10) The line x = -1+t,y = 2 +t,z 2t + 7 intersects the surface z = x2 + y?. Find the cosine of the acute angle between the given line and the line normal to the surface.

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

A:

Q: 8. If A-a- cos0)à, - phå, +zcos*¢â, what is 9. For the conical surface 0= 30",0SOS 27,0Sr52, the…

A: 8. Consider the given vector, A=ρ41-cosϕa^ρ-ρϕa^ϕ+zcos2ϕa^z The formula for divergence in spherical…

Q: (7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) =…

A: To convert the cartesian coordinates into cylindrical coordinates put  And the integral will be…

Q: If a parametric surface given by r₁ (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -2 ≤ u ≤ 2, -3 ≤ v ≤…

A:

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: Consider the surface z = (x+ 1)² + (y – 2)² – 1 Does the point (1, 3, 1) belong to this surface?

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Q: Prove that the parabola y = x^2 at the points where the line has an angle of inclination "o" the…

A: Curvature of  a graph y= f(x)  k=d2ydx21+dydx232

Q: mine an equatio

A: Here we have to find the equation of rectifying plane to We have,

Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

A:

Q: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

A: Introduction :Given, two points P and Q .P= (1,0)Q= (0,1)We have asked for the line integral of

Q: Which of the following is the total length of the curve of intersection of the surfaces x2 + y? + 22…

A:

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

A:

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: Sketch the section of the surface at y = 0. 9x^2+4z^2=36

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Q: 4 and Consider the region in the second and third quadrants between the circles x² + y² = x² + y² =…

A: Concept: cartesian coordinates can be converted into polar coordinates using trigonometric functions…

Q: Find the angle of inclination 6 of the tangent plane to the surface at the given point. x2 + y2 =…

A:

Q: Demonstrate that the circles (x- 2)² + y² = 2 and x? + (y – 2)? = 2 share tangent at point (1,1),…

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Q: Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral %3D Q…

A: The line joining P1,0 and Q0,1 is     x-11-0=y-00-1=t(say)⇒x=t+1,y=-t⇒dx=dt,dy=-dt

Q: locus of the circumcentre of variable triangle having sides x = 0 , y = 2 and lx + my = 1 where (l ,…

A: Ans:-             C=0,1m, B=1-2ml,2,A0,2           let h,k be the circumcenter 07 ∆ABC…

Q: Consider the level surface 3x?y + 14z° = 3, the angle in degrees that the z-axis makes with the…

A: The given level surface: The angle in degrees that the z-axis makes with the tangent plane at point…

Q: If the line r = (2-t, -2 + 13t, 8t) is the normal tangent line to the level surface axyz²by² = -14…

A: answer is in next step . please give a like !!

Q: A surface in R³ is defined by the equation 4z = x² + 4y².

A: Given:-                 The surface in  is given by  . Sketch the intersections (traces) of this…

Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

A:

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

A:

Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

A:

Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 4) Find the families of lines of curvature of the surface : =+ y² .

A: Given: z=x2+y2

Q: Which type of surface does the curvex= cos(3t),y= sin(3t),z=t, lie on?

A:

Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

A:

Q: Let C be the intersection curve of the parabolic cylinder √2x2 = 2y and the surface 3z =√2xy. Find…

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

A:

Q: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

A: Verify Green's theorem Where C is the boundary of the triangle formed by x=3 , y=0 , x2= 3y

Q: 4) Suppose that the level curves of a function z = f (x, y) consists of straight lines. Must the…

A: Given that level curve of a function z=f(x,y) consists of straight lines.

Q: 6.2 Finl the Voune of the Selid enclosed by the curves y=eX, y=0 x=0,'= "about the x-axs.

A: Given: y=ex, y=0, x=0, x=1 From the given curves the bounded region is as shown below; Apply the…

Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: 3. Use traces to sketch and identify the following surface 25x2 + 4y² + z2 = 100.

A: Consider the given: Given:25x2+4y2+z2=100Let x=k∴25x2+4y2+z2=100             4y2+z2=100−25x2Hence,…

Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

A:

Q: Let C be the curve of intersection of the parabolic cylinder x? = 2y, and the surface 3z = xy. Find…

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Q: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

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Q: The surface that is linear with the three variables, x, y, and z is called cylinder plane sphere O…

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Q: What is the equation of the plane that is tangent to the graph of z = x coS y – ye“, when (x, y) =…

A: Equation of the plane tangent to the surface z=f(x,y) :               Let   F(x,y,z) =0 ,then…

Q: 15) Consider curve C which is the intersection of the surfaces shown in the attached figure. The…

A: The equation of the graphs given are as follows: x=-34y2+3y=yz=y22 We are asked to evaluate the…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.