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3 years ago

A mass of 100 grams of a particular radioactive substance decays according to the function m(t)=100e−t850

Physics

1 answer:

AleksandrR [38]3 years ago

8 0

Answer:

After 1023.4 years the mass of the substance will be 30 g.

Explanation:

Hi there!

Let´s write the function (according to what I found on the web):

$m(t) = 100e^{-t/850}$

We have to find the time "t1" at which the mass of the substance is 30 g. Mathematically:

m(t1) = 30

Then:

$30 = 100e^{-t1/850}$

Let´s solve the equation for t1. First, divide by 100 both sides of the equation:

$0.3 = e^{-t1/850}$ [/tex]

Apply ln to both sides of the equation:

$ln(0.3) = ln(e^{-t/850})$

Use the logarithm property: ln (aᵇ) = b ln(a)

ln(0.3) = -t/850 · ln (e) (ln (e) = 1)

ln(0.3) = -t/850

850 ln(0.3) = -t

t = -850 ln(0.3)

t = 1023.4

After 1023.4 years the mass of the substance will be 30 g.

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The force exerted by the wind on the sails of a sailboat is Fsail = 330 N north. The water exerts a force of Fkeel = 210 N east.

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Answer:

The magnitude of the acceleration is $a_r = 1.50 \ m/s^2$

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Explanation:

From the question we are told that

The force exerted by the wind is $F_{sail} = (330 ) \ N \ north$

The force exerted by water is $F_{keel} = (210 ) \ N \ east$

The mass of the boat(+ crew) is $m_b = 260 \ kg$

Now Force is mathematically represented as

$F = ma$

Now the acceleration towards the north is mathematically represented as

$a_n = \frac{F_{sail}}{m_b}$

substituting values

$a_n = \frac{330 }{260}$

$a_n = 1.269 \ m/s^2$

Now the acceleration towards the east is mathematically represented as

$a_e = \frac{F_{keel}}{m_b }$

substituting values

$a_e = \frac{210}{260}$

$a_e =0.808 \ m/s^2$

The resultant acceleration is

$a_r = \sqrt{a_e^2 + a_n^2}$

substituting values

$a_r = \sqrt{(0.808)^2 + (1.269)^2}$

$a_r = 1.50 \ m/s^2$

The direction with reference from the north is evaluated as

Apply SOHCAHTOA

$tan \theta = \frac{a_e}{a_n}$

$\theta = tan ^{-1} [\frac{a_e}{a_n } ]$

substituting values

$\theta = tan ^{-1} [\frac{0.808}{1.269 } ]$

$\theta = tan ^{-1} [0.636 ]$

$\theta = 32.5 6^o$

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Answer:

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