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skad [1K]
3 years ago
8

Sketch a possible curve of f(x) given the graphs of f ‘ (x) and f’’ (x) below:

Mathematics
1 answer:
Temka [501]3 years ago
4 0

Step-by-step explanation:

Graph 1 is a parabola and has 2 x points and a turning point

meaning it has a minimum and a maximum point.

conclave points are the highs and lows, once you show this in table then you can interpreted them on a graph see the examples attached.

Graph 1 is opposite to shown interpreted conclave so instead of --c++

we write  + + c - - and draw on quadrant 1 instead of quadrant 3

graph 2 is decreasing so instead of -+ c then + + it would show + -  c then - - so the curve stays in quadrant 3 and 4. Also where c is we draw a 0 and say whether it is minimum or maximum point.

Both graph 1 and 2 demonstrate minimum points for their f(x) for c.

so in your workings within the table you write min as seen in red within the attachment. They wrote max, but you write min as you are in decreasing conclave fx values that reach min point c then they increase and become parabolas.

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Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
Aleonysh [2.5K]

Answer:

t=5.18 minute

Step-by-step explanation:

Using Newton's law of cooling

\frac{dT}{dt}=-k(T-T_{s})

T is temperature of a cup of coffee at any time t T_{s}, is the temperature of the surrounding and k is a constant of proportionality in this negative because temperature is decreasing.

T(0)=190\\T(1)=170\\T_{s}=66

\frac{dT}{dt}=-k(T-T_{s})\\\frac{dT}{(T-T_{s})}=-k*dt\\\int\limits {\frac{1}{T-T_{s} } } \, dT=-\int\limits {k} \, dt\\ln(T-T_{s})=k*t+C\\e*ln(T-T_{s})=e^{k*t+C} \\T-T_{s}=e^{k*t}*e^{C}\\e^{C}=C\\T-T_{s}=e^{k*t}*C\\T=T_{s}+e^{k*t}*C

To find constant knowing the time and the temperature the first step of the change of energy in cup of coffee

T=T_{s} +e^{-k*t}*C\\ C=190-66=124\\170=66+124*e^{-k*2}\\ 170-66=124*e^{-k*2}\\ln(\frac{104}{124})=ln*e^{-k*2}\\-0.175=-k*2\\k=0.08794

Now using the constant of decreasing can find the time to be a 145 temperature the cup of coffee

145=66+124*e^{-k*t} \\145-66=124*^{-0.087*t}

ln(0.637)=ln*e(-0.087*t)\\-0.45=-0.087*t\\t=5.18minutes

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Step-by-step explanation:

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