Compute the irertia móment by x ( Ix=Sy?JA) tor number off segment n=s hyte multple-trapezoidal Rule. 40 the ile tarandi 0 48 12 16 20

Q: known as the loop of Descortes lea ond tor EECO,00) O(t)= ( 3+2 %3D Calculate the oreo of the region…

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Q: Use špheričal čoördiñatės. Evaluate tet dv, where E is the portion of the unit ball x2 + y² + z² s 1…

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Q: . Let T be the triangular lamina in Figure 21. O Show that the horizontal cut at height y has length…

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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: Determine the y.coordinate of ater a diation with a scale tactor of 1.5 centered at the origin O00

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Q: (a) Consider the following line integral L(adar + ydy + (az – y)dz) along a curve C given by r =…

A: Given integral    ∫Cx dx +y dy +xz-ydz

Q: 2) usins Culcuulus for parametrre curres. Show trat the aren of a idis e of radius Ris siren by…

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Q: What is the anticlockwise moment acting on this crane? 25 m 5m load 4000 N O 120000 Nm O 100000 Nm O…

A: To find the anticlockwise momentum acting on the body :-

Q: Find the curvature K, where s is the arc length parameter. 5s i+5sin /706 5s 6. sk V706 r(s) =5 cos…

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Q: he area bounded by the curve y = 3Vz and the lines z = 5 and z = 9 above the r – aris is_ quare…

A: Find the area of bounded curve with line x=5 and x= 9 above x-axis

Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z? = 16 and x2 + y2 + z2 = 64 in the first…

A: The region E lies between the spheres: x2+y2+z2=16  and  x2+y2+z2=64  in first octant.

Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

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Q: O show mat me Nomal point @ X= a( Coro +o Smo) y= a(8in0-o Cor0) dy Sine %3D ep" of Normal S-ゴ」=…

A: the parametric function is x=a(cosθ+θsinθ) y=asinθ-θcosθ Differentiate each with respect to theta…

Q: 1. Evaluate SSSE z dV where E lies between the spheres x2 + y? + 2² = 1 and a? + y² + z² = 4 in the…

A: Given, ∫∫∫EzdV where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4 in the first octant.

Q: 93. which f the follouwing repreeents ene - dimenalional heat Sqeation? 46) du c2 au %3D (d)u + azu

A: Some definitions: Wave equation: ∂2u∂t2=c2∂2u∂x2 Where c∈ℝ is called wave speed. Laplace equation:…

Q: (2) Find a lmnenr funetron (y=c,+Gx) that best fits the given data (Hint: Use (1) above) b31

A: Linear regression attempts to model the relationship between two variables by fitting a linear…

Q: Find the anea of the vegion in quadrant Ps bou nodod ist 4 the conie the by the right by the line…

A: Given curves, y=ex+12,y=e-x+12,x=2 ln2 To find the area of region bounded by these curves.

Q: Use Gauss Divergence theorem to calculate (5zi+ 4yj- 2z k).n dA over the sphere S: 2 + y? + 22 = 9.

A: This is a problem related to vector calculus. Based on the general formula of gauss divergence…

Q: Find the moment of inertia of a solid sphere of radius a about a diameter. (Take d = 1.)

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Q: Find thequahen. perpenditar to i fine -個 epe at OD pr Find tha liit ultpy cen gale (ro a) Po FO…

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Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: Given the curve X = 2y – y and the line X = 0 Find the moment of R with respect to the y-axis M. y…

A: Given problem:- Given the curve x = 2y-y2 and the line x = 0 Find the moment of R with respect to…

Q: The value of the line integral | F(r).dr when C F(F) = [-y, -xy]and C is the upper half circle arc…

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Q: On cogely the r y Mesiduer to Cualiete Calular (os node

A: Using the Residue theorem these types of questions can be solved by integration around the unit…

Q: 18. Use spherical coordinatcs Evaluate dV,where E is the portion of the unit ball X ty +z²<! that…

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Q: sphere will reach point B as it swings about 'O' (a) If OA is a rope vertical plane. Determine the…

A: Answer:

Q: Approximate the arc length of the curve y = x over the interval [1, 2] using the trapezoidal rule…

A: Given y=14x4 in [1,2] , 7 sub intervals  y'=14×4x3 = x3 Area length = ∫ab1+y'2dx…

Q: 2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = (f* cos (u²) du, f *cos (u²) du,…

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Q: The area enclosed between the curves p(a) =2 +*+ 3 and g(@) = -22 - * + is O 16 47 %3D 18 49 O -49…

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Q: The cable AB carries a tension of 400 N. Determine the moment about O (positive if counterclockwise,…

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Q: 4) By Diskuethod Detremin the volup Hiw Dx=1 and lnes y=1 aboat x=0 2) fex) = x? and line y:1 in the…

A: Given

Q: Calculate the trapezoid approximation of 5dx using four subintervals. O T5 = 0.60 O T5 = 0.40 O T5 =…

A: The trapezoid approximation of the given integral is given below.

Q: 14) Find aset of parametnic equetians for the rectangular aquetiag d= 4x2 tust Setisfies fue…

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Q: Q 6/ Compute the moment of * the Inertia for the shaded area with respect to the Y- — axis? 2 ft --…

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Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

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Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

Q: Given the curve y = x' and the line y = 2 – x. Find the moment of R with respect to the y-axis М of…

A: Given problem:- Given the curve y = x2 and the line y = 2-x. Find the moment of R with respect to…

Q: 16. Evaluate * :- S S $6(x² + y² + z? )dV В where B is the ball with center at the origin and radius…

A: (16).  We have to find the integral∫∫∫B 6x2+y2+z2 dV  ;      where B is the ball with center at…

Q: 6. Find the arc length of the helix, r(t)=bcosti+bsintj+V1-b²tk from t= 0 to 27.

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Q: 3. Givea parametrie description fora sphere with radis, ineluding the intervats for the peremeter

A: Given : radius = a

Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: Q1. а. r. crude moment is defined as ΣΧ Mr N and centered r. moment is defined as E(X; – µ)" M, %3D…

A: The crude moment s is defined as, mr=ΣxirN The centered r moment is defined as, Mr=Σ(xi-µ)rN

Q: Let R be the annulus defined by {1<x² +y² < 4}. Is R connected? Is it simply connected? Describe C =…

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Q: Possible units of the moment M, are

A: Moment= Force ×  perpendicular distance

Q: 1 SI. Evaluate dV, where E lies between the spheres x2 + y? + z? a2 + y? + z2 = 1 and æ? + y? + z²…

A: According to bartleby guidelines when student post more than one question then expert must have to…

Q: E(X is called the second moment about orgin ylgn İhi

A: In this question we have to verify about the second moment about origin in the concept of mean and…

Q: Find dyldy and xz4 Sint, y² Scost, OCtca24 For which vakes Of t is Hhe cure concave puars? anguer n…

A: x=4sint  , y=5cost

Q: Verify the given moment(s) of inertia and find i and ỹ. Assume that each lamina has a density of p =…

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Q: a) [12 pts] C1 is the path along the arc of the unit circle from z = 1 to z = -i. Provide a sketch…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.