The answer is 4.5 l
To calculate this, we will use the Boyle's law using constant k, pressure P, and volume V:
PV = k
We can forget temperature since it is constant.
We have:
P1V1 = k
P2V2 = k
So, P1V1 = P2V2
P1 = 3 atm
V1 = 1.5 l
P2 = 1 atm
V2 = ?
_____
P1V1 = P2V2
3 atm * 1.5 l = 1 atm * V2
4.5 atm/l = 1 atm * V2
V2 = 4.5 atm l / 1 atm
V2 = 4.5 l
Answer:
16
Step-by-step explanation:
Answer:

Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if
. Recall that given two vectors a,b a⊥ b if and only if
where
is the dot product defined in
. Suposse that
. We want to find γ such that
. Given that the dot product can be distributed and that it is linear, the following equation is obtained

Recall that
are both real numbers, so by solving the value of γ, we get that

By construction, this γ is unique if
, since if there was a
such that
, then
