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2 years ago

13

Ari is recording the number of laps he walks around the track each day, On Day 1, he walks 8 laps. On Day 2, his number of laps

2 answers:

poizon [28]2 years ago

7 0

Answer:

10 percent decrease

Step-by-step explanation:

Kobotan [32]2 years ago

6 0

$mdqwbf$ Answer: 10

Step-by-step explanation:

10 because trusting other people is just the right way to go right just trust me

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The half-life of a radioactive element is 130 days, but your sample will not be useful to you after 80% of the radioactive nu

gtnhenbr [62]

Answer:

We can use the sample about 42 days.

Step-by-step explanation:

Decay Equation:

$\frac{dN}{dt}\propto -N$

$\Rightarrow \frac{dN}{dt} =-\lambda N$

$\Rightarrow \frac{dN}{N} =-\lambda dt$

Integrating both sides

$\int \frac{dN}{N} =\int\lambda dt$

$\Rightarrow ln|N|=-\lambda t+c$

When t=0, N= $N_0$ = initial amount

$\Rightarrow ln|N_0|=-\lambda .0+c$

$\Rightarrow c= ln|N_0|$

$\therefore ln|N|=-\lambda t+ln|N_0|$

$\Rightarrow ln|N|-ln|N_0|=-\lambda t$

$\Rightarrow ln|\frac{N}{N_0}|=-\lambda t$ .......(1)

$\frac{N}{N_0}=e^{-\lambda t}$ .........(2)

Logarithm:

$ln|\frac mn|= ln|m|-ln|n|$
$ln|ab|=ln|a|+ln|b|$

$ln|e^a|=a$

$ln|a|=b \Rightarrow a=e^b$
$ln|1|=0$

130 days is the half-life of the given radioactive element.

For half life,

$N=\frac12 N_0$ , $t=t_\frac12=130$ days.

we plug all values in equation (1)

$ln|\frac{\frac12N_0}{N_0}|=-\lambda \times 130$

$\rightarrow ln|\frac{\frac12}{1}|=-\lambda \times 130$

$\rightarrow ln|1|-ln|2|-ln|1|=-\lambda \times 130$

$\rightarrow -ln|2|=-\lambda \times 130$

$\rightarrow \lambda= \frac{-ln|2|}{-130}$

$\rightarrow \lambda= \frac{ln|2|}{130}$

We need to find the time when the sample remains 80% of its original.

$N=\frac{80}{100}N_0$

$\therefore ln|{\frac{\frac {80}{100}N_0}{N_0}|=-\frac{ln2}{130}t$

$\Rightarrow ln|{{\frac {80}{100}|=-\frac{ln2}{130}t$

$\Rightarrow ln|{{ {80}|-ln|{100}|=-\frac{ln2}{130}t$

$\Rightarrow t=\frac{ln|80|-ln|100|}{-\frac{ln|2|}{130}}$

$\Rightarrow t=\frac{(ln|80|-ln|100|)\times 130}{-{ln|2|}}$

$\Rightarrow t\approx 42$

We can use the sample about 42 days.

7 0

3 years ago

Simplify this expression<br> 10a + 6x-2a-3x

kondor19780726 [428]

Answer:

$3x+8a$

Step-by-step explanation:

Given the following question:

$10a+6x-2a-3x$

In order to find the answer, we combine like terms and then simplify.

$10a+6x-2a-3x$
$=6x-3x+10a-2a$
$6x-3x=3x$
$10a-2a=8a$
$=3x+8a$
$3x+8a$

Hope this helps.

4 0

2 years ago

What is the answer to -3 to the second power + 4.6 times -0.1

vagabundo [1.1K]

The answer is -9.46 yeah i think thats correct

8 0

3 years ago

Read 2 more answers

3. If you took out a car loan for $22,000, with a rate of 2% compounded semi-annually over

charle [14.2K]

Answer:

c.

Step-by-step explanation:

it's been a while since I've done this but I'm about 90% sure

7 0

2 years ago

Read 2 more answers

PLS HELP ASAP I GVE BRINALIEST AND EPOINTS AND STUFF ONIFENVSDFLKFVIDLFJVFDLFVSNJDFUIVL. If a train was moving south east with a

Romashka-Z-Leto [24]

Answer:

about 6-8 ounces on earth

If in space then it weights 0.00000000000001 ounces

Step-by-step explanation:

8 0

2 years ago