Show that (u, v) = (8u + 3, u – v, 15u + v) parametrizes the plane 2x – y – z = 6. Then: (a) Calculate Tu , Tv, and n(u, v). (b) Find the area of S = #(D), where D = (u, v) : 0

Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

A:

Q: Find the average height of the hemispherical surface z = sqrt(a2 - x2 - y2 )above the disk x2 + y2…

A:

Q: Find the area of the surface. The part of the plane  z = 3 + 2x + 5y  that lies above the rectangle…

A:

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: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

A:

Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: The figure shows a parallelepiped spanned by vectors a,b and c Which of the following formulas…

A: The formula to calculate the volume is given by, Volume=area of base⋅height             =∥b×c∥ ∥a∥…

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: Determine the constants a, B, y such that the surfaces ax?z – xy? = B, yaz – y² = 0, - intersect…

A:

Q: Express the plane  z = x  in cylindrical and spherical coordinates.

A: it is merely z-x=0.

Q: The vector (x, 2y, –3z) is normal to the surface x2 + 2y? – 32 – 4 = 0 at any point (x, y, z). - - -

A: Let's find.

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: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

A:

Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

A:

Q: Find a parametrization and the equation associated with the cylindrical surface whose directrix and…

A: answer is in step 2

Q: = xyi + yzĵ + de is a in x-y plane.

A:

Q: Find a vector parametrization for the intersection of the plane x + y+z = 3 and the cylinder x² + z2…

A: solution given below..

Q: Find the area of the surface of the part of the plane 3x + 2u + z = 6 that lies in the first octant.

A:

Q: Find a vector that is perpendicular to the surface 4e^{(z-1)}+x^{2}y=xyz at the point (−1,−2,1).

A: Given the surface :

Q: the trace of the surface in the plane x=1?

A:

Q: Calculate fc((3x + 5y) i + (3x + 4y) j) - dr where C is the circular path with center (a, b) and…

A: According to the greens theorem:

Q: Find the surface area of the part of the plane z = 4+ 7x + 6y that lies above the rectangle [1, 6] ×…

A: We can use integral calculus to find the surface area of the part of the plane above the given…

Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

A:

Q: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

A:

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

Q: Find the area of the surface cut from the paraboloid x2 + y2 - z = 0 by the plane z = 2.

A:

Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

A:

Q: Find the area of the surface. The part of the plane z = 7 + 5x + 2y that lies above the rectangle…

A: The given equation is, z=7+5x+2y The partial derivatives are, fx=5fy=2

Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

Q: Find the area of the surface. The part of the plane  z = 4 + 3x + 2y  that lies above the rectangle…

A: Consider the part of the plane that lies above the rectangle .

Q: Find the distance between two planes a and a1 that are tangent to the ellipsoid 2 +2y? + z² = 5/8…

A: We have to find the distance between the two tangent planes parallel to x+y+z=0  that are tangent to…

Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

A:

Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y<=2, that lies above the…

A:

Q: Find the surface area of the plane ( 15x-5z+20y=35) if it is in the first ? octant

A: Solution

Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

A:

Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: Use t = y to parametrize the part of the line of intersection of the two planes y = 2x – 4 and z =…

A:

Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

A:

Q: Find a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

A:

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.