time to fill tank when input, output valves open; 7+9i / 1+i

[Deathscyth3]

Hi any help you can give me would be greatly appreciated.
thanks,
Andria

1. At a dairy plant a milk tank can be filled in 3 hours ( using the in value). Using the out value, the tank can be emptied in 6 hour. If both valves are open and milk is being pumped into the tank how long will it take to fill the tank?

2. 7+9i / 1+i

 

[Loren]

1. At a dairy plant a milk tank can be filled in 3 hours ( using the in value). Using the out value, the tank can be emptied in 6 hour. If both valves are open and milk is being pumped into the tank how long will it take to fill the tank?

2. 7+9i / 1+i

For #1: Let x represent how long it will take to fill the tank. What fraction of the tank is filled in one hour? (Answer: 1/3) What fraction of the tank is emptied in one hour? When these two are combined what fraction of the tank will be filled in one hour? Basis for your equation is "amount of tank filled in one hour minus the amount of tank emptied in one hour equals the amount of tank that remains in one hour.

2: Multiply both numerator and denominator by the conjugate of the denominator and simplify.
P.S. 7+9i / 1+i means \(\displaystyle 7+\frac{9i}{1}+i\). Learn to use parenthesis properly. It will pay you off in the end. I think you meant (7+9i) / (1+i).

 

[Deathscyth3]

Re: Help please!

Thanks for the help but I'm now even more confused. I somehow came to the answer of 4.5 hours is this correct?
as for the second one i am aware that you need to change the denom to the conjugate but i am unsure as of how to multiply the "i"s correctly.

 

[stapel]

Thanks for the help but I'm now even more confused. I somehow came to the answer of 4.5 hours is this correct?

How did you arrive at your answer? Does the answer work in the original exercise?

(And if you're saying that the step-by-step instructions depended too heavily on your being familiar with the topic, and you aren't, then try this lesson for the necessary background knowledge.)

as for the second one i am aware that you need to change the denom to the conjugate but i am unsure as of how to multiply the "i"s correctly.

They were supposed to explain how to multiply binomials and how to work with complex numbers before homework was assigned on this. :shock:

The number "i" is defined as being the square root of minus one, so you multiply two i's together as the square of the square root of minus one, or -1. For instance:

. . . . .\(\displaystyle (3\, +\, i)(4\, -\, 2i)\,=\,(3)(4)\,+\,(i)(4)\, +\, (3)(-2i)\, +\, (i)(-2i)\)

. . . . . . . .\(\displaystyle =\, 12\, +\, 4i\, -\, 6i\, -\, 2i^2\, =\, 12\, -\, 2i\, -\, 2(-1)\)

. . . . . . . .\(\displaystyle =\, 12\, -\, 2i\, +\, 2\, =\, 14\, -\, 2i\)

Follow the same process for your exercise. (And make sure you study the lessons in the links, so you can understand the help you've been given here.)