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3 years ago

14

Amanda wants to move to a nelghborhood in Florida that has a dog restriction. Each home owner is allowed one dog with a welght l

imit of 30 pounds. Amanda just went to the vet and he told her that her dog welghed 12 kilograms. Does Amanda's dog meet the weight requirement so that they can move to Florida? In complete sentences explain how to convert kilograms Into pounds, and decide whether or not Amanda can move to this nelghborhood with her dog.

1 answer:

suter [353]3 years ago

3 0

Yes it can as 30 pounds is 13.6078 kg

1 pound is 0.453592 so u just have to multiple it with 30

0.453592 x 30= 13.6078

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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,

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

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

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

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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

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

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Then,

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

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Now, take the natural log of both sides

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

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This is the value of the constant $k$

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From

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

Then

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

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

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

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

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