Which of these sequences is a geometric sequence?
1 answer:
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Answer:
Step-by-step explanation:
I solved this using initial conditions and calculus, so I hope that's what you are doing in math. It's actually NOT calculus, just a concept that is taught in calculus.
The initial condition formula we need is
Filling in our formula with the 2 conditions we are given:
and
With those 2 equations, we have 2 unknowns, the C (initial value) and the k (the constant). We know that the initial value (or starting temp) for both conditions is the same, so we solve for C in one equation, sub it into the other equation and solve for k. If
then
which, by exponential rules is the same as
Since that value of C is the same as the value of C in the other equation, we sub it in:
Divide both sides by 65 and use the rules of exponents again to get
which simplifies down to
Take the natural log of both sides to get
Do the log thing on your calculator to get
.2682639866 = 5k and divide both sides by 5 to find k:
k = .0536527973
Now that we have k, we sub THAT value in to one of the original equations to find C:
which simplifies down to
Raise e to that power on your calculator to get
65 = C(1.710059171) and divide to solve for C:
C = 38.01038064
Now sub in k and C to the final problem when t = 23:
which simplifies a bit to
Raise e to that power on your calculator to get
y = 38.01038064(3.434991111) and
finally, the temp at 23 minutes is
130.565
ANSWER
EXPLANATION
The given right triangle is an isosceles triangle because
This implies that,
From the Pythagoras Theorem,
EXPLANATION
The given right triangle is an isosceles triangle because
This implies that,
From the Pythagoras Theorem,