Find the mass of a disk of radius a cm whose centre is at the origin in the xy-plane if the areal density at position (x, y) is o = k(2a + x) g/cm². Here k is a constant.

Q: Find the coordinates of the centroid of the homogeneous plate OPBA shown in Figure Q3.c. The plate…

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Q: Problem 7: Two vectors in Cartesian coordinates have components A = (3, 2, 3) and B = (4, -1, 7).…

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Q: A = (2, -4) and B = (-3,3). Determine the distance between points A and B and find their polar…

A: Two points given in the xy plane  A = (2, -4) and B = (-3,3)   Find: Distance between the A and B…

Q: A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on…

A: We will first write relations connecting cartesian and spherical coordinates. Using these, we…

Q: Vectors A→A→ and B→B→ both have a magnitude of 8. If their resultant has a magnitude of 10, what is…

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Q: A curve in three dimensional space is parametrized as F(u) = cos(u)i + sin(u)j + cos(3u)k, и є [0,…

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Q: Find the cross product A x C for the following. (Express your answers in vector form.) (a) A = 8.01…

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Q: Consider the two vectors G = (4.55 N)i + (4.99 N)j + (8.16 N)k and H = (2.08 N)i + (5.89 N)j. 1.…

A: The objective of the question is to find the component of vector G along vector H. This can be done…

Q: A uniform rectangular plate of length B = 39 cm and height A = 19 cm has a rectangular corner cut…

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Q: In an orthorhombic system, consider the planes (100), (100). If a = 1.0 Å, b = 2.0 Å and c = 3.0 Å,…

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Q: Show a[1 2 1] direction on a simple cubic unit cell and give the location (in correct notation) for…

A: The required direction vector for [1 2 1] is shown in the figure below.

Q: (a) If G(x)=x²-7x + 7, find G'(a) and use it to find equations of the tangent lines to the curve y =…

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Q: Given vectors T = 2a, 2a, 6a, + 3a, and S = a + 2a, + a., find: (a) the scalar projec- tion of T on…

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Q: Find the total mass of an L-shaped rod consisting of the segments(2t, 2) and (2, 2 − 2t) for 0 ≤ t ≤…

A: Given data: Segments of rod, 2t,2; 2,2-2t  for 0≤t≤1 Mass density, ρx,y=x2y g/cm

Q: Two points in the xy plane have Cartesian coordinates (6.00, -4.00) m and (-7.00, 7.00) m. (a)…

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Q: A non-homogeneous bar is 50 cm long and its linear density is given by the function λ(x)=32 + 25x² ,…

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Q: Two points in the xy plane have Cartesian coordinates (5.50, -7.00) m and (-6.50, 6.50) m. (a)…

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Q: Consider two vectors à = (1, – 3,0) and B = (0 ,0,7). Let C be their cross product: Č = Ã × В. a)…

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Q: In cylindrical coordinates, P = Peyt(1, 90°, 1) and Q = Qeyl(0,0°, 1). (a) Determine the length of…

A: Given:Coordinates of P: P=Pcyl1,90°,1Coordinates of Q: Q=Qcyl0,0°,1 To obtain:The length of the line…

Q: The three vertices of a triangle are located at A(6, -1, 2), B(-2, 3, -4) and C(-3, 1, 5). Find: (а)…

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Q: Consider the line element of the sphere of radius a: ds² = a ² (d0² + sin² 0 do ²). The only…

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Q: The density of a spherical solid at a point P = (x, y, z) is given by f(x, y, z) = c(x² + y² + z²) ,…

A: The density of spherical solid at any point P(x,y,z) is given by,  Therefore, the density at point…

Q: Using the methods of this article, determine the surface area A and volume V of the body formed by…

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Q: Since neutron stars consist totally of neutrons, they are extremely massive and have a density that…

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Q: Consider the differential volume element Y10Q1 [r,r+ dr] [0,0+ d0] [o,6+ do] shown in the Cartesian…

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Q: magnitude of A

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Q: Consider a solid sphere, determined by the volume x^2 + y^2 + z^2 ≤ R^2 , with a non uniform density…

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Q: What are (a) the x component, (b) they component, and (c) the z component of 7 = à − b + c if à =…

A: It is given that, a→=2.8i^+5.7j^-8.1k^ b→=-4.9i^+4.4j^+3.8k^ c→=1.8i^+2.8j^+4.6k^ and, r→=a→-b→+c→…

Q: Using alternate form of the Torricelli law. What is the theoritical time to empty a hemispherical…

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Q: The demand function for specialty steel products is given, where p is in dollars and q is the number…

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Q: A vector field is given in spherical coordinates as B=RR² cos(6/2) + Rsin(0) sin(0/2) . Evaluate (V…

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Q: Consider the 2-sphere with the metric dr² 1-p² (1) ds² = gabdxdxb =a² +r²d0² where a is a constant…

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Q: a certain corner of a room is selected as the origin of a retangualr coordinate system. A fly is…

A: Point 1: Here we can take the certain corner as origin. So the coordinates of the origin is O(0 ,…

Q: Problem 9: Consider a rod of length L with a non-uniform mass distribution given by A = A + Bx where…

A: Given that  Mass distribution of rod of length L is given by λ=A+Bx2 Part (c) To find the moment of…

Q: Two vectors in Cartisian coordinates have components A= (2,2,3) and B =(4,-1,7). What is the dot…

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Q: Let vectors A⃗=(2,−4) A → = ( 2 , − 4 ) and B⃗=(−3,1) B → = ( − 3 , 1 ) . Calculate the following:…

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Q: Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise…

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Q: (9) You have 4 vectors, a, b, c, and d for which you know their magnitude and directions. How would…

A: Given  We have four vectors  a , b , c and d.  We know the Magnitude and direction of each of these…

Q: Two points in the xy plane have Cartesian coordinates (5.50, -7.00) m and (-6.50, 6.50) m. (a)…

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Q: Question 6: The volume of a box with sides of length a,b and c is V = abc . The surface area of the…

A: Given V= abc S = ( ab+bc+ac) Derive an expression for the change in the volume associated with…