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3 years ago

Reduce 105 in the ratio 3:5

Mathematics

1 answer:

Komok [63]3 years ago

3 0

9514 1404 393

Answer:

39.375 : 65.625

Step-by-step explanation:

The meaning of "reduce" in this context is unclear. We assume you want to divide the quantity 105 into parts that have a ratio of 3 : 5. Then the smaller part will be 3/(3+5) = 3/8 of the total; the larger part will be 5/8 of the total.

3/8 × 105 = 39 3/8

5/8 × 105 = 65 5/8

The divided quantities are ...

39.375 : 65.625

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Answer:

$A=0.0122\ gr$

Step-by-step explanation:

The exponential decrease formula that we must use is:

$A=A_0e^ {-kt}$

Where A is the amount of thorium as a function of time

$A_0$ is the initial amount and k is the decrease rate

We know that initially there are 50 gr and that you decay 50% every 1.9 years.

$A=A_0*0.5=50*0.5 = 25\\\\t=1.9$

$25=50e^ {-k(1.9)}$

We solve the equation for k

$0.5=e^ {-k(1.9)}$

$ln(0.5)=ln(e^ {-k(1.9)})$

$ln(0.5)=-k(1.9)$

$-1.9k=ln(0.5)$

$k=-\frac{ln(0.5)}{1.9}\\\\k=0.3648$

After 22.8 years the amount of thorium that exists is:

$A=50e^ {-0.3648(22.8)}$

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