Use De moivrés theorem to ealculate the sauare Toot Of It,

Q: Find the volume of the following solid bounded by two paraboloids. laces

A: In this question, we find the volume bounded by two surfaces. Here first we use the integral to find…

Q: show that the rectaugle that has mancimum Qree for given PerimeTer is e sequare. in

A: Consider the provided question, We need to prove that the rectangle that has maximum area for a…

Q: Given a 60 microcoulomb point charge located at the origin, find the total electric flux passing…

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Q: O FIND THE レ-く,2,3> VOLUME oF TAE PARALLELEPIPED VECTURS WITH V = <4,10,87 w = <1,0,17 and AS ADJA…

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Q: Evaluate , ydV where E is the hemispherical solid region x? + y? + z? 0.

A: x^2+y^2+z^2 &lt;=64, y&gt;=0

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: ind the valume of the portion of the Solid. Sphere x+y2,+2-10 that les between the Surfaces

A: We need to find the volume of the portion of the solid sphere x2+y2+z2 = 10 that lies between the…

Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: Suppose a sphere of radius r is sliced by two horizontal planes h units apart (as shown). Show that…

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Q: 2. Find the volume of the wedge cut from the cylinder r? + y? = 1 by the planes z = -y and z = 0.

A: Given the wedge cut from the cylinder x2+y2=1 by the planes z=-y and z=0.

Q: Verify Euler's formula for the solids below. (i)

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Q: Which of the following conditions do not have to be met to prove two solids have equal volumes using…

A: Given query is to find the condition which is not required to prove volume of solid are equal.

Q: In the strip of rectangles shown below, a certain rigid motion applied to the leftmost rectangle…

A: The given pattern has vertical reflection symmetry since it would have two mirror images if we draw…

Q: Use the Theorem of Pappus to find the exact volume of a general cone c with vertices (0, 0), (3, 0),…

A: Step:-1 Pappu's Theorem:- According to this theorem, the Volume V of a solid of revolution generated…

Q: By integrating all three surface elements of a cylinder, find the surface area of a cylindrical pie:…

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Q: What solid is formed when this net is folded? B D

A: there is no introduction for the above question.

Q: In Exercises 23 to 25, complete a paragraph proof. 23. Given: Tangent AB to ©0 at point B mZA = mZB…

A: Given: AB¯ is tangent to the circle with center O at point B. m∠A=m∠B To prove: mBD^=2·mBC^

Q: ) show thet the pants ACいらり)。 B(2,2,2)) c(o,1,5) and D(1,0,5) are coplanear (in the Same plane). )If…

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Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Given data: *The vertices of the triangle is (2,2), (2,7) and (4,7) From the coordinates of the…

Q: 2-By revolving the semicircle: X= r cos t, Y=r sin t, (0<t<n) About the x-axis, Show that the…

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Q: Exercise 11. Compute the area of the pseudo-sphere, i.e. the surface of revolution obtained by…

A: Area= ∫2πrds=2π∫r.dr/sin(ϕ)∫2πrds=2π∫r.dr/sin(ϕ) Due to tangent property: r/sin(ϕ)=a,r/sin(ϕ)=a, and…

Q: e hy inluetin on m76 thut an cam be subdivileed into equel atiral sub-triamnglho lof possibly…

A: Statement:- Prove by induction on n≥6 that an equilateral triangle can be sub divided into n…

Q: The volume of the solid region, in the first octant, that lies below below the surface, z = above…

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Q: Use the boxing method as suggested in Exercise 33, to find the area of ARST, with R(-2, 4), S(-1, –…

A: Given: To find the area of ∆RST,  Using the boxing method      with  R(-2,…

Q: Find the Volume r= 2cos 0 , x2+yナ ?= 4.

A: Topic:- volume

Q: If the region that lies inside the cardioid r = 1+ cose and outside the cirele r = 1 is the base of…

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Q: (d) Consider the parallelepiped P in R³ whose adjacent sides are (0, 4, 0), (3, 0, 0) and (-1, 1,…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A: Sphere was cut at height h, radius of the circle at intersection of 2 cuts is r2-h2. Similarly…

Q: In the Fgure belcw, mL2=41? Find m ZI Im %3D

A: Topic:- right angle

Q: If the region that lies inside the cardioid r = 1+ cos 0 and outside the cirele r = 1 is the base of…

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Q: Given: Rectangle RSTU, M is the midpoint of RS. R Prove: A UMT is isosceles. IT

A: Please refer the attached image for complete solution.

Q: 5. Find the volume under the paraboloid = -a? – y?, and above the cone z = - p² + y?.

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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

A: Using direct formula

Q: Compute the volume of the solid above the cone o = , and between the spheres p = 1 and p = 3. Hint:…

A: We have to use spherical co ordinate system

Q: Find the volume of the parallelepiped shown having    u = 3i − 5j + k ,            v = 2j − 2k and w…

A: Givenu=3i−5j+kv=2j−2kw=3i+j+k

Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: Please see the attachment

Q: Find the volumes of the solids generated by revolving the triangle with vertices (2,2), (2,7), and…

A: Using washer method

Q: Locate the centroid of the plane area shown if a 25 in. 20 in. r = 15 in. 30 in.

A: Area of Rectangle equals to : Arectangle=20+3025                =1250in2 Area of semi circle equals…

Q: _Show that the following are metric on R": d,(x,y) max, isn Ixi - vil : d,(x,y) E X-Yil.

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Q: (b) Prove the volume of a parallelepiped with a vertex at the origin and edges ü,v, and w is given…

A: In the question we have to prove the formula.

Q: Prove that A Unitoy matylre U is Yemem bereel as Svuare Matsin whose colounn Vecto 8 have Cume theio…

A: The solution is in step 2

Q: Prove the corollary of the Triangle Proportionality Theorem.

A: To prove:               The corollary of the Triangle proportionality theorem.   Triangle…

Q: Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of…

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Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

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Q: find volume 31. The region in the first octant bounded by the coordinate planes, the plane x + y =…

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Q: Show that the sphere of radius 5, X(u, v) = (u, v, v25 – u? – v²) is regular.

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Q: Determine the volume of the largest rect an gu lar box in the first oct ant with three faces in the…

A: Given: The volume of the largest rectangular box is to be determined based on the first octant with…

Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…

Q: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…