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borishaifa [10]
3 years ago
14

Mrs.Long wants to rent a bounce house for her owens birthday. Inflate a rentals charges a 145 fee plus 35 per hour. If Mrs. Long

paid 355 total, how many hours did she rent the bounce house for
Mathematics
1 answer:
Blizzard [7]3 years ago
5 0

Answer:

The correct answer is 6 hours.

Step-by-step explanation:

Let Mrs. Long rent the bounce house for x hours.

Fixed price to be charged is 145.

Per hour price of the bounce house is 35. Total price of x hours is 35x.

Thus total amount charged by the rentals is 145 + 35x.

Mrs. Long paid 355 in total.

∴ 145 + 35x = 355

⇒ 35x = 210

⇒ x = 6.

Thus Mrs. Long rented the bounce house for 6 hours.

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Step-by-step explanation:

The decay of an isotope is represented by the following differential equation:

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t - Time, measured in days.

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The solution of the differential equation is:

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Where m_{o} is the initial mass of the isotope, measure in kilograms.

Now, the time constant is cleared:

\ln \frac{m(t)}{m_{o}} = -\frac{t}{\tau}

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The half-life of a isotope (t_{1/2}) as a function of time constant is:

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\Delta t_{1/2} = \left| -\left(\frac{t_{A}}{\ln \frac{m_{A}(t)}{m_{o,A}} } \right)\cdot \ln 2+\left(\frac{t_{B}}{\ln \frac{m_{B}(t)}{m_{o,B}} } \right)\cdot \ln 2\right|

If \frac{m_{A}(t)}{m_{o,A}} = \frac{m_{B}(t)}{m_{o,B}} = 0.9, t_{A} = 33\,days and t_{B} = 43\,days, the difference in the half-lives of the isotopes is:

\Delta t_{1/2} = \left|-\left(\frac{33\,days}{\ln 0.90} \right)\cdot \ln 2 + \left(\frac{43\,days}{\ln 0.90} \right)\cdot \ln 2\right|

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The approximate difference in the half-lives of the isotopes is 66 days.

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