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Calculus of exponentials and trip fcns: temp can be modeled by 𝑦 = 5π‘π‘œπ‘  π‘₯^2 + 25

sampang

New member
Joined
Dec 6, 2018
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1
Calculus of exponentials and trip fcns: temp can be modeled by 𝑦 = 5π‘π‘œπ‘  π‘₯^2 + 25

3.The weather in a given country can be modelled approximately by the curve 𝑦 = 5π‘π‘œπ‘  π‘₯2 + 25.
x is the number of the month (e.g. March is 3) and y is the average monthly temperature.
(a) Using transformations of graphs, explain why 𝑑𝑑π‘₯cosπ‘₯2= βˆ’12sinπ‘₯2
(b) Using calculus, determine which month is the hottest.
(c) During which months is the temperature increasing?
 

Dr.Peterson

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Joined
Nov 12, 2017
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2,754
3.The weather in a given country can be modelled approximately by the curve 𝑦 = 5π‘π‘œπ‘  π‘₯2 + 25.
x is the number of the month (e.g. March is 3) and y is the average monthly temperature.
(a) Using transformations of graphs, explain why 𝑑𝑑π‘₯cosπ‘₯2= βˆ’12sinπ‘₯2
(b) Using calculus, determine which month is the hottest.
(c) During which months is the temperature increasing?
In addition to showing your own thinking and giving us context, as our guidelines advise, please proofread what you submit. There are several issues here.

First, I think your title should refer to trig functions, not trip functions.

Second, I would initially guess that "𝑦 = 5π‘π‘œπ‘  π‘₯2 + 25" is supposed to be "𝑦 = 5π‘π‘œπ‘  π‘₯[SUP]2[/SUP] + 25", and "𝑑𝑑π‘₯cosπ‘₯2 = βˆ’12sinπ‘₯2" should be "𝑑/𝑑π‘₯ (cosπ‘₯[SUP]2[/SUP]) = βˆ’12sinπ‘₯[SUP]2[/SUP]".

But -- that isn't true! So my guess has to be wrong. Maybe it was really "𝑦 = 5π‘π‘œπ‘ (π‘₯/2) + 25" and "𝑑/𝑑π‘₯(cos(π‘₯/2)) = βˆ’12sin(π‘₯/2)". But that isn't right, either.

Finally, you haven't stated whether the formula assumes the cosine takes degrees, radians, or something else. That is important contextual information.

Please make sure that you copied the problem exactly. What you appear to have done is to paste from some electronic source for which copying loses part of the formatting. By not even checking what you pasted in, you have shown that you have put in no effort at all, which is not a good way to start when you ask for help.
 
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