uestion D<0 < 2n and -4sin 0 + 6 = 2V3 + 6, determine the values of 0. List your answers as exact answers in terms of t, parated by a comma if necessary.

Q: Qi:-A triengle formed hy vectous, the vectov is Central i +jtk, ond one it's 1チ Surronmding Side iy…

A: Suppose the sides of the triangle be A, B, C Let side A is i+j+k B is 2i-3j+4k Then as we know in a…

Q: 7 Find the lateral (side) surface area of the cone generated by revolving the line segment y = 3x,…

A: Given: Cone generated by revolving the line segment y=73x, 0≤x≤8, about x-axis. To Find: Lateral…

Q: Se) Define moments, skewness, and kurtosis. Mention their applications.

A: Moments are to statistical data/distribution what physical features are for human beings. In…

Q: Line tangeet Find the the equetion of the Cur ve X= 2+ Sec p und at p = to

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Q: Derive the De Moivre's Theorem with detail Explanation?

A: Statement: For any real number x, we have (cos x + i sin x)n= cos(nx)  i sin(nx) Or, (eiθ)n=eiθn…

Q: ABC is rotated around the line x=0 to produce a solid. What describes the shape of the solid?

A: While rotating the triangle around x=0 it becomes a cone

Q: There is an ant on a circular heated plate. The plate temperature is given by f(x, y) = y² – x² + 12…

A: Consider the function fx,y=y2-x2+12, with equality constraint x2+y2=121 (since the radius is given…

Q: Explain the process of parametrisation and also write 3 application ?

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Q: Express the function r = 4 cot 0 csc 0 by cartesian form %3D

A: Cartesian form is that when we write any equation in the form of x and y.

Q: Find the length of the catenary y = a cosh² from x = 0 and x = %3D X1.

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Q: Distance between two points P (x = 2, y = 3, z = -1) and Q(r = 10, 0 = 30 , q =60) %3D

A: We have to find the distance between the points P and Q.

Q: lume of a tetrahedron with adjac 1 w is Ju· (v x w)| to determine 6. tices P(-3,2,0), Q(2, 1, –3), R…

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Q: the pointS A 2) and P= (3, 1) in the coordir act answer (not a decimal approximation). 10 8十…

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Q: Q: Use Lagrange's Formula to Prove that : 1) Y = Y3 – 0.3 * [ Y5 – Y_3] + 0.2 * [Y_3 – Y_5] . -

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Q: Q R U V

A: Centroid problem....

Q: The object obtained by rotating y = sin(2x),0<x< about the x-axis. 2

A: Here in this question we need to find out the surface area of an object obtained by rotating…

Q: Find the area that is inside x2 + y² = 4 and outside (x2 + y² – 2x)² = 4(x² + y²). (Equations are…

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Q: Q. 4. Describe the loci zz – 2z – 27 – 8 = 0 expressed in terms of conjugate coordinates z, z.

A: Given: Let, Then, From the given expression.

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y= 11 x,…

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Q: Using trapezoidal, and 3/8 simpson's rule ⌠13 (1.2x3 + 0.3x2 - 2)dx

A: Given that, ∫131.2 x30.3 x2-2 dx is the function we have to solve it by using the trapezoidal and…

Q: Laplace trans form to sove the equalion, 十 4と-18 + 1, bm7) H1-て) て, inligral fit) =?

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Q: Kepler's Third Law states that the ratio T/a³/2 is equal to a con- stant C for all planetary orbits…

A: Given :        Ta32 = C , where T is the period and a is the semimajor axis.

Q: Find parametrizations The cone z = 1 + sqrt(x2 + y2), z &lt;=3

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Q: cos 2z dz, C the semicircle |z| = 7, x2 0 from - πί to πί

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Q: az over the contour C |z = 4.5 sin z (b) Сompute

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Q: y= COsax tor Osxs T Question,

A: The derivative is calculated using first principle

Q: lution of the part os x) = cos y is %3D

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Q: Find all point of discontinuityz is a complex variable, z=x+iyf(z)=(1/z)-sec(z)

A: To analyze the behaviour of the given function of the complex variable z.

Q: bordinates where R: 0 < aw the solid R. th 2 2

A: We will use relation between Cartesian and cylindrical co ordinate system to get integral  x= r cosθ…

Q: Find oveslapping Over of two equations also give ts alea geometoical representation. 2. (v-fr)-1…

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Q: Sinx Q.3 Evaluate . dA, where R is the triangle in xy- plane bounded by the x- axis, the line y = x…

A: Let us consider the triangle bounded by x-axis, that is y=0,y=x and x=1. The region R is given…

Q: Determine the moment of inertia of the area about the y-axis of the curve y2 = 2x, x=2, and the…

A: We can calculate by integrating.

Q: e center of part B measured from x-axis is (mm) - 400 mm- 50 mm 200 mm 50 mm 50 mm elect one: O 25 O…

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Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x/2, 0…

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Q: A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the…

A: A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the…

Q: Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: Given: y=fx=73x0≤x≤9 Axis of revolution is x axis.

Q: A particie mo ves along a straight line with the velouty a:) Find the displacement of the particle…

A: follow next step

Q: O parabolic cylinder

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Q: Find the surface area of the cone frustum generated by revolving the line segment y = (x/2) + (1/2),…

A: The surface area formula using integration is given by: In the question, we are given: Also x lies…

Q: Q: Using lagrange's theorem prove that 0. 1+ r

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Q: A Find the area of the surface generated by revolving the curve y = /2x-x² , 0.75sxs 1.75, about the…

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Q: parar rameter value ənre SA(z) = A sin z, = 1 %3D ·Es(2) = de*, 1 = 1/e Ex(2) = de, d = -e . Qe(x) =…

A: (d). Given, Qcx=x2+c;  c=-34 First of all let us find the fixed points. Qcx=xx2+c=xx2-x+c=0

Q: Use cylindrical or spherical coordinates to evaluate the integral. NOTE: Enter the exact answer.…

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Q: Find the length of the curve. The cardioid r = 7(1 + sin 0)

A: Given: The arc length of the cardioid is calculated by using the following formula,

Q: Use cylindrical or spherical coordinates to evaluate the integral. NOTE: Enter the exact answer.…

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Q: venify coucly's 's Tueorem for the funct Veri (b) 5 sin 2z where c is the square with verticies at

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Q: Find area the Surface generaled by revolving げ-28+1 1SI52 about y -akis

A: The area of a surface obtained by revolving a curve x=f(y) about the y axis is S=∫2π f(y)ds where…

Q: Find the approximate value of + 1) d: using Trapezoidal Rule. Trapezoidal Rules a. Single…

A: Given that,  ∫abf(x) dx = ∫04x28+1 dx a) Trapezoidal rule for single application: ∫abf(x) dx = b-a2…

Q: The force on a particle is described by 4a – 6 at a point a along the r-axis. Find the work done in…

A: