Find how many half lives have passed
seems we are measuring in days
half life formula is as follows
![A=P(\frac{1}{2})^\frac{t}{h}](https://tex.z-dn.net/?f=A%3DP%28%5Cfrac%7B1%7D%7B2%7D%29%5E%5Cfrac%7Bt%7D%7Bh%7D)
A=final amount
P=initial amount
t=time in a certain units (this time, it's days)
h=time of half life
so
we are given that P=1, A=0.6, t=3
find h
subsitute
![0.6=1(\frac{1}{2})^\frac{3}{h}](https://tex.z-dn.net/?f=0.6%3D1%28%5Cfrac%7B1%7D%7B2%7D%29%5E%5Cfrac%7B3%7D%7Bh%7D)
![0.6=(\frac{1}{2})^\frac{3}{h}](https://tex.z-dn.net/?f=0.6%3D%28%5Cfrac%7B1%7D%7B2%7D%29%5E%5Cfrac%7B3%7D%7Bh%7D)
take ln of both sides
![ln(0.6)=ln((\frac{1}{2})^\frac{3}{h})](https://tex.z-dn.net/?f=ln%280.6%29%3Dln%28%28%5Cfrac%7B1%7D%7B2%7D%29%5E%5Cfrac%7B3%7D%7Bh%7D%29)
![ln(0.6)=(\frac{3}{h})ln(\frac{1}{2})](https://tex.z-dn.net/?f=ln%280.6%29%3D%28%5Cfrac%7B3%7D%7Bh%7D%29ln%28%5Cfrac%7B1%7D%7B2%7D%29)
multiply both sides by h
![(h)ln(0.6)=3ln(\frac{1}{2})](https://tex.z-dn.net/?f=%28h%29ln%280.6%29%3D3ln%28%5Cfrac%7B1%7D%7B2%7D%29)
divide both sides by ln(0.6)
![h=\frac{3ln(\frac{1}{2})}{ln(0.6)}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B3ln%28%5Cfrac%7B1%7D%7B2%7D%29%7D%7Bln%280.6%29%7D)
use your calculator
h≈4.07075
so about 4 days is the half life
Answer: Function
Step-by-step explanation: A function is a special type of relation and for a relation to be a function, each x-term must correspond with exactly 1 y-term.
The easiest way to determine whether a relation is a function is to look at the x-coordinate of each ordered pair. If any of our ordered pairs have the same x-coordinate with a different y-coordinate, then our relation is no a function.
Since none of our x-terms repeat with different y-terms, this is a function.
Given
Alchemist wishes to mix a solution that is 10% acid.
She has on hand 6 liter of a 8% acid solution and wishes to add some 16% acid solution to obtain the desired 10% acid solution. H
To find: ow much 146 acid solution should she add?
Explanation:
It is given that,
Alchemist wishes to mix a solution that is 10% acid.
Let x be the amount o acid mixed to obtain the desired 10% solution.
Since she has on hand 6 liters of a 8% acid solution and wishes to add some 16% acid solution to obtain the desired 10% acid solution.
Then,
![\begin{gathered} 6l\text{ }of\text{ }8\%+16\%\text{ }of\text{ }x=10\%\text{ }of\text{ }(6+x) \\ 6\times\frac{8}{100}+\frac{16}{100}\times x=\frac{10}{100}\times(6+x) \\ \frac{48}{100}+\frac{16x}{100}=\frac{10}{100}(6+x) \\ 48+16x=10(6+x) \\ 48+16x=60+10x \\ 16x-10x=60-48 \\ 6x=12 \\ x=\frac{12}{6} \\ x=2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%206l%5Ctext%7B%20%7Dof%5Ctext%7B%20%7D8%5C%25%2B16%5C%25%5Ctext%7B%20%7Dof%5Ctext%7B%20%7Dx%3D10%5C%25%5Ctext%7B%20%7Dof%5Ctext%7B%20%7D%286%2Bx%29%20%5C%5C%206%5Ctimes%5Cfrac%7B8%7D%7B100%7D%2B%5Cfrac%7B16%7D%7B100%7D%5Ctimes%20x%3D%5Cfrac%7B10%7D%7B100%7D%5Ctimes%286%2Bx%29%20%5C%5C%20%5Cfrac%7B48%7D%7B100%7D%2B%5Cfrac%7B16x%7D%7B100%7D%3D%5Cfrac%7B10%7D%7B100%7D%286%2Bx%29%20%5C%5C%2048%2B16x%3D10%286%2Bx%29%20%5C%5C%2048%2B16x%3D60%2B10x%20%5C%5C%2016x-10x%3D60-48%20%5C%5C%206x%3D12%20%5C%5C%20x%3D%5Cfrac%7B12%7D%7B6%7D%20%5C%5C%20x%3D2%20%5Cend%7Bgathered%7D)
Hence, she should add 2 liters of acid solution.
Counterclockwise - add 360° per rotation
Clockwise - subtract 360° per rotation
Answer:
4.5 in, 6 in, 7.5 in
Step-by-step explanation:
The sum of the ratio units is 3+4+5 = 12. These correspond to 18 inches, so each ratio units stands for (18 in)/12 = 1.5 in.
The side lengths are ...
3×1.5 in = 4.5 in
4×1.5 in = 6.0 in
5×1.5 in = 7.5 in