Q: Find the plane tangent to the surface z=x x+ y° at the point (3,4,25). a. 6x+8y-z=25 O b. 6x-8y-z=25…
A: As we know that; The equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 And The normal vector at…
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Q: Suppose we have a quadric surface described by 1 (r, y, z) | 1 1 = 7. 1 -4 Using canonical…
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Q: Find the surface area of the portion of the paraboloid given by the equation z = 1– x2 – y² that is…
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Q: Evaluate ff.dS, where (a) v = (xy, -x², x +z) and S is the part of the plane 2x + 2y + z = 6…
A: Problem is solved using concept of double integral.
Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…
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Q: state the type of the quadric surface and describe the trace obtained by intersecting with the given…
A: Given: x2+y42+z2=1 ……1 Equation of plane is: z=14 ……2
Q: Find an equation for the plane that is tangent to the surface z = In (x³ + y²) at the point…
A: Given: A surface z = ln x3 + y2 To Find : An equation for the plane that is tangent to the…
Q: Find the points on the surface represented by x2 + y? + z2 - 4x – 6y + 2z = -10 which are closest to…
A: To find - Find the points on the surface represented by x2 + y2 + z2 - 4x - 6y + 2z = -10 which are…
Q: Identify the quadric surface satisfying each of the given equations and then make a rough sketch to…
A: identify the quadric surface satsifying each of the given equations and make rough sketch to show…
Q: Apply Stoke's theorem to calculate S. (x + y – 4)dx + (2x – z)dy + (y + z)dz, where C is the…
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Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…
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Q: Determine the constants a, B, y such that the surfaces ax?z – xy? = B, yaz – y² = 0, - intersect…
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Q: When the plane x = 3 passes through the surface x2 + y? + z² = 64, %3D the curve that forms from…
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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant
A: Solution:-
Q: Find the angle between the two planes 3x + 2y − z = 7, x − 4y + 2z = 0 and find a set of parametric…
A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d2=0 is given by…
Q: Consider the surface S: Z=4x²+5y?, an equation of the plane fangent to S fhe point P(-2,1, 21) is…
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Q: Find an equation of the tangent plane to the following parametric surface, r(u, v) = (u2 + 6) i+ (v³…
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Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant
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Q: Use inertia to classify the quadric surface given by equation. y2 − z2 − 9x − 4y + 8z − 12 = 0
A: We wish to use inertia to classify the quadric surface given by the following equation: ------(1)…
Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)
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Q: re 2" dr + (x* + 2a²y?)dy where C is the boundary of the region between the circles a² + y? = 1 and…
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Q: a) Evaluate f, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…
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Q: Find the projection in the ry plane of the curve of intersection of the surfaces 222 = r² + y? and r…
A: Find your answer below
Q: Calculate Se(5x + 3y) i + (4x + 3y) j) · dĩ where C is the circular path with center (a, b) and…
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Q: The surface 22 = x² +y? – 4x + 5 remains unchanged when rotated about the line L in R³ Which of the…
A: The given surface is z2=x2+y2-4x+5, which is as shown below: This is a hyperboloid paraboloid.…
Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.
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Q: Consider the parametric surface S given by the portion of the sphere x +y² +z² = 4 where z 2 1.
A: In this question, we have to parameterize the surface in cartesian coordinates and then find the…
Q: For planes 2x+ y – z = 2 and 2x + 3y + 5z = 4. %3D Write the parametric equations of the line at…
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Q: Calculate fc((7x + 6y) i + (4 + 7y) j) · dr where C is the circular path with center (a, b) and…
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Q: 4 Assuming that the curve ris thex + y +z = 0 intersection of the plane and the sphere , then the…
A: As per the question we are given a closed curve Γ , defined as the intersection of the plane x+y+z =…
Q: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…
A: We will find out the required value.
Q: Find the angle between the two planes 3x − y + z = 7 , 4x + 6y + 3z = 2 and find a set of…
A: Given, two planes 3x − y + z = 7 , 4x + 6y + 3z = 2 we have to find the angle between the two…
Q: Consider the level surface 2x2y + 9z = 3, the angle in degrees that the z-axis makes with the…
A: Given
Q: Consider the surface S: z = 4x2 + 2y2 . An equation of the plane tangent to S at the point P (−1, 2,…
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Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…
A: We solve this
Q: The surface area of the cap cut from the paraboloid y + z? = 3x by the plane x = 2 is Select one or…
A: Given the paraboloid y2+z2=3x we have to find the surface area of the cap cut from the paraboloid…
Q: a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r…
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Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…
A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…
Q: Given two surfaces x²y + z = 3 and xlnz – y² = -4, a) calculate the angle between the normals to…
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Q: 7. Consider the Surface S:z = 52² + 5y?. An equation of the plane tangent to Sat the point P (3, 3,…
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Q: p(x, y, z) = e¬x²-y²–z² +2yz
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Q: (b) Use Stokes' Theorem to evaluate (f, curlF .n dS, where F(x,y, 2) = x²yzi + yz?j + z³e™Yk and S…
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Q: Let S is the first-octant portion of the plane 2X+Y+Z=4. Evaluate the surface integral ∬(2Y^2+2YZ)…
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Q: Consider the planes 2x − 3y + z = 6 and −2x + 4y − 3z = 4 Find parametric equations x(t), y(t), z(t)…
A: Given :- The given planes are : 2x -3y + z = 6-2x + 4y -3z = 4 To Determine :- The Parametric…
Q: Let h, r be constant. Consider the quadric surface S of equation: (x − h)2/9 − (y − 1)2/3 + (z −…
A: Substitute y = 5 in the given equation of quadratic surface S then simplify to know the resultant…
Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…
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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…
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Q: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.
A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…
Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.
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Consider the surface S: z = 3x2 + 3y2. An equation of the plane tangent to S at the point P (2, −2, 24) is given by:
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- If U1 and U2 are both upper triangularmatrices, and L1 and L2 are lower triangular which of the following are triangular? [U1+U2, U1U2, U2^2, U1+L1, U1L1, L1+L2].21 - Find the standart devition. Standart sapmayı bulunuz. A) 7,39B) 14,78C) 54,64D) 92,5E) 9,37Let →a=⟨−3,5,4⟩ and →b=⟨−4,3,k⟩.Find k so that a and b will be orthogonal.
- Prove using the IVT. 2x = bx has a solution if b > 2.Q 3: (a) Suppose two members of the group of twelve insist on working as a pair---any team must contain either both or neither. How many five-person teams can be formed? (b) Suppose two members of the group of twelve dont get along and refuse to work together on a team. How many five-person teams can be formed?Can u plz show work also?
- Let u1 = (1, 3, 2, 1), u2= (2, −2, −5, 4), u3 = (2, −1, 3, 6). If v = (2, 5, −4, 0), write v as a linear combination of u1, u2, u3. If it is not possible say so.If its TRUE: don't prove, but DO create an example that demonstrates the statement.IF FALSE: construct a counterexample.Can u plz provide solution to this question?