Answer:
Yes
Step-by-step explanation:
Let's take any random multiple of 4 as an example:
8 = 2 • 4
64 = 2 • 32
20 = 2 • 10
Try any multiple of 4—this pattern continues.
Answer:
See below.
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336).. (Answer).
If
is the amount of salt in the tank at time
, then the rate at which this amount changes over time is given by the ODE
We're told that the tank initially starts with no salt in the water, so
.
Multiply both sides by an integrating factor,
:
Since
, we have
so that the amount of salt in the tank over time is given by
After 10 minutes, the amount of salt in the tank is