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2 years ago

The initial temperature of a cup of tea is 200ºF. The surrounding temperature is 70ºF, and the value of the constant k is 0.6.

1 answer:

6 0

Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.

Therefore when expressed mathematically, this is equivalent to:

dT = - k (T – Ts) dt

dT / (T – Ts) = - k dt

Integrating:

ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)

Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.

R = ˚F + 460

T1 = 200 + 460 = 660 R

Ts = 70 + 460 = 530 R

ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)

T2 = 569.16 R

T2 = 109 ºF

Answer: After 2 hours, it will be 109 ºF

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Gary won $70,000 in the lottery after all tax deductions. He invested part of the money at 11% and deposited the remainder in ta

Paraphin [41]

Let x represent the amount of money he invested at 11% and y money he invested at 12%. Now we write system of equations:

x*1.11 + y*1.12 = 70 000 + 7900
x + y = 70 000

We will multiply second equation with 1.11
x*1.11 + y*1.11 = 77700
and subtract if from first:
0.01*y = 200
y = 20000

x = 70000 - 20000 = 50000

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2 years ago

Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $5

ANTONII [103]

How you would set this up would be as follows:

(50*30)+4,596*.03

The 50*30 is her earning $50 a day for 30 days. Then to find her commission earnings you multiply her sales of 4,596 times the commission rate of 3%(when you move the decimal place you get .03)

Add them together and you get her total amount earned of $1,637.88

Hope this helped!

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2 years ago

Read 2 more answers

Shelley sells 5 bone-shaped treats for $3.50. How much should she charge for a package of 12 treats?

kondaur [170]

She will be charged $42

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2 years ago

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Three pounds of squid can be purchased at the market for $18. Determine the equation and represent the function that defines the

olga_2 [115]

From the information given,

3 pounds = $18

Therefore, 1 pound = 18/3 = $6 (this can be treated as a constant of proportionality) such that,

Cost,C = 6*Weight, W (pounds)

Equation;

C = 6W, where C = Cost in $, and W = Weight in pounds.

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2 years ago

The mapping diagram shows a functional relationship

Gre4nikov [31]

Answer:

$f(4)=\frac{1}{2}$

f(x) = 4 when x is 8

Step-by-step explanation:

Domain is the set of x values that make the function defined. Allowed x values for the function (mapping).

The Range is the set of y values that make the function defined. Allowed y values for the function (mapping).

Whenever we need to find f(a), suppose, then we look for "a" in the domain and see its corresponding value mapping in the range.
Whenever we will be given a value for f(x) = a, suppose, and we have to find "x", we look at the value a in the range and find corresponding x value in the domain.

Firstly, we need f(4), so we look for "4" in domain and see which number it corresponds to in range.

That is $\frac{1}{2}$

Thus,

$f(4)=\frac{1}{2}$

Next,

We want "x" value that gives us a "y" value of 4. We look for "4" in the range and see which value it corresponds to. That is "8". So,

f(8) = 4

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2 years ago