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3 years ago

What is the slope of the line that passes through the points (-2, 2), and (-4, -2)

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

3 0

Answer:

Step-by-step explanation:

(-2 - 2)/(-4 + 2)= -4/-2= 2 is the slope

y - 2 = 2(x + 2)

y - 2 = 2x + 4

y = 2x + 6 is the equation

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3 years ago

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Answer:

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

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c. $k=-0.00259$

d. $t=153.39838\\$ minutos

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:

$Tm=68$

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

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

c. After 33 minutes of serving the coffee has cooled to 180°:

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

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

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4 years ago

What is the slope of the line that passes through the points (-2, 2), and (-4, -2)​

What is the slope of the line that passes through the points (-2, 2), and (-4, -2)