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Kay [80]
3 years ago
11

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

Mathematics
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.

5 0
3 years ago
Al and Ike decide to drive to Sandy Shores Lake. As they leave home in Summerville, they notice that the car odometer reads 12,3
ArbitrLikvidat [17]

Answer: Just add all the numbers up for your answer


Step-by-step explanation:


7 0
3 years ago
What number multiplied by it's self give the product 576​
jarptica [38.1K]

Answer:

24

Step-by-step explanation:

576 root is 24

24^2= 576​

___Hope it helps___

8 0
4 years ago
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Solve the following equation <br><br>​
Alika [10]

Answer:

¶Emma Jess¶

Step-by-step explanation:

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7 0
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:

A. horizontal reflection

Step-by-step explanation:

Given:

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

g(x)=(-2x-3)^2

To identify the type of transformation.

Solution:

On close observation of the functions we find the that sign of x has changed in g(x) with other terms being constant.

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

f(x)\rightarrow f(-x)

As:

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

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

The transformation f(x)\rightarrow f(-x) describes horizontal reflection of function across the y-axis.

Thus, f(x)  is horizontally reflected across y-axis to get g(x).

8 0
4 years ago
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