Jacob is writing a speech that claims that chocolate milk is good for children. In his speech, Jacob wants to rebut the counterc
2 answers:
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Answer:
1) w₁=4 - i w₂= -4 + i
2) w₁= 3 - i w₂= -3 + i
3) w₁= 1 + 2i w₂= - 1 - 2i
4) w₁= 2- 3i w₂= -2 + 3i
5) w₁= 5 - 2i w₂= -5 + 2i
6) w₁= 5 - 3i w₂= -5 + 3i
Step-by-step explanation:
The root of a complex number is given by:
where:
r: is the module of the complex number
θ: is the angle of the complex number to the positive axis x
n: index of the root
1) z = 15 − 8i ⇒ r=17 θ= -0.4899 rad
w₁==4-i
w₂==-1+i
2) z = 8 − 6i ⇒ r=10 θ= -0.6435 rad
w₁== 3 - i
w₂== -3 + i
3) z = −3 + 4i ⇒ r=5 θ= -0.9316 rad
w₁== 1 + 2i
w₂== -1 - 2i
4) z = −5 − 12i ⇒ r=13 θ= 0.4426 rad
w₁== 2- 3i
w₂== -2 + 3i
5) z = 21 − 20i ⇒ r=29 θ= -0.8098 rad
w₁== 5 - 2i
w₂== -5 + 2i
6) z = 16 − 30i ⇒ r=34 θ= -1.0808 rad
w₁== 5 - 3i
w₂== -5 + 3i
Answer:
The quantity of salt at time t is , where t is measured in minutes.
Step-by-step explanation:
The law of mass conservation for control volume indicates that:
Where mass flow is the product of salt concentration and water volume flow.
The model of the tank according to the statement is:
Where:
- The salt concentration in the tank, as well at the exit of the tank, measured in
.
- Concentration rate of change in the tank, measured in
.
- Volume of the tank, measured in gallons.
The following first-order linear non-homogeneous differential equation is found:
This equation is solved as follows:
The initial concentration in the tank is:
Now, the integration constant is:
The solution of the differential equation is:
Now, the quantity of salt at time t is:
Where t is measured in minutes.