16/3 is rational simply because it is a fraction made up of whole numbers.
Irrational numbers cannot be expressed as fractions made up of whole numbers.
Answer:
The given equation is
Which represents an elipse.
To find its elements, we need to divide the equation by 100
Where 
and 
. Remember that the greatest denominator is 
, and the least is 
. So, we extract the square root on each equation.
and 
.
In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.
The length of the major axis is 
.
The length of the minor axis is 
.
The vertices are 
and 
.
Now, the main parameters of an elipse are related by
, which we are gonna use to find 
, the parameter of the focus.
So, the coordinates of each focus are 
and 
The eccentricity of a elipse is defined
The latus rectum is defined
Finally, the graph of the elipse is attached.
Answer:
{x: x ∈ ℝ, x ≥ 0}
Step-by-step explanation:
The relation is only defined for non-negative values of x, so that is what the domain consists of: real numbers greater than or equal to zero.
First, you need to find the derivative of this function. This is done by multiplying the exponent of the variable by the coefficient, and then reducing the exponent by 1.
f'(x)=3x^2-3
Now, set this function equal to 0 to find x-values of the relative max and min.
0=3x^2-3
0=3(x^2-1)
0=3(x+1)(x-1)
x=-1, 1
To determine which is the max and which is the min, plug in values to f'(x) that are greater than and less than each. We will use -2, 0, 2.
f'(-2)=3(-2)^2-3=3(4)-3=12-3=9
f'(0)=3(0)^2-3=3(0)-3=0-3=-3
f'(2)=3(2)^2=3(4)-3=12-3=9
We examine the sign changes to determine whether it is a max or a min. If the sign goes from + to -, then it is a maximum. If it goes from - to +, it is a minimum. Therefore, x=-1 is a relative maximum and x=1 is a relative miminum.
To determine the values of the relative max and min, plug in the x-values to f(x).
f(-1)=(-1)^3-3(-1)+1=-1+3+1=3
f(1)=(1)^3-3(1)+1=1-3+1=-1
Hope this helps!!
