Double integrate under the hyperbolic paraboloid z=x2-y2 on the triangular footprint made by the x and y axes and the line y=-x+1?

Q: Sketch the surface..........CYLINDERS............. x2 + y2 = 4

A: x2+y2=4 Now, rewrite the above surface for the function as, z=fx,y. z=fx,y=4-x2-y2

Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: find a parametrization for the curve.  1. the left half of the parabola y = x2 + 2x  2. the ray…

A: Part 1;Given curve is

Q: find a parametrization for the curve. the left half of the parabola y = x^2 + 2x

A: First, we will find the symmetric line of the given parabola y=x2+2x. We know that the symmetric…

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin.

A: Given data:     The expression of the function is: x2-z2-1=0.     The expression for the distance…

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: Ir te line x34+2¢, もー4t paralled he plane 3x +y+そこ子-

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Q: Find a point on the ellipsoid x² + 2y2 + z2 = 19 where the tangent plane is perpendicular to the…

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Q: Find the center of mass of a thin plate of constant density ô covering the given region. The region…

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Q: How can I parametrize this 3D shape with two variables? x ≥ 0, 0 ≤ y ≤ x, x^2 + y^2 ≤ z ≤…

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Q: (a) S,(Iz – il2 – z) dz along the semicircle y = 1+ et“, 0 < t < n; -

A: ∫γz-i2-zdz=∫0π1+eit-i2-1-eitieitdt=∫0π1+cost2+sint-12-1-eitieitdt=∫0π1+cos2t+2cost+sin2t+1-2sint-1-e…

Q: Q R U V

A: Centroid problem....

Q: A cylindrical surface in an xyz-coordinate system is an equation that contains only two of the…

A: In this question we have to state whether the given statement is true or false.

Q: usuƏp seu pin 100 kg/m and flowS With Ve Zk, whei y, and z are measurec in meters, and the…

A: Density of fluid=1100kg/m3 Flow with velocity v=xi^+yj^+kz^ To find the rate of flow outward through…

Q: Classify and sketch the surface x − y2 − 4z2 = 0.

A: The surface is given as x-y2-4z2=0. Rewrite the equation x-y2-4z2=0 as follows. x-y2-4z2=0x=y2+4z2…

Q: Find the area of the surface x^2-2y-2z =0 that lies above the triangle bounded by the lines x=2,y=0…

A: From the given equation. 2z=x2-2yz=x2-2y2z=x22-ydzdx=x, dzdy=-1 From the limits x limits from 0 to 2…

Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: characteristic

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Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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Q: Find parametric equations for the intersection of the surfaces y = x² and 2x² + y² + 6z² = 24 and…

A: Find out the parametric equations for the intersection of the surfaces y=x2 and 2x2+y2+6z2=24…

Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

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Q: The curve y = sqrt(x2 + 1), 0&lt;=x&lt;=sqrt(2), which is part of the upper branch of the hyperbola…

A: Find dy/dx from the given curve using power rule and chain rule.

Q: 2) Use polar coordinate dydx (1+ x² + y° )'?

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Q: 1. (x² + y² +z²)®/2: cylindrical, spherical, or Cartesian? List the conversion factors needed to…

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Q: Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about…

A: Find lateral surface area.

Q: A line tangent to the hyperbola 4x² −y² = 36 intersects the y-axis at the point (0, 4). Find the…

A: Consider the given hyperbola 4x2-y2=36 Let the point Pα, β be on the the hyperbola. To find the…

Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: The ellipsoid 4x² +2y² + z² arametric equations for the tangent. line to this ellipse at th = 16…

A: The given equation of ellipsoid is 4x2+2y2+z2=16 intersects the plane y=2 in an ellipse. Let…

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

A: I am attaching image so that you understand each and every step.

Q: Find the area of the surface. The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find the center of mass of a thin plate of constant density d covering the given region. The region…

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Q: the moment of inertia of the area bounded by the cubic parabola a^2 y = x3, the y – axis and the…

A: To find the moment of inertia of the area bounded by the below equations about the y-axis.…

Q: Obtain the differentialequation of the family of ellipses w/center at (0, 0) having major and minor…

A: We will form the Differential equation.

Q: Re z dz, C the parabola y = 1 +3(x – 1)² from 1+ i to 3 + 3i

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Q: A space probe in the shape of the ellipsoid 4x + y +4z = 16 enters the earth's atmosphere and its…

A: To determine the hottest and coldest points on the probe's surface.

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: Find a parametrization of the line in which the planes x + 2y - 2z = 1 and 3x + 3y – 3z = 0…

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Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz=1…

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Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

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Q: point on the ellipsoid x2 + 2y2 + z2 = 19 wher x = 2 - 8t, y = 5 + 4t, and z = 4 - 2t. =) =(| )…

A: The equation of ellipsoid is x2+2y2+z2=19  ............. (1) and the equation of the line x=2-8t,…

Q: Find the area of the surfaces The surface cut from the “nose” of the paraboloid x = 1 - y2 - z2 by…

A: The surface cut from the '' nose '' of the paraboloid x=1-y2-z2 by the yz plane .…

Q: Find a point on the ellipsoid x² + 4y² + z² = 30 where the tangent plane is perpendicular to the…

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Q: Find the parametrization for the curve  the lower half of the curve x+3=y^2

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Q: ltermine the surface arca of the solid obtained by rotating y= 19- XZ about the X- axis.

A: Given:- y = √(9-x^2).  To find:- Surface area of solid obtained by rotating about the x axis [-2, 2]…

Q: Find the centroid when revolved in y-axis: y³ = x² ; y = 4.

A: As per the question we are given a solid of revolution obtained by rotating the area between y3 = x2…

Q: Find the moment of inertia of the solid formec y2 = 2x and th

A: Introduction: If a solid is formed by revolving an area about the y-axis, then the moment of inertia…

Q: Cone: x2 + y2 - z2 = 0, Plane: x + 2z = 4

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

A: Given that, the cone is generated by revolving the line segment  y = 53x,  0≤x≤4, about x-axis.