Answer:
Step-by-step explanation:
x^2
--------------------------------------------------
2x + 1 / 2x^3 - x^2 + x + 1
2x^3 + x^2
-----------------------
0 + x + 1
x + 1
The quotient is x^2 + ------------
2x + 1
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
<span>According the information given we understand that the room is a regular rectangle, We know that volume = lenght * widht * height, so we start by calculate the room area as length by width, that is 16.4 * 4.5 = 73.8 square metres. Then with 3.26 metres of height, the total volum will 73.8 * 3.26 = 240.58 cubic metres.</span>
(23+15x) when you add this you will have your answer
Given:
Radius of the cone = 3 inches
Height of the cone = 8 inches
To find:
The volume of the cone, in terms of π.
Solution:
We know that, the volume of a cone is:
Putting 
, we get
Therefore, the volume of the cone is 
.
