2 Find the volume of the parallelepiped with sides u(1, -3, -1). v3(0. 4, -2). and न् 6. 3).

Q: Use calculus to find the volume of a tetrahedron (pyramid with four triangular faces), all of whose…

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Q: A circular cylinder is to be generated by revolving a rectangle with a given perimeter p around one…

A: Step 1   Perimeter = pGiven rectangle of length = h, width = r is revolved and circular cylinder is…

Q: Calculate the volume of the parallelepiped spanned by PQ, PR and .

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Q: 1. Show that the volume ofa parallelepiped with sides A. B and C given by A (B x C)

A: As per our guidelines we are supposed to solve only one question i.e. the question no 1. For the…

Q: 1. Which has a bigger volume, a sphere with radius 2 meters or a pyramid with base 2.5 meters and…

A: Hello, thank you for the question. We’ll answer the first question since the exact one wasn’t…

Q: 24. Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,…

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Q: 6. A bax with a square base is to have an open top. If the lateral surface of the bax is 100 cm",…

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Q: Assume that a cell is a sphere with radius `10^{-3}`  or 0.001 centimeter, and that a cell’s density…

A: given: a cell is a sphere with radius or 0.001 centimeter and a cell’s density is 1.1 grams per…

Q: Find the volume of the parallelepiped defined by ?⃗= [1, 0, –4], ?⃗ = [8, –7, 9], and ?⃗ = [2, 3,…

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Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

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Q: A tank formed into a triangular prism whose base is a right triangle with legs of 8 cm and 6 cm…

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Q: 3. Determine the dimensions of the right circular cylinder, with the greatest volume, that can be…

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Q: The base of a three-dimensional figure is bound by the line y = -2x + 5 on the interval [-1, 2].…

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Q: 2. Calculate the volume of the parallelepiped created by PA, PB and PC, when P (3, - 2, 1), A(5, -…

A: Given that, parallelepiped with edges PA→, PB→ and PC→ Where, P3,-2,1, A5,-6,0, B0,-6,-4 and…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(3, 0, 3),    Q(−1, 1, 7),…

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Q: Find the volume of the tetrahedron with the given vertices.(1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1,…

A: We have given the vertices of tetrahedron; (1, 0, 0), (0, 1, 0), (0, 0, 1), (1, 1, 1) Since volume…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(5, 3, 5),…

A: Given three vectors, there is a product, called scalar triple product, that gives (the absolute…

Q: If the volume of a cone is 6 7 with radius 3, then its height is Select one: O a. 3 O b. 1 c.2 O d.…

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Q: Find the lateral surface area of the cylinder: 10 in. "u 9-

A: The cylinder has radius 6 in and height 10 in.

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS: P(-2,1,0), Q(2,3,2),…

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Q: Find the volume of the tetrahedron with the given vertices.(−3, −3, −3), (3, −1, −3), (−3, −1, −3),…

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Q: Find the volume of a parallelepiped if four of its eight vertices are P(0,0, 0), Q(3, 4, 0), R(0,…

A: Let, P, Q, R, S be the four vertices of a parallelepiped. Then, we find the vectors, a=PQb=PRc=PS…

Q: Find the volume of the tetrahedron with the given vertices. (4, 0, 0), (0, 4, 0), (0, 0, 4), (4, 4,…

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Q: 20. Find the volume of the parallelepiped with adjacent edges u = (-2, 0.75, 4), v = (6, -0.3, 8),…

A: Solution :

Q: Find the volume of the tetrahedron having the given vertices. (4, -4, 1), (3, -5, 4), (2, 1, 1), (0,…

A: The given vertices are named as follows. P(4, -4, 1), Q(3, -5, 4), R(2, 1, 1) and S( 0, 0, 1).…

Q: Find the volume of the tetrahedron having the given vertices. (5, -5, 1), (3, -4, 4), (1, 1, 1), (0,…

A: We have to find the tetrahedron

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(-2,1,0), Q(2,3,2),…

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Q: Determine the lateral surface area of a truncated circular cylinder whose longest and shortest…

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Q: Find the volume of the parallelepiped defined by the inequalities 0≤2x−3y+z≤5,1≤x+2y≤4,−3≤x−z≤6.

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Q: Find the volume of the parallelepiped with. adjacent edges PQ, PR, and PS, where P(-2,1,0),…

A: Given- P-2,1,0,Q2,3,2,R1,4,4 and S3,6,1 To Find- The volume of the parallelepiped with the adjacent…

Q: What are the dimensions of the lightest open-top right circular cylindrical can that will hold a…

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Q: Find the volume of the parallelepiped with the sides ü = (3,1,2), v =(4,5,1), w=(1,2,4). %|

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Q: Find the volume of the parallelepiped with adjacent edges PQ, where P (1,1, 1), Q (2,0,3,), R =…

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Q: Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0,…

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Q: Calculate the volume of the parallelepided defined by ü = [3, – 2, 6], v = [5, 0, -1] and w =[-7, 6,…

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Q: What fraction of the volume of the pyramid must be cut off by a plane parallel to the base so that…

A: Here  What fraction of the volume of the pyramid must be cut off by a plane parallel to the base…

Q: 2. Calculate the volume of the parallelepiped created by PA, PB and PC , when Р (3, — 2, 1), A(5, —…

A: The formula for the volume of a parallelepiped determined by the vectors a, b, and c (where a, b and…

Q: The volume of the parallelepiped whose adjacent edges are V = (2,3,4), ū = (1,2,–1) and w= (3,–1,2)…

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Q: What are the dimensions of the lightest open top right circular cylindrical can that will hold the…

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Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P(-2, 1, 0), Q(3, 4, 3),…

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Q: Find the volume of the tetrahedron with the given vertices.(5, 4, −3), (4, −6, −4), (−6, −6, −5),…

A: The vertices of the tetrahedron are: A(5, 4, −3), B(4, −6, −4), C(−6, −6, −5), D(0, 0, 10) We need…

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P(3, 0, 1), Q(2, 3,…

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Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(-2, -1, -3), Q(0, 2,…

A: The given points P-2,-1,-3, Q0,2,0, R-3,-2,-4, S4,-3,-1

Q: Find the volume of the parallelepiped whose edges are represented by: A=2i-3j+4k , B=i+2j-k and C=…

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Q: Find the volume of the parallelopiped with adjacent edges PQ, PR, PS where P(3, -4, -1), Q(5, -1,…

A: Given Points are:

Q: 2. Find the volume of tetraherdon with the vertices A(-1, 2,0), B(0,3,-1), C(3,3,0), and D(1,1,-1).…

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Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

A: Given : The radius of the sphere is b. The radius of the hole is a. We have to show that the volume…

Q: 3. WHAT IS THE VOLUME OF THE SPHERICAL CAP FROM GRID 1-3 (

A: We have to calculate volume of hemisphere.

Q: Find the volume of the tetrahedron having the given vertices. (4, -3, 1), (5, -4, 4), (2, 1, 1), (0,…

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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.