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3 years ago

Divide 180 in a ratio of 4:5:9

2 answers:

azamat3 years ago

8 0

When dividing by a ratio add the ratio together
so
4+5+9=18
then
180/18=10
10*4=40
10*5=50
10*9=90
so your answer is
40:50:90

Ulleksa [173]3 years ago

3 0

If you would like to divide 180 in the ratio of 4 : 5 : 9, you can do this using the following two steps:

First, add the numbers: 4 + 5 + 9 = 18
Second, divide and multiply: 4 / 18 * 180 = 40
5 / 18 * 180 = 50
9 / 18 * 180 = 90

The result you are looking for is 40 : 50 : 90.

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Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 3%. If the rate of deca

Hitman42 [59]

Answer:

The half-life of the radioactive substance is 135.9 hours.

Step-by-step explanation:

The rate of decay is proportional to the amount of the substance present at time t

This means that the amount of the substance can be modeled by the following differential equation:

$\frac{dQ}{dt} = -rt$

Which has the following solution:

$Q(t) = Q(0)e^{-rt}$

In which Q(t) is the amount after t hours, Q(0) is the initial amount and r is the decay rate.

After 6 hours the mass had decreased by 3%.

This means that $Q(6) = (1-0.03)Q(0) = 0.97Q(0)$ . We use this to find r.

$Q(t) = Q(0)e^{-rt}$

$0.97Q(0) = Q(0)e^{-6r}$

$e^{-6r} = 0.97$

$\ln{e^{-6r}} = \ln{0.97}$

$-6r = \ln{0.97}$

$r = -\frac{\ln{0.97}}{6}$

$r = 0.0051$

$Q(t) = Q(0)e^{-0.0051t}$

Determine the half-life of the radioactive substance.

This is t for which Q(t) = 0.5Q(0). So

$Q(t) = Q(0)e^{-0.0051t}$

$0.5Q(0) = Q(0)e^{-0.0051t}$

$e^{-0.0051t} = 0.5$

$\ln{e^{-0.0051t}} = \ln{0.5}$

$-0.0051t = \ln{0.5}$

$t = -\frac{\ln{0.5}}{0.0051}$

$t = 135.9$

The half-life of the radioactive substance is 135.9 hours.

6 0

3 years ago

Eleven subtracted from the quotient of a number and five is -13

madam [21]

X/5 - 11 = -13

x/5 - 11 (+11) = -13 (+11)

x/5 = -2

x/5 (5) = -2(5)

x = -10

-10 is your number

hope this helps

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3 years ago

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Citrus2011 [14]

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vlabodo [156]

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