Let u = i−5k, v = 2i−4j + k,and w = 3i−2j + 5k. (a) u · (v × w) = ______. (b) The volume of the parallelepiped that has u, v,and w as adjacent edges is V = ______ .

Q: 4. Find the surface area of the paraboloid S defined by the equation: (r, y, z) = (u cos v, usin v,…

A: We will find surface area by using formula.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), E (0,4,0), and (0,0,2)

A: The vertices of the tetrahedron are (0,0,0),(1,0,0),(0,4,0),(0,0,2).  x varies from x:0→1y varies…

Q: A surface S lies on the paraboloid z = 1 /2 x2 + 1/ 2 y2 directly above the triangle in the xy-plane…

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Q: Consider the parallelepiped with adjacent edges u = 7i + 7j + k v = i+j+ 3k w = i+ 7j + 5k Find the…

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Q: A solid is constructed so that one side is the region between the lines z = a, x = b, the graph of y…

A: The cross-section of the solid are perpendicular to the x-axis and are isosceles right triangles so…

Q: Find c > 0 c > 0 such that the area of the region enclosed by the parabolas y = x 2 − c 2 y = x 2 -…

A: To find the value of c given area between the curves.

Q: Consider the parallelepiped with adjacent edges u = 9i + 8j + k v = i+j+ 9k w = i+ 6j + 5k Find the…

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Q: The volume in the first octant bounded by the surface x = 1 and x2 = y + 2z.   Group of answer…

A:

Q: 14 13 12 11 10 9 8 7 4- 3- 2- Find the volume of the solid S obtained by rotating R about the line y…

A: Here R is the region bounded by y=9x,x=2.5 and the x-axis i.e.(y=0)and the solid…

Q: Consider the parallelepiped with adjacent edges u = 8i + 9j + k v = i+j+ 8k w = i+ 3j + 4k Find the…

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Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

A:

Q: ind the volume of the solid that lies under the hyperbolic paraboloid z = 3y2 - x2 + 4 and above the…

A: Using the double integral formula.

Q: Consider the parallelepiped with adjacent edges u = 5i + 7j + k v = i+j+7k w = i+ 8j + 7k Find the…

A: Volume of the parallelepiped is 238 cubic units.

Q: Consider the solid E determined by the inequalities x² + y² + z≤ 4, and let S denote the surface…

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

Q: 5. Find the surface area of the portion of the surface z = 2x + y? that is above the triangular…

A:

Q: Consider the parallelepiped with adjacent edges u = 9i + 5j + k v = i+j+ 8k w = i+ 2j + 8k Find the…

A:

Q: Evaluate II Væ² + y? dV, where E is the region that lies inside the cylinder æ2 + y² = 16 and…

A: E is the region that lies inside the cylinder x2+y2=16 and between the planes z=-5 and z=4 Change…

Q: Evaluate (y + Vx) dA, where R is the triangular region with vertices (0, 0), (1,0), and (0, 1). R

A: The solution starts from step 2. The information presented below will be helpful to understand the…

Q: Consider the parallelepiped with adjacent edges u = 2i + 4j + k v = i + j+ 6k w = i + 2j + 5k Find…

A:

Q: 1. Find the surface area of the region S in the plane z = 3x + 2y such that 0 <x < 10 and 0 < y <…

A: We have to find the surface area of the region S in the plane z = 3x + 2y such that 0&lt;=x&lt;=10…

Q: A surface S lies on the plane 2x + 3y + 6z = 12 directly above the rectangle in the xy-plane with…

A:

Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 4x, x = 1 and x =…

A:

Q: 4 [It is given that a sphere of radius r has volume 3 cm r cm Handle Cover Disc cm Body h cm 1 cm r…

A: To find the value if r and h i use the calculator.

Q: / y cos(r*)dA. R

A: Given:- Let R be the region in R2 bounded by the x-axis, the parabola y = x2 and the line x = 2

Q: 5. Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0,0), (0, 2,0), and…

A: we can evaluate the given integral. ∫∫∫R f(x,y,z) dV =∫∫∫R f(x,y,z) dzdydx

Q: Evaluate the triple Integral. 3xyz dV, where T

A:

Q: 4. Given an example of a change of coordinates z= r(s,t), y = y(s,t) where every region in the st…

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Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,3,0), and (0,0,5)

A:

Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: 1. Evaluate I = D xy dA, where D is the triangular region with vertices (0,0), (0, 1), and (1,1).

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

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Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

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Q: Evaluate I/ V x2 + y2 dv, where E is the region that lies inside the cylinder x? + y2 = 9 and…

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Q: A) Evaluate the triple integral ydV, E vhere E is the solid region bounded by the paraboloid – x² –…

A:

Q: Consider the parallelepiped with adjacent edges u = 3i + 8j + k v = i+j+ 3k w = i+ 9j + 4k Find the…

A: u=3i+8j+kv=i+j+3kw=i+9j+4kVolume = (u×v).wu×v=ijk381113u×v= i(8(3)-1)-j(3(3)-1)+k(3-8)u×v=23i-8j-5k

Q: =valuate the double integral [2aydA, 2xy dA, where D is the triangular region with vertices (0,0),…

A: Given that a double integration and given  D is  triangular region with vertices (0,0) (1,2) and…

Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

A:

Q: EXAMPLE 6 Find the volume of the box (parallelepiped) determined by u = i+ 2j – k, v = -2i + 3k, and…

A:

Q: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method

Q: 2 Find the average height of the paraboloid z = x + y over the square 0<x<1, 0<ys1. The average…

A: Use formula of average height

Q: 1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendicular a. 1 unit b. 2…

A: 1. Determine the value of a so that A= 2i +aj +k and B= 4i-2j-2k are perpendicular. We have, A= 2i…

Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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Q: Consider the parallelepiped with adjacent edges u = 4i + 7j + k v = i+j+ 6k w = i+ 4j + 9k Find the…

A: The adjacent edges of the parallelepipedu=4i+7j+kv=i+j+6kw=i+4j+9k

Q: Find: the values of the constants a and b.

A: In this question, we find the surface area of the surface M in the first octant bounded by…

Q: (x - y) dv, where E is enclosed by the surfaces z = x² - 1, z = 1 - x², y = 0, and y = 4

A: Consider the given function fx,y,z=x-y.  The region E is enclosed by the surfaces…

Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), (0,4,0), and (0,0,1)

A: We have to find the volume integral of the given function.