generated by revolving the para- metric curve x =t, y = 21² (0 <…

A:

Q: The volume of the solid that lies above the cone θ=π4 and below the sphere r=cos(θ) is: (Here,…

A:

Q: The lateral (side) surface area of a cone of height h and base radius r should be πr√r2 + h2, the…

A:

Q: R

A: Volume =1/3 * pi * r^2 * h

Q: Find the area of the ellipse cut from the plane z= 8x by the cylinder x +y = 4. Surface area = (Type…

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

A:

Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: Surface at 0 = 40° and r = 20 is a.. Cylinder Plane Circle Cone

A: Given:  r=20, θ=40°

Q: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

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Q: Q1/Find the distance between(5,3I10to(5, Z10) in Cylindrical Coordinnde? Ans:lo

A: According to question Distance between 5,3π2,0 to 5,π2,10Let P1x1,y1,z1 and P2(x2,…

Q: 10. Using Stoke's theorem, evaluate y dx+ xz dy+x² dz where C is the boundary of the triangle cut…

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Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

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Q: ind the area of the surface generated when the give curve is revolve about the x-axis    y=(x^3)…

A: Consider the given curve: Here the objective is to determine the area of the surface generated when…

Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

A:

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: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: Find the area of the ellipse cut from the plane z = 6x by the cylinder x + y = 9. .... Surface area…

A: Substitute the equation of plane in the cylinder equation

Q: (a) Find the point of intersection between the curv urve r(t) = (cos(at), sin(at), t²) and the…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…

A: This is a problem related to maxima and minima. Based on the general formula we will answer the…

Q: Find the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

A: To the area of the surface that is generated by revolving the portion of y=x2 between x=1 and x=2…

Q: 35. Find the area of the surface generated by revolving the para- metric curve x =1, y= 21² (0 <…

A: Given: The curves,  x =t,  y = 2t2,   0 ≤ t ≤ 1 To find: The area of the surface generated by…

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: find the surface area obtained by rotating the circle (x – 4)2 + y? =1 about the y-axis. %3D

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Q: The lateral (side) surface area of a cone of height h and base radius r should be pai rsqrt(r2 +…

A: Obtain the lateral surface area as follows.

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: The radius of the sphere x2+y2+z2+2x-2z-14=0 is r= (Round your answer correct to three decimal…

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Q: The area of the surface generated by revolving the curve y = y9 - x2,-2 < x < 2 about the x-axis is…

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Q: The exact area of the surface obtained by rotating the following curve 6x = y + 12, 2 < x < 3 about…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.