The half-life of a radioactive element is five years. A scientist has 18 grams of the element. The equation

Mathematics

1 answer:

lianna [129]2 years ago

7 0

Answer:

The equation that describes the amount of mass left after a time t of a radioactive isotope is the following:

where

is the mass of the sample at t = 0

is the half-life of the sample

For the element X in this problem,

We want to find the time t at which

So we need to re-arrange the equation making t the subject:

Step-by-step explanation:

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What is 7/21 in its simplest form

olasank [31]

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5 0

3 years ago

Read 2 more answers

Please help!!

yarga [219]

Because this is a fourth degree that will be tricky to factor as it is, we will do a u substitution. Let $x^2=u$ . We can now rewrite that polynomial in terms of u: $u^2-7u-8=0$ . Filling into the quadratic formula we have $u=\frac{7+/-\sqrt{49-4(1)(-8)}}{2}$ . Simplifying down $u=\frac{7+/-\sqrt{81}}{2}$ and $u=\frac{7+9}{2}$ or $u=\frac{7-9}{2}$ . That means that u = 8 or u = -1. But don't forget that we let $u=x^2$ , so we have to put x-squared back in for u. That gives us $x^2=8$ which simplifies down to $+/-2\sqrt{2}$ . That also gives us $x^2=-1$ . When we take the square root of -1, we have to use the fact that -1 = i^2, so we sub that in to get $x=+/-i$ . All in all, your solutions are as follows: $2\sqrt{2},-2\sqrt{2},i,-i$ which is choice b.