Y = - M2 - 4, - 2 √ 3 ≤ x ≤ 0 inverse function

Y = - M2 - 4, - 2 √ 3 ≤ x ≤ 0 inverse function

m=-√-y-4
So the inverse function is y = - √ - M-4
In addition, the original function is incremented, and the range of value [- 16, - 4] can be obtained, so the domain of definition of the inverse function [- 16, - 4]

If the bottom area of a cone is 4 π and its axis section is an equilateral triangle, then its side area is ()
A. 2πB. 4πC. 8πD. 16π

According to the meaning of the title, let the bottom radius of the cone be r, the length of the generatrix be l, and the height be H. ∵ the bottom area is 4 π, ∵ π R2 = 4 π, and the solution is r = 2. And ∵ the axial section of the cone is an equilateral triangle, ∵ L = 2R = 4, H = 3R = 23, and the side area of the cone is s = π RL = π × 2 × 4 = 8 π

The cross section of a cone passing through its axis is an equilateral triangle with a side length of 2 cm. What is the bottom area of the cone?

Analysis: the cross section of a cone passing through the axis is an equilateral triangle with side length of 2 cm, which indicates that the bottom diameter of the cone is 2 cm;
The bottom area of this cone is: 3.14 × (2 △ 2) = 3.14 × 1 = 3.14 ( & sup2;)
A: the bottom area of this cone is 3.14 CM & sup2

Draw the image of a function y = 2X-4 in the rectangular coordinate system? What are the points?

Take any two points ～

In the plane angle coordinate system, if the points a (- 3,4), B (- 1, - 2) are known, the area of the triangle AOB is
Please write down all the procedures

Let AB linear equation y = KX + B
-3k+b=4
-k+b=-2
The solution is k = - 3, B = - 5
y=-3x-5
3x+y+5=0
Distance from 0 to line ab
h=|0+0+5|/√(9+1)=5/√10
S=(1/2)*|AB|*h
=1/2*√(2^2+6^2)*5/√10
=1/2*2√10*5/√10
=5

In the rectangular coordinate system, a (2,0), B (- 3, - 4), O (0,0), find the area of triangle AOB

The height of the triangle is the distance from B to X axis, which is 4, the bottom is OA, which is 2, and the area s = 0.5 * 4 * 2 = 4

As shown in the figure, in the rectangular coordinate system, a (- 1,3), B (3, - 2). (1) find the area of △ AOB; (2) let AB intersect Y axis at point C, find the coordinates of point C

When y = 0, x = 75, that is, the intersection of the line and the x-axis is d (75, 0). (1) s △ AOB = s △ AOD + s △ BOD = 12od × 3 + 12od × 2 = 12od × (3 + 2) = 12 × 75 × 5 = 72. That is, s △ AOB = 72; (2) when x = 0, y = 74, that is, the coordinates of the intersection of the line 4Y + 5x-7 = 0 and the x-axis are (0, 74)

The image of quadratic function y = x2 + BX + C passes through point a (- 2,5), and when x = 2, y = - 3, find the analytic expression of the quadratic function and judge the point
Is (0,3) on this function image

X = - 2, y = 5 is substituted into the equation: 5 = 4-2b + C
X = 2, y = - 3 is substituted into the equation: - 3 = 4 + 2B + C
The simultaneous equations are: B = - 2, C = - 3
So the equation is y = x-2x-3
Substitute x = 0 into the equation: y = - 3
So (0,3) is not on this function image

Given the image of quadratic function y = ax ^ 2 + BX + C (a is non-zero), how to judge the positive and negative values of the following algebraic expression?
Image description: the opening of the parabola is upward, the symmetry axis is on the right side of the Y axis, the parabola intersects the positive half axis of the Y axis, the vertex coordinates are below the X axis, and the two intersections of the parabola and the X axis are x1, X2, 1 > x1 > 0, X2 > 2
Algebraic formula:
1)a+b+c 2)a-b+c 3)abc 4)4a+b 5)b^2-4ac

The parabolic opening is upward, so a > 0
The symmetry axis is on the right side of Y-axis and 1 > X1 > 0, X2 > 2, so 1

In a rectangular coordinate system, the midpoint a (m, M + 1), B (M + 3, m-1) are on the image with inverse scale function y = x / K

Substituting the coordinates of a and B into y = K / x, we get the following results
k=m(m+1)
k=(m+3)(m-1)
Then: m (M + 1) = (M + 3) (m-1)
m=2m-3
m=3
So, k = m (M + 1) = 12
So, the inverse scale function is y = 12 / X
Coordinates of point a (3,4)
Coordinates of point B (6,2)