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3 years ago

14

Look at points C and D on the graph: point C (-2,0), point D (2,4)

1 answer:

Svetach [21]3 years ago

6 0

The answer to the question you are looking for is right in front of u

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The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

6 0

2 years ago

Read 2 more answers

Given the functions, f(x) = x2 + 2 and g(x) = 4x - 1, perform the indicated operation. When applicable, state the domain restric

Naya [18.7K]

Answer:

3rd option

Step-by-step explanation:

substitute x = f(x) into g(x)

g(f(x))

= g(x² + 2)

= 4(x² + 2) - 1

= 4x² + 8 - 1

= 4x² + 7

5 0

2 years ago

If the sphere shown above has a radius of 16 units, then what is the approximate volume of the sphere?

Nastasia [14]

V≈17157.28 and the radius is 16

4 0

3 years ago

Please help! Please explain how to do this, I am so lost.

alexdok [17]

Ok, so we know that RST is equal to 6x+12
And RST is also equal to 78 + 3x-12
so we set them equal to each other

6x + 12 = 3x - 12 + 78
And simplify
3x = 54
x = 18

Finally, we solve for the angle with 18 for x

6(18) + 12
108 + 12
120

Hope this helps

8 0

2 years ago

PLZ HELP ME !!!!!!!!!!! what is -3+5=11.6

Vinvika [58]

Answer:

The answer is 2 not 11.6

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers