Answer:
Population of dice mice after one year = 2000
Population of wood rats after one year = 1000
The population of deer mice is growing faster than the popular of wood rats
Step-by-step explanation:
The expression for population = dN/dt = rN
Upon integration N = rN²/2
Therefore for population N = 200 and r= 0.1
N after one year = (0.1 x 200²)/ 2 = 2000
Therefore for population N = 100 and r= 0.2
N after one year = (0.2 x 100²)/ 2 = 1000
Hence the population of deer mice is growing faster than the popular of wood rats
Answer:
At 0.77 mi/min, Matt travels faster than Jennifer, who averages
only 0.67 mi/min.
Step-by-step explanation:
Average speed = distance/time
<em>For Samantha,
</em>
Average speed = 10/15
Average speed = 0.67 mi/min
<em>For Matt,
</em>
Average speed = 23/30
Average speed = 0.77 mi/min
Answer:
x and y
Step-by-step explanation:
Answer:
x = - 8, y = 2
Step-by-step explanation:
![x = - 4y......(1) \\ x + 5y = 2....(2) \\ plug \: x = - 4y \: in \: equation \: (2) \\ - 4y + 5y = 2 \\ y = 2 \\ plug \: y = 2 \: in \: equation \: (1) \\ x = - 4(2) \\ x = - 8\\](https://tex.z-dn.net/?f=x%20%3D%20%20-%204y......%281%29%20%5C%5C%20x%20%2B%205y%20%3D%202....%282%29%20%5C%5C%20plug%20%5C%3A%20x%20%3D%20%20-%204y%20%5C%3A%20in%20%5C%3A%20equation%20%5C%3A%20%282%29%20%5C%5C%20%20-%204y%20%2B%205y%20%3D%202%20%5C%5C%20y%20%3D%202%20%5C%5C%20plug%20%5C%3A%20y%20%3D%202%20%5C%3A%20in%20%5C%3A%20equation%20%5C%3A%20%281%29%20%5C%5C%20x%20%3D%20%20-%204%282%29%20%5C%5C%20x%20%3D%20%20-%208%5C%5C)
Answer:
1130.97336 units^3
Step-by-step explanation:
The volume of a cylinder can be found using:
![v=\pi r^2h](https://tex.z-dn.net/?f=v%3D%5Cpi%20r%5E2h)
We have the area of the base, but not the radius
![a=\pi r^2](https://tex.z-dn.net/?f=a%3D%5Cpi%20r%5E2)
We know the area is
, so we can substitute that in for a
![36\pi =\pi r^2](https://tex.z-dn.net/?f=36%5Cpi%20%3D%5Cpi%20r%5E2)
We want to find r, so we need to isolate it
Divide both sides by pi
36=r^2
Take the square root of both sides
6=r
Now we know the radius, and can substitute it into the volume formula, and we can substitute the height (10) in
![v=\pi r^2h](https://tex.z-dn.net/?f=v%3D%5Cpi%20r%5E2h)
![v=\pi 6^210](https://tex.z-dn.net/?f=v%3D%5Cpi%206%5E210)
Solve the exponent
![v=\pi 36(10)](https://tex.z-dn.net/?f=v%3D%5Cpi%2036%2810%29)
![v=\pi 360](https://tex.z-dn.net/?f=v%3D%5Cpi%20360)
v=1130.97336
The volume is 1130.97336 units^3