Determine whether each function is or is not periodic. if it is find the period

Newton’s law of cooling states that for a cooling substance with initial temperature t0, the temperature t(t) after t minutes ca

antoniya [11.8K]

The cooling rate of the substance is approximately 0.0732.

According to the statement, the Newton's law of cooling is defined by the following formula:

$T(t) = T_{s} + (T_{o}-T_{s})\cdot e^{-k\cdot t}$ (1)

Where:

$T_{s}$ - Final temperature, in degrees Celsius.
$T_{o}$ - Initial temperature, in degrees Celsius.
$t$ - Time, in minutes.
$k$ - Cooling rate, in $\frac{1}{min}$ .
$T(t)$ - Current temperature, in degrees Celsius.

Please notice that substance reaches thermal equilibrium when $T(t) = T_{s}$ , that is when temperature of the substance is equal to the temperature of surrounding air.

If we know that $T_{o} = 80\,^{\circ}C$ , $t = 15\,min$ , $T_{s} = 50\,^{\circ}C$ and $T(15) = 60\,^{\circ}C$ , then the cooling rate of the substance is:

$60 = 50 + (80 - 50)\cdot e^{-15\cdot k}$

$\frac{60-50}{80-50}= e^{-15\cdot k}$

$\frac{1}{3} = e^{-15\cdot k}$

$k = -\frac{1}{15}\cdot \ln \frac{1}{3}$

$k \approx 0.0732$

The cooling rate of the substance is approximately 0.0732.

To learn more on Newton's law of cooling, we kindly invite to check this verified question: brainly.com/question/13748261

7 0

2 years ago

Which equation is an example of the commutative property of multiplication? (4 2i) = (2i 4) (4 2i)(3 – 5i) = (3 – 5i)(4 2i) (4 2

kozerog [31]

Option B is correct. (4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i) satisfies the commutative property of multiplication

Given two values A and B, according to the commutative property of multiplication;

AB = BA

This shows that the product of A and B stays the same no matter the arrangement.

From the given option, we can see that (4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i) satisfies the commutative property of multiplication where we can say;

A = 4 + 2i and B = 3 - 5i

Learn more here: brainly.com/question/17955280

4 0

2 years ago

Can someone help me please

zloy xaker [14]

It would make sense to buy it in pounds because there are 454 grams in a pound and if your serving 500 people with a cupcake that holds 20 grams than that would take 10,000 grams so u would need about 23 pounds of sugar to make 500 cupcake <span />

7 0

3 years ago

The manor system provided peasants not only protection from invaders, but also ease and relaxation. schools and leisure activite

Vsevolod [243]

Answer: hii

Explanation:

6 0

2 years ago

Action movies often present what George Gerbner calls "happy violence." Which of the following is a good example of "happy viole

larisa86 [58]

The example of "happy violence" that George Gerbner describes is c. Mean-world syndrome.

<h3>What is the mean-world syndrome?</h3>

The mean-world syndrome is a belief by people that the world is more dangerous than it actually is.

As a result, they enjoy action movies which reinforce this belief and leads to happy violence where people are glad that the danger in the world is being taken care of.

Options for this question include:

A. Entertainomericials

B. Cultivation Theory

C, Mean-world syndrome

Find out more on George Gerbner at brainly.com/question/14100989.

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6 0

1 year ago