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Ann [662]
2 years ago
8

Is d y / d x the exact same as f ' ( x ) ? If yes, which is more commonly used?

Mathematics
1 answer:
Murrr4er [49]2 years ago
7 0
It's dependent on the context. A book may ask you to find the f'(x) of a function and you may have to use a u sub in your problem which requires you to find the dy/dx of what you substitute. So in this case both would be used.
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At Thanksgiving, Mrs. Jones overcooked the turkey so all but 5 of it had to be thrown away. The 8 people at dinner that
VashaNatasha [74]

<em>The question has inconsistent or incomplete data, so I'm filling the holes with key data.</em>

Answer:

<em>Every people at dinner received one-tenth of the original turkey= 0.1</em>

Step-by-step explanation:

<u>Proportions</u>

If some fraction a/b of a whole total M is to be computed and later removed, we proceed as follows

* Compute the portion to be removed as a/b*M

* Subtract it from the total quantity: M-a/b*M=M(1-a/b)

I'm assuming 1/5 of the turkey was lost due to overcooking. It means that (1-1/5) of the turkey remained for dinner, that is, 4/5 of the turkey.

Each people at dinner received the same amount of the remaining, so we must divide 4/5 by 8, to get 4/40, or 1/10. It means that every people at dinner received one-tenth of the original turkey

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3 years ago
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lesya [120]

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If you go to desmos.com, select the graphing calculator, and enter in y = 3x you should be able to see how it's graphed! Hope this helps!

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3 years ago
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This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x). 
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<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>

<span>The left side is the derivative of ye^(6x), hence </span>

<span>d/dx[ye^(6x)] = e^(12x) </span>

<span>Integrating </span>

<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>

<span>y = (1/12)e^(6x) + ce^(-6x) </span>

<span>Use the initial condition y(0)=-8 to find c: </span>

<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>

<span>Hence </span>

<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
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3 years ago
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ss7ja [257]

Answer:

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