Prove
1 answer:
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Answer:
(a) 13.85 °C
Step-by-step explanation:
The temperature difference is a decaying exponential function of time. Here, it decreases from an initial difference of 15 °C to 10 °C after 25 minutes. So, that temperature difference can be modeled as ...
ΔT = 15(10/15)^(t/25)
We want to find the value of this at t=55. It is ...
ΔT = 15(2/3)^(55/25) ≈ 6.15
This is the amount the temperature of the drink is below room temperature.
drink temperature = (20 - 6.15) °C = 13.85 °C
The temperature of the drink after 55 minutes is about 13.85 °C.
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Solve the trigonometric equation:
Make a substitution:
and the equation becomes
Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:
Factor out 2t + 1:
Substitute back for t = cos x:
Therefore,
where k is an integer.
Solution set:
I hope this helps. =)
——————————
Solve the trigonometric equation:
Make a substitution:
and the equation becomes
Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:
Factor out 2t + 1:
Substitute back for t = cos x:
Therefore,
where k is an integer.
Solution set:
I hope this helps. =)