Find the common difference of the arithmetic sequence.
2 answers:
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<span>we have that
H(t) = −16t</span>²<span> + 96t + 80
</span><span>g(t) = 31 + 32.2t
Part A)
see the attached table
</span><span>the solution to H(t) = g(t) is between t=4 sec and t=5 sec
for t=4 sec
H(4)=208 ft and g(4)=159.8 ft
so
H(t) > g(t)
</span>for t=5 sec
H(5)=160 ft and g(5)=192 ft
so
H(t) < g(t)
<span>that change of H(t) from being greater to becoming smaller tells me that the solution is in that interval [4, 5]
</span>
Part B)<span>Explain what the solution from Part A means in the context of the problem
</span>when H(t)=g(t) means <span>that the projectile destroyed the object N 2 in the interval [4,5]
to find the exact solution
</span>−16t² + 96t + 80=31 + 32.2t
−16t² + 96t + 80-31-32.2t=0
−16t² + 63.8t + 49=0<span>
using a graph tool
see the attached figure
the exact solution is
t=4.65 sec</span>
H(t) = −16t</span>²<span> + 96t + 80
</span><span>g(t) = 31 + 32.2t
Part A)
see the attached table
</span><span>the solution to H(t) = g(t) is between t=4 sec and t=5 sec
for t=4 sec
H(4)=208 ft and g(4)=159.8 ft
so
H(t) > g(t)
</span>for t=5 sec
H(5)=160 ft and g(5)=192 ft
so
H(t) < g(t)
<span>that change of H(t) from being greater to becoming smaller tells me that the solution is in that interval [4, 5]
</span>
Part B)<span>Explain what the solution from Part A means in the context of the problem
</span>when H(t)=g(t) means <span>that the projectile destroyed the object N 2 in the interval [4,5]
to find the exact solution
</span>−16t² + 96t + 80=31 + 32.2t
−16t² + 96t + 80-31-32.2t=0
−16t² + 63.8t + 49=0<span>
using a graph tool
see the attached figure
the exact solution is
t=4.65 sec</span>