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3 years ago

9

The money you earn varies directly with the number of lawns you mow. You earn $36 for mowing three lawns. a. Write an equation f

or the relationship between money earned and lawns mowed. b. How much money will you earn for mowing seven lawns?

1 answer:

nika2105 [10]3 years ago

5 0

Answer:

a. y = 36x, b. $252

Step-by-step explanation:

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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

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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)

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

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

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

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

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

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.

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4 years ago

The directions on a sewing pattern say to buy an extra 12.5% of fabric to account for error. Sam needs 2.75 yards of fabric to m

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Answer:

Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

Step-by-step explanation:

Total fabric needed by Sam = 2.75

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So, extra fabric would be: 12.5% of 2.75

Solving

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Now adding 0.343 into 2.75 to get extra fabric quantity:

2.75+0.343

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Therefore Sam should have bought 3.09 yards of fabric instead of 2.4 yards

So, Option D is correct.

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