Answer:
13 miles
Step-by-step explanation:
The taxicab charges a fixed amount of $3.10 plus $0.60 per mile.
This can be modeled by the equation.
where f is the total fare and m is the number of miles traveled.
If Carmen paid a fare of $10.90, then we substitute for f and solve for m.
Therefore Carmen traveled 13 miles.
X = longest side , y = middle side , z = shortest side
P = x + y + z
P = 82
x = 2z + 7
y = z + 15
82 = (2z + 7) + (z + 15) + z...combine like terms
82 = 4z + 22
82 - 22 = 4z
60 = 4z
60/4 = z
15 = z
so the shortest side (z) is 15 cm
the second side (y) is : z + 15......15 + 15 = 30 cm
and the longest side (x) is : 2z + 7.....2(15) + 7 = 37 cm
by the double angle identity for sine. Move everything to one side and factor out the cosine term.
Now the zero product property tells us that there are two cases where this is true,
In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of
, so
where
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which occurs twice in the interval
for
and
. More generally, if you think of
as a point on the unit circle, this occurs whenever
also completes a full revolution about the origin. This means for any integer
, the general solution in this case would be
and
.
