Calculate ∫ ∫ ∑ (x ^ 2 + y ^ 2) ds, where ∑ is the part of paraboloid z = 2-x ^ 2 + y ^ 2 above the xoy plane If ∑ is the entire boundary surface bounded by the cone z = √ (x ^ 2 + y ^ 2) and the plane z = 1, how to find it?

Calculate ∫ ∫ ∑ (x ^ 2 + y ^ 2) ds, where ∑ is the part of paraboloid z = 2-x ^ 2 + y ^ 2 above the xoy plane If ∑ is the entire boundary surface bounded by the cone z = √ (x ^ 2 + y ^ 2) and the plane z = 1, how to find it?

Symmetry by rotation

How to draw an image with xy = 1

It's a hyperbola in one or three quadrants

Who knows the meaning of construction coordinate setting out drawing XY?
For example, what is the unit of the number after x123456.123 and y123456.123? How to calculate the difference?

The survey coordinate is the plane rectangular coordinate system established in the survey and design of the building area, which is consistent with the national geodetic coordinate. The vertical axis of the coordinate is north-south direction, expressed by X, and the horizontal axis is east-west direction, expressed by y
The unit of number is millimeter

The normal vector of surface z = x + XY-1 at point (1,1,1) is

Let f (x, y, z) = x + xy-z-1,
Then f'x (x, y, z) = 1 + y = 2, f'y (x, y, z) = x = 1, f'z (x, y, z) = - 1,
Therefore, the normal vector at point (1,1,1) is (2,1, - 1)

As shown in the figure: the area of the shadow part is 50 square centimeters, find the area of the ring in the figure

Let the radius of the big circle be r and the radius of the small circle be r, then: 2R × R △ 2-2r × R △ 2 = 50, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & r2-r2 = 50 (square centimeter); the area of the ring: π R2 - π R2, = π × (r2-r2), = 3.14 × 50, = 157 (square centimeter); answer: the area of the ring is 157 square centimeter

As shown in the figure: the area of the shadow part is 50 square centimeters, find the area of the ring in the figure

Let the radius of the big circle be r and the radius of the small circle be r, then: 2R × R △ 2-2r × R △ 2 = 50, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & r2-r2 = 50 (square centimeter); the area of the ring: π R2 - π R2, = π × (r2-r2), = 3.14 × 50, = 157 (square centimeter); answer: the area of the ring is 157 square centimeter

As shown in the figure: the area of the shadow part is 50 square centimeters, find the area of the ring in the figure

Let the radius of the big circle be r, and the radius of the small circle be r, then: 2R × R △ 2-2r × R △ 2 = 50, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & r2-r2 = 50 (square centimeter); the area of the ring: π R2 - π R2, = π × (r2-r2), = 3

The perimeter of a circular pond is 157m, and a 3M wide road is paved around it to calculate the area of cement road

Inner radius 157 △ 3.14 △ 2 = 25m
Outer radius 25 + 3 = 28m
Cement road area 3.14 * (28 & sup2; - 25 & sup2;) = 499.26 square meters

A circular garden is 31.4 meters in circumference. A 2-meter-wide circular stone road should be paved around the garden, and the area of the circular road should be calculated

Inner radius 31.4 △ 3.14 △ 2 = 5m
Outer radius 5 + 5 = 7M
Annular area 3.14 × (7 × 7-5 × 5)
=3.14×24
=75.36 square meters

Put a circular scissors into a rectangle. The perimeter of the rectangle is 6.28 meters. Then the original radius of the circle is (), the perimeter is (), and the area is ()

Radius r = 6.28 / (2 + 2pi) = 6.28/8.28 = 0.7584, the rest is calculated by yourself