iven: v(t)=t"-2t in m Iscc where os ts find the displacement of this objcct

Q: Compute the surface area of the cone generated by revolving c(t) = (8t + 5, 7t) about the x-axis for…

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Q: A membranc of uniform density area is stracthed on a Circular frame of radius A to uniform stress…

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Q: Q5. Consíder y = e+3 on [o,s]. Set up the surface area obtained by rotating The corve about y= 1 Ca)…

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Q: x³ +1 Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = 1+²dy into the surface area of the object…

A: Find the arc length of y=x+2, 1≤x≤7 using the differential element ds=1+dxdy2dy. For formula for…

Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: The work done W, to stretch a spring from its natural length to an extension of 4 meters Is given by…

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Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

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Q: 1. What is the differential for the total surface area of a frustum of a cone with l as the slant…

A: Given slant height l. Let r and R be the radii of the frustum. Let h be the height of the frustum.…

Q: Find the surface area of the solid generated by revolving the cycloid x= a(0- sin g). y =a(1-cos ).…

A: We have to find the surface area of the solid generated by revolving the following cycloid about the…

Q: For an area A in the x-y plane, in the expression I₂ = Ix+ly, the term /₂ is the: Minimum…

A: Introduction : As per definition, The polar amount of inertia is the total sum of the moment of…

Q: Evaluate dx dy x² – y? where Ris the right half-disk of radius ½ and centered at (0, ½ ).

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Q: The folium of Descartes is defined impliciHy as given nee here a) determine dy dx

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Q: Evaluate the line integral L(r – y*)dx + (1+ y² + =*)dy, where Cis the circle of radius 2 centered…

A: We have to evaluate the value of the integral

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Find the surface area of the figure generated by revolving x = 6 cos(t), y = 6 sin(t) where 0 <ts…

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Q: Where ds is calculated using the are length formulas from before (which ever is easiest)! 3. Find…

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Q: Find all finchons Man sanisty he Mowing inihal problim dy %3D dy dx =4 ex ーメ how mam solwhin does t…

A: Given,           dydx=y2e-x    and y(0) = 12

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral (5 + Væ…

A: The function is: ∫065+x+123 dxn=10

Q: sin z dz (z²–1) 2 where c = |Z – 1| =; valuate at oriented lockwise? (12 M)

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Q: Use cylindrical coordinates. Evaluate |/| 6(x3 + xy²) dv, where E is the solid in the first octant…

A: We have to evaluate the integral ∬∫E6x3+xy2dV, where E:z=4-x2-y2 in the first octant.

Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: dx Evaluate LJv by using Trapezoidal rule (up to three 1 + x? decimal places). [Ch-4(B), Expl-2]

A: We have to evaluate ∫01 dx1+x2 by using Trapezoidal rule.

Q: Which of the following is the surface area of the surface generated by revolving the curve y = 폴 in…

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Q: Evaluate the triple integral 1 V1-y V4-z? y? COS cos (z? + y? + z?) dzdzdy. V12 + y? + z2

A: Given triple integral is ∫-11∫01-yz∫04-x2-y2cosx2+y2+z2x2+y2+z2dzdxdy To evaluate the integral.

Q: Given YZ tangent to OJ at point Y, and mzWYZ = 104°, what is mW XY ? W mWXY

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Q: Determine the moment of inertia of the shaded area about the x-axis. 2" 10" y Answer: Ix Parabolic =…

A: To determine the moment of inertia about the x axis.

Q: to find 2y dx-xdy, Use where C is the green's theorem the the eircle wi'th radivs 4 Centered at…

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Q: the EXACT Salutian to the equation belaw/de not decimal apprakimatea) give %3D

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Q: Find the length s of the spiral c(t) = (t cos(t), t sin(t)) for 0 <t < 9n. Hint: Use the formula…

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Q: The surface area of the solid of revolution generated by rotating 3 x = (y² + 2)ž,1 sys2 about the…

A: Given function is x=13y2+332 where 1≤y≤2. The surface area of revolution of the function is given by…

Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

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Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: Evaluate the cylindrical coordinate integral. бл 8 LL dzr dr de 4л 8

A: = ∫4π6π ∫48(9r-8r)rdrdz =∫4π6π(8-4)dz = 4(2π) = 8π

Q: Use the method e muiti plíers of Lagrange to fird the mini mum Value of f(^ig) = x*+4y²-22+8y…

A: Given that: fx,y=x2+4y2-2x+8yg(x,y)=x+2y=7

Q: Q1/Find the distance between(5,3I10to(5, Z10) in Cylindrical Coordinnde? Ans:lo

A: According to question Distance between 5,3π2,0 to 5,π2,10Let P1x1,y1,z1 and P2(x2,…

Q: The total surface area S of a right circularcylinder is related to the base radius r and height h by…

A: We have to find dSdt related to drdt and dhdt where neither r nor h is constant and total surface…

Q: Given that D=p²z?sina,C/m², calculate the total charge enclosed by a cylinder with radius = R1 meter…

A: Total charge enclosed = volume integral (volume charge density dv) volume charge density =…

Q: The lateral surface area S of a right circularcone is related to the base radius r and height h by…

A: Since, the lateral surface area S of a right circular cone is related to the base radius 'r' and…

Q: eiz dz around (a) |z – in| = 2 (b)|z - | = 2 (c)|z| = 2 sinhz

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Q: JT 9 cos' t and y 9 sin't (where t E R) is A- then what is 8. If the area enclosed by the curve x =…

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Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: Jind the Surface area of the part of the para boloid 2=X+y" lyrng Orer the regron R

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Q: guen that the te kt is t Cs) :! laplace trangorm derive tho StK? Caplace transqorm using the…

A: It is given that Laplace transformation of te-kt is F(s)=1(s+k)2

Q: valuate the line integral J xev% ds where C is the line segment from > (1, 1, 1). This yields:

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Q: 3 2 Use a line integral to calculate the length of the helix ř(t) = (a cost, a sint, bt) 0<t < 2n…

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Q: Find dy Sor The Sullowing Suetien? ) y = Cot 2) y = Ln [cosx) %3D

A: Please refer to the image below.

Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Find a cubic approximation of r(θ) = (θ 2 , eθ , θ) at θ = 0.

A: given rθ=θ2,eθ,θ to find - cubic approximation at θ=0

Q: Compute the surface area of the cone generated by revolving c(t) = (2t + 2, 6t) about the x-axis for…

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