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aivan3 [116]
2 years ago
11

Radioactive Decay:

Mathematics
1 answer:
Vadim26 [7]2 years ago
7 0

The question is incomplete, here is the complete question:

The half-life of a certain radioactive substance is 46 days. There are 12.6 g present initially.

When will there be less than 1 g remaining?

<u>Answer:</u> The time required for a radioactive substance to remain less than 1 gram is 168.27 days.

<u>Step-by-step explanation:</u>

All radioactive decay processes follow first order reaction.

To calculate the rate constant by given half life of the reaction, we use the equation:

k=\frac{0.693}{t_{1/2}}

where,

t_{1/2} = half life period of the reaction = 46 days

k = rate constant = ?

Putting values in above equation, we get:

k=\frac{0.693}{46days}\\\\k=0.01506days^{-1}

The formula used to calculate the time period for a first order reaction follows:

t=\frac{2.303}{k}\log \frac{a}{(a-x)}

where,

k = rate constant = 0.01506days^{-1}

t = time period = ? days

a = initial concentration of the reactant = 12.6 g

a - x = concentration of reactant left after time 't' = 1 g

Putting values in above equation, we get:

t=\frac{2.303}{0.01506days^{-1}}\log \frac{12.6g}{1g}\\\\t=168.27days

Hence, the time required for a radioactive substance to remain less than 1 gram is 168.27 days.

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Step-by-step explanation:

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sin ( x + y ) = sin(x)*cos(y) + cos(x)*sin(y)   (1)   and

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cos(2x) cos(x) + sin(2x) sin(x)  (3)

Subtition of sin(2x) and cos(2x)  in eq. 3

[cos²(x)-sin²(x)]*cos(x) + [(2sen(x)cos(x)]*sin(x)

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Tarun has 4 more than the twice the number of tshirts Deepak has.Mahesh has 2 more than thrice the number of T-shirts that Tarun
Dafna11 [192]

Answer:

Deepak: 4 t-shirts,

Tarun: 12 t-shirts,

Mahesh: 14 t-shirts.

Step-by-step explanation:

Let x represent number of t-shirts that Deepak has.

Please consider the complete question.

Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has. Mahesh has 2 more than thrice the number of T-shirts Deepak has. If the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, find out the number of the t-shirt each of them has.​

Since Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has, so the number of t-shirts that Tarun has would be 2x+4.

We are also told that Mahesh has 2 more than thrice the number of T-shirts Deepak has. So the number of t-shirts that Mahesh has would be 3x+2.

Since the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, so we can represent this information in an equation as:

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Cross multiply:

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18x-14x+12-12=14x-14x+28-12

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Therefore, Deepak has 4 t-shirts.

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Therefore, Tarun has 12 t-shirts.

The number of t-shirts that Mahesh has would be 3x+2\Rightarrow 3(4)+2=12+2=14

Therefore, Mahesh has 14 t-shirts.

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