Formula One Winners
can you help me with my math homework? (tenth grade) geometry?
h(t)= -16t^2 +112t
convert formula to vertex form and give:
domain, range, vertex, max/min, x-intercepts.
Last season the volleyball team played in an invitational tournament held at the Emory university. during the tournament, each invited team played one match against each other participating team. In volleyball, the first tean to win three games, or sets, wins a match. At this tournament every match required five sets to determine the winner.
-write a formula that expresses the total number of sets as a function of the total numbber of teams in the tournament.
-if there were a total of 140 sets played during the tournament, how many teams participated?
thanks you guys (:
wow, so many questions in a question, I’ll try my best to go through one by one.
Converting to vertex form (using the formula from the reference) where a= -16, b=112, c=0 gives
h(t) = -16(x – 7/2) + 196
x-intersects: -16x^2 +112x = x( -16x + 112), So, x= 0 and x= 112/16 = 7.
domain: all possible real numbers.
max/min: a= -16 so the function is a maximum.
vertex: (7/2, 196).
range: [196, -infinity)
x= number of teams
The number of matches between each team is x choose 2
So, the formula to express the total number of sets f(x) = (x choose 2) * 5 = (x! * 5) / 2!(x – 2)!
For 140 sets,
f(x) = (x choose 2) * 5 = (x! * 5) / 2!(x – 2)! = 140
x choose 2 = 140/5 = 28
x = 8
gl
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