Given:
The figure of a right angle triangle.
Hypotenuse = 
in.
To find:
The missing lengths of the sides.
Solution:
In the given right angle triangle both legs a and b are equal, and hypotenuse is in.
Using Pythagoras theorem, we get
![[\because a=b]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%3Db%5D)
Divide both sides by 2.
Taking square root on both sides.
Side cannot be negative. So,
Thus, the missing side lengths are a=9 in and b=9 in.
Therefore, the correct option is C.
To check for continuity at the edges of each piece, you need to consider the limit as 
approaches the edges. For example,
has two pieces, 
and 
, both of which are continuous by themselves on the provided intervals. In order for 
to be continuous everywhere, we need to have
By definition of , we have 
, and the limits are
The limits match, so is continuous.
For the others: Each of the individual pieces of 
are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.
The answer is 28 years
At = A0 * e^(-k * t)
At = 12 g
A0 = 15 g
k = 7.9 × 10^-3 = 0.0079
t = ?
12 = 15 * e^(-0.0079 * t)
12/15 = e^(-0.0079 * t)
0.8 = e^(-0.0079 * t)
Logarithm both sides (because ln(e) = 1:
ln(0.8) = ln(e^(-0.0079 * t))
ln(0.8) = (-0.0079 * t) * ln(e)
-0.223 = -0.0079 * t
t = -0.223 / -0.0079
t = 28.23
t ≈ 28 years
