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olga nikolaevna [1]
3 years ago
13

The composition of a function and its inverse is always _____?

Mathematics
2 answers:
Step2247 [10]3 years ago
7 0

The composition of a function and its inverse is always <u>x</u>.

I hope this helps! :D

puteri [66]3 years ago
7 0
The composition of a function and its inverse is always X.
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Show that the equation represent a sphere, and find its center and radius. 3x2+3y2+3z2=10+6y+12z
mihalych1998 [28]

Answer:

Center of sphere = (0, 1, 2)

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Step-by-step explanation:

We are given the following in the question:

Equation of sphere:

3x^2+3y^2+3z^2=10+6y+12z

Formula:

The equation of sphere is of the form

(x-a)^2 + (y-b)^2 + (z-c)^2 = r^2\\\text{where (a,b,c) is the centre of sphere and r is the radius of sphere.}

Simplifying the given equation we get,

3x^2+3y^2+3z^2=10+6y+12z\\\text{Dividing by 3}\\x^2 + y^2 + z^2 = \dfrac{10}{3} + 2y + 4z\\\\x^2 + y^2 -2y + z^2-4z = \dfrac{10}{3}\\\\\text{Adding 1 and 4 on both sides, we get,}\\\\x^2 + y^2 -2y +1 + z^2-4z + 4 = \dfrac{10}{3} + 1+ 4\\\\(x-0)^2 + (y-1)^2 + (z-2)^2 = \dfrac{25}{3}\\\\\text{Comparing with the equation of sphere}\\a = 0\\b = 1\\c = 2\\\\r^2 = \dfrac{25}{3}\\\\r = \sqrt{\dfrac{25}{3}}= \dfrac{5}{\sqrt3}

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Radius of sphere = \dfrac{5}{\sqrt3}\text{ units}

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3.2555555 as a fraction
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