13) De termine the surface area of the spiral ramp parametrized by = u cosQu) i + usin(2v)5 +vk with (u,u) ranging over the set D : OLUL1, OLUEJ. (There is a picture of spiral ramp on the rext page) the next

Q: Lo and Li are lines in 3-space whose parametric equations are Loix = x0 + aot, y = yo + bot, z = zo…

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Q: Use a projection to derive a formula for the distance from a point (x,y) to the line ax+by=c, where…

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Q: Find distance between the point Plane Containing p oints c li21-1) (315/9) f (-12,-8) Coiojo) and…

A: Given, the points (1, 2, -1), (3, 5, 9), and (-1, 2, -8) are on the plane. We have to find the…

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: UZ. A curve C is defined by the parametric equations x=²-31, y=3²-9, -2<1<2. a) Find the points…

A: According to our answering guidelines we can answer 3 subparts at a time, rest you can repost later,…

Q: Let S be a sphere or radius a. (a) Compute ff(² + y² + ²)dS. (b) Use symmetry and part (a) to find…

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: II-2. If z = 7e15-3 , find In z in rectangular form correct to three decimal places. a) 3.400 –…

A: Given : z=7e1.5-j3 We need to find ln z

Q: .Calculate the dstance between tve point (3, -2) and the plane Z Xty-2+1=0.

A: The distance between the point (a, b, c) and the plane Ax+By+Cz+D=0 is given by,

Q: Transform (0, 5, 2) from rectangular into spherical form (here z is any negative number).

A: given rectangular coordinates is of the form (x, y, z) are (0,5,z) Now we are going to find…

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: 14.) Find a set of parametric equations for the line of intersection of the planes. 4x + y + 3z = 13…

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Q: In each case, determine if ₁ and ₂ are parallel, perpendicular, or neither. Explain. a) ₁: 4x-6y=9…

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Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: 1) let L be the line of intersection of the planes x+y+z=6 and x-y + 2z = 0. Find parametric…

A: To find the parametric equation for the line through the point that is perpendicular to the line of…

Q: A Hermite cubic spline starts at point (0, 0, 1) and ends at point (1, 2, 3). The tangent vectors at…

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Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

Q: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is a)…

A: The circle of radius 1 centered at (-3, 4,1) and lying in a plane parallel to the yz-axis is Then x…

Q: 1) Let S be the surface of the cylinder r+y = 4 with y >0 and -15z<1. Find a parametric equation…

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Q: Must the centroid of an isosceles triangle lie on the altitude to the base?

A: The centroid of an isosceles triangle lie on the altitude.

Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

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Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

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Q: 5. Express the flowing quantities in rectangular form. a) sec( + j1) cot(17/12 + j3 cosh(2 + j3) b)…

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Q: What is the distance from the point (1,9,3) to the xz-plane?

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Q: A secant to two congruent circles, which is parallel to the line of centers OO', meets the first…

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Q: 11) A point on the surface 2x + y? + z? = 4 at which the tangent plane is parallel to the plane x -…

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

Q: Find rectifying plane of et, é, t at the curve t%3DL

A: Given curve is αt=et,e-t,2t.  To find the rectifying plane of the curve . Result: Let rt→=xt,yt,zt…

Q: a) Let Q = (2, –1). Express pog as a composition of two reflections.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.