MATHEMATICS COLLEGE

The rate of change of the temperature T(t) of a body is still governed bydT
/dt
= âk(T â A), T(0) = T0,

when the ambient temperature A(t) varies with time. Suppose the body is known to have

k = 0.2

and initially is at 32°C; suppose also that

A(t) = 20eât.

Find the temperature T(t).

Answers

Answer 1
Answer:

Answer:

T(t)=5e^(-t)+27e^(-0.2t)

Step-by-step explanation:

QUESTION

The rate of change of the temperature T(t) of a body is still governed by

(dT)/(dt)=-k(T-A), T(0)=T_0  when the ambient temperature A(t) varies with time. Suppose the body is known to have  k = 0.2  and initially is at 32°C; suppose also that  A(t) = 20e^(-t). Find the temperature T(t).

SOLUTION

(dT)/(dt)=-k(T-A), T(0)=T_0, A(t) = 20e^(-t), k=0.2

(dT)/(dt)=-0.2T+20(0.2)e^(-t)\n(dT)/(dt)+0.2T=4e^(-t)\n\text{Integrating factor}=e^(0.2t)\n(dTe^(0.2t))/(dt)=4e^(-t)e^(0.2t)\ndTe^(0.2t)=4e^(-t)e^(0.2t)dt\n\int d[Te^(0.2t)]=4\int e^(-t(1-0.2))dt\nTe^(0.2t)=4\int e^(-0.8t)dt\nTe^(0.2t)=(4)/(-0.8) e^(-0.8t)+C, \text{C a constant of integration}\nTe^(0.2t)=-5 e^(-0.8t)+C\nT(t)=5 e^(-0.8t)e^(-0.2t)+Ce^(-0.2t)\nT(t)=5e^(-t)+Ce^(-0.2t)\nWhen t=0, T_0=32\n32=5+C\nC=27

Therefore:

T(t)=5e^(-t)+27e^(-0.2t)

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IQ scores are normally distributed with a mean of 105 and a standard deviation of 17. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

Answers

Answer:

Mean 105

Standard deviation 1.89

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = (\sigma)/(√(n))

In this problem, we have that:

\mu = 105, \sigma = 17

If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

By the Central limit theorem

mean 105

Standard deviation

s = (17)/(√(81)) = 1.89

Find the measure of angle 'y'. 49° A. 60 degrees B. 70 degrees C. 80 degrees D. 110 degrees​

Answers

Answer:

70°

Step-by-step explanation:

61° + 49° + y = 180° (sum of angles of a triangle is always 180°)

so,

y= 180° - 61° - 49° = 70°

The volume V of an ideal gas varies directly with the temperature T and inversely with thepressure P. A cylinder contains oxygen at a temperature of 320 degrees Kelvin and a pressure of


25 atmospheres in a volume of 120 liters. Find the pressure if the volume is decreased to 110


liters and the temperature is increased to 335 degrees Kelvin.


Hint: Look at the equation V = k* Then use the initial values to solve for k. Then plug in the


values you know for the second set of values and solve for your unknown.

Answers

Answer:

Pressure=22.55 atmospheres

Step-by-step explanation:

Let

V=volume of the ideal gas

P=pressure

T=temperature

Volume varies directly with temperature and inversely with pressure

V=kT/P

t=320°K

P=25 atmospheres

V=120 liters

V=kT/P

120=k*320/25

120=320k/25

120×25=320k

3000=320k

k=300/320

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k=9.375

V=110 liters

p=?

t=335°K

V=kT/P

110=9.375*335/p

110=3,140.625/p

110p=3,140.625

P=3,140.625/110

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P=22.55 atmospheres

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Answers

Answer:

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What is the image of 2,-1 after a reflection over the y axis

Answers

The image of the point after a reflection over the y-axis is (-2, -1)

Calculating the image of the point after a reflection over the y-axis?

From the question, we have the following parameters that can be used in our computation:

Point = (2, -1)

Transformation rule

A reflection over the y-axis

The rule of a reflection over the y-axis is

(x, y) = (-x, y)

Using the above as a guide, we have the following:

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Hence the image of the point after a reflection over the y-axis is (-2, -1)

Read more about transformation at

brainly.com/question/27224272

#SPJ3

There are no images included, but it would be -2,-1.

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Answers

Answer:

21

Step-by-step explanation:

Let the smallest of the numbers be N

The other two numbers (consecutive) would be written as (n + 2), (n + 4)

Expressing these as an equation gives : (n) + (n+2) + (n+4) = 69

opening the bracket and collecting like terms, we have:

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3n = 69 - 6

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Note, the other numbers are: 21, 23, and 25

They are all odd numbers

Their sum equals to 69
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