Let's call the length of the rectangular fence 
and the width of the rectangular fence 
.
Based on the information in the problem, we can make two equations, based on the formulas for perimeter and area:
Now, let's substitute in the values we are given in the problem:
Now, let's solve the system using substitution.
- Solve for from the first equation
- Substitute this value into the second equation
- Multiply both sides of the equation by
- Subtract
from both sides of the equation
and 
- Use the Zero Product Property and solve both factors
We are given two possible lengths. However, the funny thing is that both produce the same dimensions: 24 ft by 10 ft:
Thus, our answer is Choice C, or 10 feet by 24 feet.
Answer: 18pi^2
Step-by-step explanation:
Volume of cone formula = 1/3 x base area x height
so 1/3 x 9pi^2 x 6
= 18pi^2
Answer:
A 1.9
Step-by-step explanation:
Nt = No e^(-kt)
Where Nt is the ending amount
No is the starting amount
k is the decay constant
and t is the time
We need to determine the half life
Nt/No = e ^ -kt
1/2 of the original amount is left for 1/2 life. The time is 40 years. We will calculate k
1/2 = e ^ -k * 40
Take the natural log of each side
ln(1/2) = ln (e ^ -k * 40)
ln (1/2) = -40k
-ln(2) = -40k
ln 2 = 40k
1/40 ln (2) = k
Now we can calculate now much is left after 160 years of a 30 g sample
Nt = 30 e^(- 1/40 ln(2) * 160)
= 30 e^(-4ln(2))
= 15/8
=1.875
When you multiplied both sides by a NEGATIVE number, what WAS negative became positive, and what WAS positive became negative! Everything that was larger became small, and what was smaller became large. Everything REVERSED
