How to find the projection of space surface on coordinate plane?

How to find the projection of space surface on coordinate plane?

To find the projection area of the surface z = f (x, y) in the xoy plane, we only need to project the boundary curve of the surface to the xoy plane, and the area enclosed by the projection curve in the xoy plane is what we want to find

1. What are the types of planar objects and their projection characteristics? 2. What are the types of curved objects and their projection characteristics

The plane can be divided into cube (projection features: square, rectangle, hexagon), cuboid (projection features: square, rectangle, hexagon), prism (projection features: square, rectangle, polygon), etc;
Curved surface can be divided into sphere (projection feature: circle), cylinder (projection feature: square, rectangle, circle, ellipse, racetrack, other irregular shapes), cone (projection feature: triangle, circle, ellipse, sector)

How to find the projection equation of a surface equation on the coordinate plane?
For example, the projection equation of Z = f (x, y) on the xoy plane must be shown by drawing

Let z = a (i.e. make the section with xoy plane to get the section) and get a = f (x, y). This is the equation of the projection of the section on xoy plane. If the projection of the whole surface is set as point set a and the value set of a is set as m, then a = {(x, y) / F (x, y) = a, a belongs to a}

The circumference of a semicircle with an area of () square meters is 15.42 meters

Let the radius be r meters
1/2*2*3.14r+2r=15.42
5.14r=15.42
r=3
1 / 2 * 3.14 * 3 ^ 2 = 14.13 square meters
The circumference of a semicircle with an area of (14.13) square meters is 15.42 meters

25 / 9 / 5 / 4 / 4 / 5 simple operation
Fast, at 21:00

Mathematical answer group for you to answer, I hope to help you
25/9÷5/4÷4/5
=25/9÷(5/4×4/5)
=25/9÷1
=25/9

As shown in the figure, in △ ABC, ab = 3aD, AC = 3cg, be = EF = FC, and the area of △ FCG is 1 square centimeter

Connect AE, AF and DC, as shown in the figure, because AC = 3cg, in △ AFC and △ GFC, AC: CG = 1:3, so s △ AFC = 3S △ GFC = 3 × 1 = 3 (square centimeter), in △ Abe, △ AEF and △ AFC, because be = ef = FC, their heights are equal, so s △ Abe = s △ AEF = s △ AFC = 3 (square centimeter) s △ ABC = 3S △ AFC = 3 × 3 = 9 (square centimeter), and because AB = 3aD, so BD: ab = 2:3, so s △ AFC = 3 Delta DBE = 23S delta Abe = 23 × 3 = 2 (square centimeter), in triangle ADC and triangle ABC, ad = 13ab, their height is equal, so s delta ADC = 13s delta ABC = 13 × 9 = 3 (square centimeter), in delta ADG and delta ADC, AC = 3gc, Ag = 23ac, and their height is equal, so s delta ADG = 23S delta ADC = 23 × 3 = 2 (square centimeter), the area of shadow part: s Delta abc-s Delta dbe-s Delta adg-s delta GFC = 9-2-2-1 = 4 (square centimeter) A: the area of the shadow is 4 square centimeters

In all permutations of 1,2,3,4,5: A1, A2, A3, A4, A5, what is the number of different permutations satisfying the conditions A1 > A2, A3 > A2, A3 > A4, A5 > A4?

A1 > A2, A3 > a2a3 > A4, A5 > a4a2, A4 must have one. If A2 = 1, then A4 can only be 2 or 3A4 = 2 (A1, A3, A5 can be 3 or 4 or 5). There are six permutations satisfying the condition. When A4 = 3 (A1 can only be 2, A3, A5 can be 4 or 5), there are two permutations satisfying the condition. Similarly, if A4

The area of a trapezoid is 18 square decimeters. Its upper bottom is 3 decimeters and its height is 4 decimeters. How many decimeters is the lower bottom

Trapezoid bottom = trapezoid area × 2 △ height - upper bottom
18 × 2 △ 4-3 = 6 decimeters

Given f (2 / x + 1) = lgx, find the analytic expression of F (x)

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A room is 6 meters long, 4 meters wide and 3.5 meters high. To paint the roof, four walls and ceiling of the room, excluding the area of doors and windows of 5 square meters, how many square meters is the painting area?

6 × 4 + 6 × 3.5 × 2 + 4 × 3.5 × 2-5 = 89 square meters