1.Find the area of a triangle that has a base of 30 feet and a height of 12 feet.
1 answer:
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Answer: They meet after 1 hour 42 minutes.
Step-by-step explanation:
Since we have given that
Dana leaves Las Vegas for LA at 2 p.m. driving at 55 mph.
Let the time taken by Dana be 't'.
Distance traveled by Dana would be 55t.
At 4 p.m. Lance leaves LA for Las Vegas driving at 45 mph along the same route.
It means after 2 hours Lance leave for LA.
So, time taken by Lance be 't-2'.
Distance traveled by Lance would be 45(t-2)
Total distance = 260 miles
According to question, it becomes,
Hence, they meet after 1 hour 42 minutes.
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.