soccer toys
Can someone help me with these word problems?
During the championship soccer game, the goalkeeper, Brandon, kicked the ball straight up to the Mid-Fielder, Alex, with an initial velocity of 32 feet per second. The height of the ball relative to the ground is a function of time given by the following equation: f(t)=-16t^2+32t What is the maximum height reached by this soccer ball?
A manufacturing company uses the following function to model the unit cost in dollars to produce the x number of toys.
f(x)=0.02x^2-3.4x+150
For what number of toys is the unit cost at its minimum? What is the unit cost at that level of production?
Chris buys a box of TNT and one M16. He decides to spend no more than $27 for both items. If the TNT box costs $6 more than twice the M16, how much did he spend at most for the M16 ?
first problem:
f(t) = -16t^2 +32t and you have initial velocity at 32ft/sec
you need to find the max/min of equation so how do you do that? you get the derivative...
f'(t) = -32t+32 .........set f'(t)=0 and solve for t
0 = -32t+32
-32 = -32t
1 = t
max is when t=1
so f(1)= -16(1)^2+32(1)
f(1) = 16 ft
max height = 16 ft at 1 sec
second problem:
same thing...get derivative, set = 0, solve
f'(x)= 2(.02)x -3.4
0 = .04 x -3.4
3.4 = .04 x
x=3.4/.04=85
x=85
solve for x in f(x)=.02x^2-3.4x+150
f(85)=.02(85^2)-3.4(85)+150
f(85)=144.5-289+150
f(85)=5.5
so at 85 toys is the minimum..and the unit cost is 5.5 dollars
third problem:
27 dollars max
TNT = 2(M16) + 6
27> TNT + M16 substitute TNT...to get
27 > 2(M16) + 6 + M16
27 > 3(M16) + 6
21 > 3 (M16)
7 > M16
Chris spends no more than 7 bucks for M16....
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