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3 years ago

The function P(d) = 1 + + gives the pressure, in atmospheres (atm), at a depth d feet in

Mathematics

1 answer:

mylen [45]3 years ago

7 0

Answer:

c) 39; At a depth of 59 feet, the pressure is atm.

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Mrs. Clearwater paid $38.64 to fill up 12 gallons of gasoline in her car. What is the price for 1 gallon of gasoline?

vfiekz [6]

Answer: $3.22

Step-by-step explanation:

We will start by doing 38.64 divided by 12

Then we will get the answer 3.22.

$3.22 is the answer.

6 0

2 years ago

Read 2 more answers

(3x+2) and (5x-6) solve for x

HACTEHA [7]

Answer:

x=3X 2 + 5x -6

Step-by-step explanation:

3X2 + 5X-6= 3X2 + 5X 6

X=3X2 +5X -6

6 0

3 years ago

Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isot

Andrews [41]

Answer:

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

Step-by-step explanation:

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

$\frac{dm}{dt} = -\frac{t}{\tau}$

Where:

$m$ - Current mass of the isotope, measured in kilograms.

$t$ - Time, measured in days.

$\tau$ - Time constant, measured in days.

The solution of the differential equation is:

$m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$

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

Now, the time constant is cleared:

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

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

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

$t_{1/2} = \tau \cdot \ln2$

$t_{1/2} = -\left(\frac{t}{\ln\frac{m(t)}{m_{o}} }\right) \cdot \ln 2$

The half-life difference between isotope B and isotope A is:

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

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: