Surface x2 + Y2 + Z = 9 tangent plane equation at point 124

Surface x2 + Y2 + Z = 9 tangent plane equation at point 124

Fx=2x Fy=2y Fz=1
Tangent plane equation:
2(x-1)+4(y-2)+(z-4)=0 2x+4y+z-14=0
Normal equation:
(x-1)/2=(y-2)/4=(z-4)/1

The equation of the point in the plane whose distance from the origin is equal to 2

The radius is 2, so the standard equation is:
x²+y²=4
Don't know how to ask me

Find ∫ ∫ zdxdy, K is the outer side of ellipsoid X & # 178 / / A & # 178; + Y & # 178 / / B & # 178; + Z & # 178 / / C & # 178; = 1

From Gauss formula
The original formula = ∫∫∫ 1dxdydz = (4 / 3) π ABC
The integrand function is 1, the integral result is the volume of the region, and the ellipsoid volume formula is (4 / 3) π ABC

For the ellipsoid equation x & # 178; + Y & # 178; + Z & # 178; - YZ = 1, find the graph
What I want is a stereo image. Just cut a picture. In addition, by the way, I can find the projection of this surface on three planes of the spatial coordinate system. This only needs the equation

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The radius of the small round field is increased by 5m to get the large round field. The area of the field is increased by three times

Make an equation to solve it
The problem is not very difficult
(r+5)^2=4*r^2
3r^2-10r-25=0

If the radius of the large circular site is reduced by 5m, the area of the small circular site is only 1 / 4 of the original site, then the radius of the small circular site is?

Small circle radius = root sign (1 / 4) = 1 / 2 big circle radius
Small circle radius = 5m

As shown in the figure, the area of the shadow part is 30 square centimeters, and the annular area is calculated

∵ s shadow = s large △ - s small △ = (R & # 178; - R & # 178;) / 2 = 30, that is: (R & # 178; - R & # 178;) = 60
S ring = 3.14 * (R & # 178; - R & # 178;) = 3.14 * 60 = 188.4cm & # 178;

The area of the shadow is 160 square centimeters. What is the area of the ring?

According to the stem analysis: r2-r2 = 160 square centimeter, so the area of the ring = π (r2-r2), = 3.14 × 160, = 502.4 (square centimeter), answer: the area of the ring is 502.4 square centimeter

Given that the area of the shadow part in the figure is 40 square centimeters, how many square centimeters is the area of the ring? (& nbsp; π = 3.14)

Let the radius of the big circle be r, and the radius of the small circle be r, then the side length of the big square is r, and the side length of the small square is r, because the area of the shadow part = r2-r2 = 40 square centimeter, so the area of the ring = the area of the big circle - the area of the circle: π (r2-r2) = 3.14 × 40 = 125.6 (square centimeter) a: the area of the ring is 125.6 square centimeter

The area of the shadow part in the figure is 50 square centimeters. Find the area of the circle

Radius of large circle R, radius of small circle R
Shadow area = large square area - small square area = R & # 178; - R & # 178; = 50 square centimeters
Ring area = π R & # 178; - π R & # 178; = π × (R & # 178; - R & # 178;) = 3.14 × 50 = 157 square centimeter (when π is 3.14) = 50 π