Answer:
Step-by-step explanation:
define the function:
As both 
and x are continuous functions, 
will also be continuous.
Now, what can we say about 
?
we know that 
, thus:
thus 
is non-negative.
What about 
? Again we have:
That means that is not positive.
Now, we can imagine two cases, either one of 
or is equal to zero, or none of them is. If either of them is equal to zero, we have found a fixed point! In fact, any point 
for which 
is a fixed point, because:
Now, if 
and 
, then we have that
and 
. And by Bolzano's theorem we can assert that there must exist a point c between a and b for which . And as we have shown before that point would be a fixed point. This completes the proof.
Answer:
309.00 and Good luck with your test !
Answer: (a) 11.8
(b) 13
Step-by-step explanation:
Since George wants to put a string of lights around , it means we will have to consider the perimeter of the shape.
Perimeter of a rectangle is given by :
P = 2( L+B)
P = 2 ( 2.5 + 3.4)
P = 2 ( 5.9)
P = 11.8 meters
(b) Since he wants to put an addition to his wooden deck that is 0.6 meters longer , then the perimeter will be the perimeter of the first shape + 2(0.6). We used 2(0.6) because the two lengths of the rectangle must be considered
Therefore, we have
P = 11.8 meters + 2(0.6)
= 11. 8 + 1.2
= 13 meters
Therefore George needs 13 meters length of light
Answer:
1.) No
2.) 40 goals
Step-by-step explanation:
Given the following :
Last season:
Games played = 15
Points scored = 41
Current season:
Games played = 9
Points scored = 24
A)
Last season:
Goals per game = total points / number of games
Goals per game = 41 / 15 = 2.733
Current season :
Goals per game = total points / number of games
Goals per game = 24 / 9 = 2.667
Last season's goal per game is greater than that of current season.
B)
Current rate = goals / games = 24/9 - - - (1)
Let points to be scored this season = y
Ratio of y to number of games played last season = y / 15 - - - (2)
Equate both
24 / 9 = y / 15
9 * y = 24 * 15
y = 360 / 9
y = 40
