Answer:
None
Step-by-step explanation:
They have the same slope so they are parallel and will never intersect.
Notice that the condition <em>x</em> ≠ 2<em>πk</em> for (presumably) integer <em>k</em> means cos(<em>x</em>) ≠ ±1, and in particular cos(<em>x</em>) ≠ 1 so that we could divide both sides by (1 - cos(<em>x</em>)) safely. Doing so lets us separate the variables:
(1 - cos(<em>x</em>)) <em>y'</em> - <em>y</em> sin(<em>x</em>) = 0
==> (1 - cos(<em>x</em>)) <em>y'</em> = <em>y</em> sin(<em>x</em>)
==> <em>y'</em>/<em>y</em> = sin(<em>x</em>)/(1 - cos(<em>x</em>))
==> d<em>y</em>/<em>y</em> = sin(<em>x</em>)/(1 - cos(<em>x</em>)) d<em>x</em>
Integrate both sides and solve for <em>y</em>. On the right, substitute <em>u</em> = 1 - cos(<em>x</em>) and d<em>u</em> = sin(<em>x</em>) d<em>x</em>.
∫ d<em>y</em>/<em>y</em> = ∫ sin(<em>x</em>)/(1 - cos(<em>x</em>)) d<em>x</em>
∫ d<em>y</em>/<em>y</em> = ∫ d<em>u</em>/<em>u</em>
ln|<em>y</em>| = ln|<em>u</em>| + <em>C</em>
exp(ln|<em>y</em>|) = exp(ln|<em>u</em>| + <em>C </em>)
exp(ln|<em>y</em>|) = exp(ln|<em>u</em>|) exp(<em>C </em>)
<em>y</em> = <em>Cu</em>
<em>y</em> = <em>C</em> (1 - cos(<em>x</em>))
Answer:
This is a guess!
When looking at the given equation I can not help but think of compound interest. So I am going to convert this into that format.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Within the context of financial interest:
Looking for:
P
(
1
−
x
)
n
Where P is the principle sum,
x
is the interest and n is the number of interest cycles (annual)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given:
y
=
5100
(
0.95
)
x
But
0.95
=
1
−
0.05
so we have
y
=
5100
(
1
−
0.05
)
x
But
.
0.05
=
5
100
So we have
y
=
5100
(
1
−
5
100
)
x
Thus the percentage change each year is
−
5
%
Step-by-step explanation:
Answer:
It took Kim one hour and 17 minutes for her to finish her homework.
Step-by-step explanation:
Assuming it was 6:15 p.m. and 7:32 p.m., it took Kim 1 hour and 17 minutes to finish her homework. An hour after 6:15 p.m. is 7:15 p.m., and 17 minutes after 7:15 is 7:32. So, it took Kim an hour and 17 minutes to finish her homework.