A cone with height of 16 is connected to a sphere with volume of 972 π, and there is another inscribed sphere in the cone. Find (1) the side area of the cone; (2) the volume of the inscribed sphere of the cone

(1) As shown in the figure, if we make an axial section, then the isosceles triangle cab is inscribed on the circle O, and the circle O1 is inscribed on the △ cab. Let the radius of the circle o be r. according to the meaning of the title, we get 43 π R3 = 972 π, ∧ R3 = 729, r = 9 ∧ CE = 18; (3 points) known CD = 16, ∧ ed = 2, connected AE, ∧ CE is the diameter, ∧ Ca ⊥ AE, Ca2 = CD ∧ CE =

If the point (2,14) is on the image of both the function y = 2aX + B and its inverse function, then a= ，b=

∵ point (2,14) is on the image of the inverse function of the function y = 2aX + B. according to the symmetric relation between the inverse function and the original function, ∵ point (14,2) is on the image of the function y = 2aX + B. substituting points (2,14) and (14,2) into the function y = 2aX + B, we can get. 2A + B = - 2 ①14a+b＝1… ② The solution is a = − 127b = 107, so the answer is: − 127; 107

The first question: what is the inverse function of the function y = x ^ 2 + 2x + 3? The second question: what is the maximum value of the function FX = x ^ 3-3x ^ 2 + 2 in the interval [- 1,1]?

The first problem: the function y = x ^ 2 + 2x + 3 is not strictly monotone in its domain of definition, so its inverse function does not exist
If a function exists, then one X corresponds to two YS);
The second problem: F (x) = x ^ 3-3x ^ 2 + 2
f ‘（x）=3x^2-6x
When x0, when x > 2, f '> 0
When x = 0 or x = 2, f '= 0
Therefore, in the interval [- 1,1], when x = 0, f (x) takes the maximum value and is substituted into the solution to get 2

What is the inverse function of the function y = 2x + 6 + 10F (x + 15) x ∈ R, y ∈ r

Y = F-1 (0.1 * (x + 2Y + 24)) uncertain=

How to find the inverse function of y = e ^ 2x - (1 / E) ^ 2x
How to seek
Inverse function of y = e ^ 2x - (1 / E) ^ 2x

Y = e ^ 2x - (1 / E) ^ 2x two sides of the equation multiplied by e ^ 2x become
e^2x*y=e^4x-1
Finally, the equation E ^ 4x-y * e ^ 2x-1 = 0
It is OK to regard it as a quadratic equation of one variable with e ^ 2x as an unknown number and add roots

Mathematics: what is the inverse function of y = e ^ 2x?

y=0.5lnx

In the four points P (1,1), q (1,2), m (2,3), n (1 / 2,1 / 4), what is the common point between the image of function y = a ^ X and its inverse function
It's the process and the answer

As a multiple-choice question, you can get the answer quickly by special methods. When the base of the intersection of the image of exponential function and logarithmic function (its inverse function) is greater than 1, the intersection must exist on the straight line y = x, that is, the abscissa and ordinate are equal, and both are greater than 1; when the base is less than 1, the intersection

1. Given the function FX = x + 1 / X-1 (x ≠ 1), find the inverse function of F (1 / x)
2. Given the function FX = x + 1 / X-1 (x ≠ 1), find F-1 (1 / x)

Analysis
f(x)=(x+1)/(x-1)
f(1/x)=(1+x)/(1-x)
therefore
f(1/x)(1-x)=1+x
f(1/x)-xf(1/x)=1+x
f(1/x)-xf(1/x)-1-x=0
f(1/x)-1-x(f(1/x)+1）=0
x=(f(1/x)-1)/(f(1/x)+1）
X f (1 / x) interchange
f-1(1/x)=(x-1)/(x+1)

The inverse function of known function FX = LG [(x + 3) / (x-3)]

A:
y=f(x)=lg[(x+3)/(x-3)]
So: (x + 3) / (x-3) = 10 ^ y
So: (x-3 + 6) / (x-3) = 10 ^ y
1+6/(x-3)=10^y
6/(x-3)=10^y-1
x-3=6/(10^y-1)
x=3+6/(10^y-1)
So: the inverse function is y = F-1 (x) = 3 + 6 / (10 ^ x-1)

Given that the image of the function FX logax + K passes through the point (3.1) and the image of its inverse function passes through the point (0,2), the analytic expression of the function is obtained

The image of F (x) = log (a, x) + K passes through the point (3,1), and its inverse function f ^ (- 1) (x) image passes through the point (0,2) ∵ the inverse function image and the original function image are symmetric with respect to y = x, so the original function passes through the point (2,0) so f (3) = log (a, 3) + k = 1F (2) = log (a, 2) + k = 0. The simultaneous solution is = > A = 3 / 2, k = 1, so f (x) = log (3 / 2, x) ∵

A cone with height of 16 is connected to a sphere with volume of 972 π, and there is another inscribed sphere in the cone. Find (1) the side area of the cone; (2) the volume of the inscribed sphere of the cone