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

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If the original lengths are multiplied by 2, what are the new coordinates?

Bad White [126]

Answer:

Find an answer to your question If the original lengths are multiplied by 2, what is the new coordinate of point A? Assume that the point at (0,0) ...

Step-by-step explanation:

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3 years ago

Helppppp meeeeee!!!!. The first ten multiples of 7 and the first four multiples of 9 are listed in the table below. Fill in the

vova2212 [387]

Answer:

Step-by-step explanation:

7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

9, 18, 27, 36, 45, 54, 63, 72, 81, 90.

A:63

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2 years ago

What is the volume of the cone shown below?

STatiana [176]

The formula to calculate the volume of a cone is:

$V= \frac{1}{3} \pi (radius)^2h$

So, replace radius = 3in and h = 8 in.

The result is: [1/3] π (3in)^2 (8in) = [1/3]π(9)(8) in^3 = 24 π in^3

Answer: option b. 24 π in^3

3 0

3 years ago