2 years ago

Simplify the expression by combining like terms.

Mathematics

1 answer:

podryga [215]2 years ago

3 0

Answer:

The answer: is 118

I hope this help you enjoy :D

Step-by-step explanation:

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According to newton law of cooling

$\dfrac{d T}{dt} = k (T - T_a)$

and

$T = Ce^{kt} + T_a$

now At Ta = 100

T₀ = 10 °C

T₁ = 12° C

$T(0) = Ce^{0} + T_a$

10 = C + 100

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now,

$12 = -90e^k + 100$

$e^k = \dfrac{88}{90}$

$k = ln{\dfrac{88}{90}}$

at time equal to t

T(t) = 70

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$70 = -90(\dfrac{88}{90})^t + 100$

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$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{3})$

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hence, after 48.88 s the temperature of the body will be 70°C

b) time taken to reach 98°C

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$98 = -90(\dfrac{88}{90})^t + 100$

$(\dfrac{88}{90})^t = \dfrac{1}{45}$

$t\times ln(\dfrac{88}{90}) = ln(\dfrac{1}{45})$

t = 390 s

hence, after 390 s the temperature of the body will be 98°C

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2 years ago