The half life of a decaying substance is defined as the time at which the substance decreases to one-half of its original value. In this case, given hlf-life of 10 years and an original mass of 50 grams, after 10 years, the isotope mass becomes 50*0.5 or 25 grams. Answer is B.
Solution:
1) Add 80 to both sides
-np<60+80
2) Simplify 60+80 to 140
-np<140
3) Divide both sides by p
-n<\frac{140}{p}
4) Multiply both sides by -1
n>-\frac{140}{p}
Done!
The bottom answer is correct. I had some trouble with this so I had to find x and y in separate parts.
TO FIND X
notice that the top triangle and bottom triangles are similar, meaning if you multiple all three sides of one by a specific number, it becomes the same size as the bottom triangle.
17 x n = 8, therefore n=8/17
8 x n = X, therefore X=64/17
For some reason, this does not give a correct value for Y, so I had to use trig
TO FIND Y
Notice that the angle DAB is the same as DBC (lets call this angle Ø)
Using trig rule, we know that the cos of an angle is equal to the adjacent side divided by the hypotenuses.
We can now form some equations:
cosØ = 15/17 (from the top triangle)
cosØ = 8/Y (from bottom triangle)
Now we know that Y=(8x17)/15 = 136/15
X=64/15 Y=136/15
4 1/5 should be your answer
