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3 years ago

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How many 14-1/4" long pieces can be cut from a 86' long piece of angle iron? Allow 1/8 waste for each cut

1 answer:

kkurt [141]3 years ago

6 0

The number of pieces that we could have in 86' if were going to cut it by 14 1/4 long with 1/8 waste for each cut is 5.98 pieces. This is computed by converting first the fractions into decimal, 14.25 and 0.125, then add it together since there is a waste in every cut, 14.375. Then we will divide 86 inches by 14.375 inches.

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Element X decays radioactively with a half life of 11 minutes. If there are 870 grams of Element X, how long, to the nearest ten

serg [7]

Answer:

It would take 27.5 minutes the element to decay to 154 grams.

Step-by-step explanation:

The decay equation:

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

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

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

Integrating both sides

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

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

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

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

$\Rightarrow c=ln|N_0|$

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

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

$\Rightarrow ln|\frac{N}{N_0}|=-\lambda t$

Decay equation:

$ln|\frac{N}{N_0}|=-\lambda t$

Given that, the half life of of element X is 11 minutes.

For half life, $N=\frac12 N_0$ , t= 11 min.

$ln|\frac{N}{N_0}|=-\lambda t$

$\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11$

$\Rightarrow ln|\frac12}|=-\lambda . 11$

$\Rightarrow -\lambda . 11=ln|\frac12}|$

$\Rightarrow \lambda =\frac{ln|\frac12|}{-11}$

$\Rightarrow \lambda =\frac{ln|2|}{11}$ [ $ln|\frac12|=ln|1|-ln|2|=-ln|2|$ , since ln|1|=0]

N=154 grams, $N_0$ = 870 grams, t=?

$ln|\frac{N}{N_0}|=-\lambda t$

$\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t$

$\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}$

=27.5 minutes

It would take 27.5 minutes the element to decay to 154 grams.

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

If the function f(x) = (2x - 3)2 is transformed to g(x) = (-2x - 3), which type of transformation occurred?

san4es73 [151]

Answer:

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Step-by-step explanation:

Given:

$f(x)=(2x-3)^2$

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Solution:

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<em>Thus, the transformation statement can be given as:</em>

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