1+1 = 84, explanation is quite simple. i should get brainliiest
Answer:
120 minutes
Step-by-step explanation:
the total bill was $58 so we have to subtract the $40 monthly bill part to find how much extra money she paid because her call was over 200 minutes
58-40=18
Then divide the $18 by $0.15 since the $18 is the total amount of each time she was charged $0.15 for going 1 minute over 200 minutes
18÷0.15 = 120
120 is te Amount Of minutes she went over her 200 minute limit
Answer:
Step-by-step explanation:
As the statement is ‘‘if and only if’’ we need to prove two implications
is surjective implies there exists a function
such that
.- If there exists a function
such that
, then
is surjective
Let us start by the first implication.
Our hypothesis is that the function
is surjective. From this we know that for every
there exist, at least, one
such that
.
Now, define the sets
. Notice that the set
is the pre-image of the element
. Also, from the fact that
is a function we deduce that
, and because
the sets
are no empty.
From each set
choose only one element
, and notice that
.
So, we can define the function
as
. It is no difficult to conclude that
. With this we have that
, and the prove is complete.
Now, let us prove the second implication.
We have that there exists a function
such that
.
Take an element
, then
. Now, write
and notice that
. Also, with this we have that
.
So, for every element
we have found that an element
(recall that
) such that
, which is equivalent to the fact that
is surjective. Therefore, the prove is complete.
The given equation of the ellipse is x^2
+ y^2 = 2 x + 2 y
At tangent line, the point is horizontal with the x-axis
therefore slope = dy / dx = 0
<span>So we have to take the 1st derivative of the equation
then equate dy / dx to zero.</span>
x^2 + y^2 = 2 x + 2 y
x^2 – 2 x = 2 y – y^2
(2x – 2) dx = (2 – 2y) dy
(2x – 2) / (2 – 2y) = 0
2x – 2 = 0
x = 1
To find for y, we go back to the original equation then substitute
the value of x.
x^2 + y^2 = 2 x + 2 y
1^2 + y^2 = 2 * 1 + 2 y
y^2 – 2y + 1 – 2 = 0
y^2 – 2y – 1 = 0
Finding the roots using the quadratic formula:
y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1
y = 1 ± 2.828
y = -1.828 , 3.828
<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828)
and (1, 3.828).</span>