Pe^{rt} = Compound interest formula
100e^{30r} = 170
e^{30r} = 17/10
30r = ln (17/10)
r = [ln (17/10)]/30
r = .02 = 2 percent
Answer:
Steven Jobs spent his childhood in Silicon Valley. He was the type of child who liked to stick to himself. He only did competitive swimming, and no team sports.
The correct answer is - A large Hindu village on a major river.
The people that practice Hinduism are not having the same way of saying goodbye and expressing respect to the dead as in the other major religions. While most of the religions have it as a rule that the people should be buried in a cemetery, often with the presence and blessing of a priest, the Hindus are not like that. In the Hinduism the people that passed away are cremated. The cremation takes place on the biggest river in the area, with the river having a big religious symbolism. The leftovers from the body form the cremation are dispersed into the river which should take that persons soul into the other world.
Solution. To check whether the vectors are linearly independent, we must answer the following question: if a linear combination of the vectors is the zero vector, is it necessarily true that all the coefficients are zeros?
Suppose that
x 1 ⃗v 1 + x 2 ⃗v 2 + x 3 ( ⃗v 1 + ⃗v 2 + ⃗v 3 ) = ⃗0
(a linear combination of the vectors is the zero vector). Is it necessarily true that x1 =x2 =x3 =0?
We have
x1⃗v1 + x2⃗v2 + x3(⃗v1 + ⃗v2 + ⃗v3) = x1⃗v1 + x2⃗v2 + x3⃗v1 + x3⃗v2 + x3⃗v3
=(x1 + x3)⃗v1 + (x2 + x3)⃗v2 + x3⃗v3 = ⃗0.
Since ⃗v1, ⃗v2, and ⃗v3 are linearly independent, we must have the coeffi-
cients of the linear combination equal to 0, that is, we must have
x1 + x3 = 0 x2 + x3 = 0 ,
x3 = 0
from which it follows that we must have x1 = x2 = x3 = 0. Hence the
vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
Answer. The vectors ⃗v1, ⃗v2, and ⃗v1 + ⃗v2 + ⃗v3 are linearly independent.
