Answer:
x(t) = −39e
−0.03t + 40.
Explanation:
Let V (t) be the volume of solution (water and
nitric acid) measured in liters after t minutes. Let x(t) be the volume of nitric acid
measured in liters after t minutes, and let c(t) be the concentration (by volume) of
nitric acid in solution after t minutes.
The volume of solution V (t) doesn’t change over time since the inflow and outflow
of solution is equal. Thus V = 200 L. The concentration of nitric acid c(t) is
c(t) = x(t)
V (t)
=
x(t)
200
.
We model this problem as
dx
dt = I(t) − O(t),
where I(t) is the input rate of nitric acid and O(t) is the output rate of nitric acid,
both measured in liters of nitric acid per minute. The input rate is
I(t) = 6 Lsol.
1 min
·
20 Lnit.
100 Lsol.
=
120 Lnit.
100 min
= 1.2 Lnit./min.
The output rate is
O(t) = (6 Lsol./min)c(t) = 6 Lsol.
1 min
·
x(t) Lnit.
200 Lsol.
=
3x(t) Lnit.
100 min
= 0.03 x(t) Lnit./min.
The equation is then
dx
dt = 1.2 − 0.03x,
or
dx
dt + 0.03x = 1.2, (1)
which is a linear equation. The initial condition condition is found in the following
way:
c(0) = 0.5% = 5 Lnit.
1000 Lsol.
=
x(0) Lnit.
200 Lsol.
.
Thus x(0) = 1.
In Eq. (1) we let P(t) = 0.03 and Q(t) = 1.2. The integrating factor for Eq. (1) is
µ(t) = exp Z
P(t) dt
= exp
0.03 Z
dt
= e
0.03t
.
The solution is
x(t) = 1
µ(t)
Z
µ(t)Q(t) dt + C
= Ce−0.03t + 1.2e
−0.03t
Z
e
0.03t
dt
= Ce−0.03t +
1.2
0.03
e
−0.03t
e
0.03t
= Ce−0.03t +
1.2
0.03
= Ce−0.03t + 40.
The constant is found using x(t) = 1:
x(0) = Ce−0.03(0) + 40 = C + 40 = 1.
Thus C = −39, and the solution is
x(t) = −39e
−0.03t + 40.
Answer:
C.It remains at rest or moves at constant speed in the same direction.
Explanation:
First, remember the Newton's 1st law of motion which states that the object at rest will remain at rest and that in motion will stay in motion with the same speed and same direction unless acted by unbalance forces.
Balanced forces on an object occur when two forces at act on an object are equal in size and act in opposite direction. In this case, a stationary object will stay at rest while an object moving will continue to move at the same speed and same direction.
An object acted by balanced forces is said to be at equilibrium, thus the state of motion will be maintained.The object will not accelerate. A good example of an object acted by balanced forces is an object at rest or in constant motion such as a car that stopped at red-light signal or a car travelling at a constant speed.
Seven diatomic elements are H₂, Cl₂, N₂, F₂, Br₂, I₂ and O₂.
<h3>Which are diatomic molecules?</h3>
Diatomic molecules are those molecules in which two atoms of same elements are present, and they are combined to attain the stability.
The seven diatomic molecules which are exist in the chemistry are:
- Hydrogen gas (H₂)
- Chlorine gas (Cl₂)
- Nitrogen gas (N₂)
- Fluorine gas (F₂)
- Bromine gas (Br₂)
- Iodine gas (I₂)
- Oxygen gas (O₂)
Hence H₂, Cl₂, N₂, F₂, Br₂, I₂ and O₂ are 7 diatomic molecules.
To know more about diatomic molecules, visit the below link:
brainly.com/question/14466404
#SPJ1
Answer:
If the atom has more electrons than protons, it is a negative ion or ANION. If it has more protons than electrons, it is a positive ion.
Explanation:
Positive ions are typically metals or act like metals. Many common materials contain these ions. Mercury is found in thermometers, for instance, and aluminum is a metal that is found in a surprising amount of things.
Because the ring is hollow
