सदस्य: Melody

guest:
Dear All,

Please help to check my answer below :

Question :

MC = Q/(6Q²-7)⁵

Determine the Total Cost if the Fixed Cost is $40

Answer :

TC = ∫ MC dQ YES
= ∫ Q/(6Q²-7)⁵ dQ YES
= ∫ Q/(7776Q¹⁰-45360Q⁸+105840Q⁶-123480Q⁴+72030Q²-16807) dQ NO
= ∫ Q/(706.91Q¹¹-5040Q⁹+15120Q⁷-24696Q⁵+24010Q³-16807Q NO

I don't know the next step, please help me..

Thank you.

Sorry guest ( you really need a name )
This one is completely different from the last one because the complicated stuff is on the bottom. You can't separate them into individual terms so you have to look for hints on how else it could be done.
I'm trying to think how to explain it ummm.

TC = ∫ MC dQ
TC = ∫ Q/(6Q ²-7) ⁵ dQ
TC = ∫ Q(6Q ²-7) ^-5 dQ

Do you understand what I just did? If i swap a term from one side of the fraction line to the other I have to change the power from + to - or vise versa.

Now, I have noticed that if I differentiate the stuff inside the bracket i get 12Q. (And Q is out the front of the bracket) This is the helpful fact that I am going to use.
That is: d/dQ [ 6Q ²-7 ] = 12Q

This means that the answer will have (6Q ²-7) ^-5+1 = > (6Q ²-7) ^-4 in it.
-------------------------------------------------------------------------------------------------------------------------------------------------------------
Now, other people may well have a more straight forward method than me but now I look at that last expression and see what happens if I differentiate it
d/dQ (6Q ²-7) ^-4
= -4(6Q ²-7) ^-4 ) ^-5 * 12Q
= -48Q(6Q ²-7) ^-4 ) ^-5

so if I divide everything by -48 the answer will be what I want.
That is

d/dQ [1/-48](6Q ²-7) ^-4
=[1/-48]* -4(6Q ²-7) ^-4 ) ^-5 * 12Q
=[1/-48]* -48Q(6Q ²-7) ^-4 ) ^-5
= Q(6Q ²-7) ^-4 ) ^-5
This is exactly what you wanted.

Therefore
TC = ∫ Q(6Q ²-7) ^-5 dQ
TC = [1/-48](6Q ²-7) ^-4 + k (where k is a constant)
TC = [1/-48](6Q ²-7) ^-4 + k
TC = - (6Q ²-7) ^-4 / 48 + k

Now it is time to look at this statement
Determine the Total Cost if the Fixed Cost is $40
This means that if the quantity is 0 the Total cost will be $40
(You have to spend $40 before you start producing anything.)
Substitute TC=40, Q=0 to find k
40 = 0 + k
so k = 40
The answer is
TC = - [(6Q ²-7) ^-4 / 48] + 40

I hope you understand

Melody28 Jan 2014

+118691

the-ate-tah:
point # 1 = (x1,y1)
x1 = 0
y1 = 50

point # 2 = (x2,y1)
x2 = 0
y1 = 25

point # 3 = (x2,y2)
x2 = 75
y2 = 25

OPP = ABS(x1-x2)
ADJ = ABS(y1-y2)

TAN(T) = OPP/ADJ

T = (OPP/ADJ)(1/TAN)

How do I calculate the Theata ? Am I heading in the right direction ?

Hi the-ate-tah,

First make sure your calculator is in degrees mode. There should be a tiny little D at the top of the screen.
Now,
I am not sure if you are heading in the right direction because I am not sure what you are trying to do.
Now, I have drawn a pretty little picture to show you what I think that you are trying to do.
When you get to
tan theta = 3
It is the angle that you have to find. If you want to find an angle you have to press shift or inv or 2nd to bring up the correct function.
so press
2nd tan 3 and then if you want to get it into degress , minutes and seconds you will need to press the ⁰ ' " button.

The way I have done it T and theta refer to the same angle.
You can't just separate tan from the angle the way you have done it. It doesn't work that way. they stay together until the very end when you get the value of T from the calculator.

140128 coordinate geometry triangle.JPG

Melody28 Jan 2014

+118691

olden:
( 8/9 )3=

Do you mean (8/9) ³ ?

this is 8 ³ / 9 ³ => 512 / 729

and this cannot be simplified.

Melody28 Jan 2014

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