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Gwar [14]
3 years ago
5

The admission fee for a charity event is $7 for children and $10 for adults. The event was attended by 700 people and the total

collected in admissions was$6400. There were how many children and how many adults.
Mathematics
1 answer:
Hitman42 [59]3 years ago
3 0
X = 7
y = 10
x + y = 700
7x + 10y = 6400

10x + 10y = 7000
(-) 7x + 10y = 6400
______________
3x = 600
x = 200

200 + y = 700
y = 500
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(1 point) Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference betw
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Answer:

a. \frac{dT}{dt}=k(T-Tm); T(0)=190

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Step-by-step explanation:

a. Newton's law of cooling states that the speed with which a body is cooled is proportional to the difference between its temperature and that of the medium in which it is found. Then, the initial value problem is given by:

Tm=68

\frac{dT}{dt}=k(T-Tm); T(0)=190

b. The differential equation obtained is a differential equation of separable variables:

\frac{dT}{T-Tm}=kdt\\\\\int {\frac{dT}{T-Tm}}=\int{kdt}\\\\Ln|T-Tm|=kt+C\\\\T(t)=C_{0}e^{kt}+Tm=C_{0}e^{kt}+68\\\\T(0)=C_{0}e^{k(0)}+68=190\\\\C_{0}=122

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T(33)=122e^{33k}+68=180\\\\e^{33k}=\frac{112}{122}\\\\33k=Ln(\frac{112}{122})\\\\k=-0.00259

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150=122e^{-0.00259t}+68\\\\Ln(\frac{150-68}{122})=-0.00259t\\\\t=153.39838\\\\

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