a) $\frac{dm}{dt} = -k\cdot m$ , b) $m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$ , c) $m(t) = 10\cdot e^{-\frac{t}{2438.155} }$ , d) $m(300) \approx 8.842\,g$

Step-by-step explanation:

a) Let assume an initial mass m decaying at a constant rate k throughout time, the differential equation is:

$\frac{dm}{dt} = -k\cdot m$

b) The general solution is found after separating variables and integrating each sides:

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

Where $\tau$ is the time constant and $k = \frac{1}{\tau}$

c) The time constant is:

$\tau = \frac{1690\,yr}{\ln 2}$

$\tau = 2438.155\,yr$

The particular solution of the differential equation is:

$m(t) = 10\cdot e^{-\frac{t}{2438.155} }$

d) The amount of radium after 300 years is:

$m(300) \approx 8.842\,g$

4 0

3 years ago

Read 2 more answers

Yolanda is making a banner for a school pep rally. She cuts fabric in the shape of a parallelogram. The angle at the bottom-left

den301095 [7]

Answer:

x=100

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Nina can ride her bike 63,360 feet in 3,400 seconds, and Sophia can ride her bike 10 miles in 1 hour. What is Nina's rate in mil

BabaBlast [244]

We know that
3600 seconds = 1 hour
Then
3400 seconds = 3400/3600
= 17/18 hours
5280 feet = 1 mile
Then
63360 feet = 63360/5280 mile
= 12 mile
So
Distance covered by Nina in 17/18 hours = 12 mile
Then
Distance covered by Nina in 1 hour = 12/(17/18) miles
= 12.71 miles.
From the above deduction, we can conclude that the speed of Nina is 12.71 miles per hour.
Speed of Sophia is 10 miles per hour. So Nina is the girl that rides at a faster speed.

4 0

3 years ago

Read 2 more answers

Based on the table of values below find the slope between points where x=2 and where x=6

kobusy [5.1K]

Slope=(12-4)/(2-6)=-2

7 0

4 years ago