Answer:
Graphic is showed in the figure below
Step-by-step explanation:
To graph the equations given, let's do a table for positive values of x, and, by replacing it in the equation, let's calculate the value of y. Knowing the coordinate points (x,y) we can build the graphic.
<em>x y= x + 1/x² y = 1/x</em>
1 2 1
2 2.25 0.2
3 3.11 0.33
4 4.06 0.25
When x->0 both equations -> ∞, because lim(1/x) x->0 = ∞
The graphic is showed below. In red there is y = 1 + 1/x² and in blue y = 1/x
Answer:
38,674.This area represents the increase in population over a 10-year period.
Step-by-step explanation:
When graphed over the interval 0 ≤ t ≤ 10, the birth rate is more than the death rate. This means the area between the two curves is the amount of births subtract the amount of deaths. This results in an area which means the increase of the population.
The birth rate is graphed in green and the death rate is graphed in blue.
To find the area, take the integral of the difference of the functions:
Answer with Step-by-step explanation:
We are given that
and
are linearly independent.
By definition of linear independent there exits three scalar and
such that
Where
We have to prove that and
are linearly independent.
Let and
such that
...(1)
..(2)
..(3)
Because and
are linearly independent.
From equation (1) and (3)
...(4)
Adding equation (2) and (4)
From equation (1) and (2)
Hence, and
area linearly independent.