The 0 in the number 402 is in the ten place. The number after it is 2. 2 is less than 5.
402 rounded to the nearest ten is 400
The 4 in the number 402 is in the hundreds place. The number after it is 0. 0 is less than 5.
402 rounded to the nearest hundred is 400
Answer:
37. {-1, -1}.
Step-by-step explanation:
I'll solve the first one . The other can be solved in a similar way. We can use the method of elimination.
x1 - x2 = 0
3x1 - 2x2 = -1
We can multiply the first equation by -2. We then have an equation containing + 2x2 so when we add this to the second equation the 2x2 will be eliminated
So the first equation becomes:
-2x1 + 2x2 = 0 Bring down the second equation:
3x1 - 2x2 = -1 Now adding, we get:
x1 + 0 = -1
so x1 = -1.
Now we substitute this value of x1 in the original first equation:
-1 - x2 = 0
-1 = x2
x2 = -1.
So the solution set is {-1, -1}.
If there are more than 2 equations you can use a combination of substitutions and eliminations.
A)If the order of the speakers is important, we have 20x19x18x17, or 116,280 different options.
b) If order is not important, then we have 20 choose 4, or 4845 different slates. ☺☺☺☺
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.
