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3 years ago

6

Aiden wrote a riddle: Five less than 1/5 times a number is same as the sum of the number and 1/3. Find the number

1 answer:

yanalaym [24]3 years ago

8 0

To solve this riddle, first we have to put it into an algebraic expression, letting the variable n represent the unknown number we are looking for.

1/5n - 5 = n + 1/3

Next, we have to add 5 to both sides, to cancel out the -5 on the left side of the equation.

1/5n = n + 5 1/3

Then, we have to subtract n from both sides of the equation to cancel out the positive n on the right side of the equation.

-4/5n = 5 1/3

Finally, we have to divide both sides by -4/5 in order to get our variable n alone on the left side by canceling out its coefficient.

n = - 6 2/3

Therefore, the number in Aiden's riddle is -6 2/3 or -20/3.

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2 years ago

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3 years ago

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3 years ago

A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling water. How long will it tak

IgorC [24]

Answer

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

C = -90

now,

$12 = -90e^k + 100$

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

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

at time equal to t

T(t) = 70

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

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

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

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

t = 48.88 s

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

b) time taken to reach 98°C

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

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

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

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

t = 390 s

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

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2 years ago