PLEASE HELP!!! i tryed by i thing I got it wrong I WILL GIVE BRANLIESS
1 answer:
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Answer:
- 168.25 ft
- 3.125 s
Step-by-step explanation:
It is almost too easy to let a graphing calculator show you the solution. (See attached)
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You may be expected to use some actual algebra (or even calculus) to find the solution.
If you've spent any time with quadratics, you know the vertex of ax²+bx+c is located at x=-b/(2a). Here, that means the time to get to the highest point is ...
... t = -100/(2·(-16)) = 100/32 = 3.125 . . . . seconds
Then the highest point is ...
... h(3.125) = -16·3.125² +100·3.125 +12 = 168.25 . . . . feet
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Or, you can put the equation into vertex form.
... h(t) = -16t² +100t +12
... = -16(t² +6.25t) +12
... = -16(t² +6.25t +3.125²) +12 +16·3.125² . . . . . add the square of half the t coefficient inside parentheses; add the opposite of the same amount outside parentheses
... = -16(t +3.125)² +168.25 . . . . . simplify
This tells us the peak of the travel of the bullet is at 168.25 ft after 3.125 seconds.
By definition, if is the least upper bound of the set
, it means two thing:
In other words, the least upper bound of a set is greater than or equal to every single element of the set, but it is "close enough" to the elements of the set, because you guaranteed to find elements in the set between and
For example, pick . Obvisouly, the least upper bound is
. In fact, every number in
is smaller than 10, but as soon as you take away something from 10, say 0.01, you get 9.99, and there are elements in
greater than 9.99, say 9.9999.
So, the claim is basically proven by definition: if , let
. By definition, there exists
.
