H(y) models the leading number of home runs for season y on the National League between the years 2000-2010, according to the ta
2 answers:
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Answer:
(a) 5.714s
(b) 0.625m
Step-by-step explanation:
Acceleration due to gravity=a=±9.8m/s/s (+ when falling, - when going upwards)
(a)
STAGE A: between start and first bounce
Initial speed=u=0m/s, Distance=s=40m, and Final velocity=v
v²=u²+2as
v²=0²+2(10)(40)
v²=794
v=28m/s (As the ball hits the ground)
v=u+at
28=0+9.8t
t=28/9.8=2.85714285714s
STAGE B: from the first bounce until it starts to fall
u=half the speed it hit the ground with=(28/2)=14m/s, and v=0m/s(when it starts to fall)
v=u+at
0=14-9.8t
t=14/9.8=1.42857142857s
STAGE C: between when it starts to fall after bounce 1, and bounce 2
We can assume that the time it takes to go from the ground to max height after bounce 1 is equal to the time it takes to fall from that same height to the ground. Therefore, t =1.42857142857s
The time from when the ball was released to when it hit the ground for the second time = t
t = t + t
+ t
t=2.85714285714+1.42857142857+1.42857142857
t=5.71428571428s≈5.714s
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(b)
Before bounce 1, u=28m/s (see stage a)
After bounce 1, u= 28/2= 14m/s
After bounce 2, u= 14/2 = 7m/s
After bounce 3, u= 7/2 =3.5m/s
u=3.5m/s and v=0m/s(when it starts to fall)
v²=u²+2as
0²=3.5²+2(-9.8)s
19.6s=12.25
s=<u>0.625m (max height after third bounce)</u>
Because he needs less than (note that he didn't say he needs no more than) 6 pounds, first inequality is C) x+y<6
Now in inequalities that have 7 and 5 in them, 7 represents the cost of first ingredient and 5 the cost of second ingredient. If we multiply each of that number with quantity of that ingredient and sum both up we get the price of the mixture.
Because he says that he wants that mixture costs no more than 30 that means that it costs less than 30 but 30 can be the answer as well.
The last answer is E) 7x + 5y
Now in inequalities that have 7 and 5 in them, 7 represents the cost of first ingredient and 5 the cost of second ingredient. If we multiply each of that number with quantity of that ingredient and sum both up we get the price of the mixture.
Because he says that he wants that mixture costs no more than 30 that means that it costs less than 30 but 30 can be the answer as well.
The last answer is E) 7x + 5y