A half-life of 9 minutes corresponds to a decay factor <em>k</em> such that
Then the time it takes for the substance to decay from 610 g to 124 g is time <em>t </em>such that
Solve for <em>t</em> :
so it takes about 20.7 min for the 610 g sample to decay down to 124 g.
Step-by-step explanation: Our first task in this problem is to setup variables representing <em>length</em> and <em>width</em> and we do that by using the second sentence.
<em><u>The length is twice the width</u></em>
So if we call our width <em>x</em>, that means that our length is 2 times <em>x</em> or 2x
Width of the rectangle ⇒ <em>x</em>
Length of the rectangle ⇒ <em>2x</em>
Before moving on, go ahead and draw a picture of your
rectangle so that you can visualize what's going on.
I have done this for you below.
We label our widths <em>x</em> and our lengths <em>2x</em>.
Now we can use the first sentence to setup our equation.
The perimeter of a rectangle is the distance
around the outside of the figure.
So if our perimeter is 60, that means that x + x + 2x + 2x = 60.
Simplifying by combining like terms, we get 6x = 60.
Now dividing both sides by 6, we find that <em>x = 10</em>.
Since <em>x</em> represents width, our width is 10.
Our length therefore with be <em>2(10)</em> or 20.
So our width is 10 and our length is 20.
