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ivolga24 [154]
3 years ago
7

Differentiate: f(x) = 3x ln(6x) − 3x

Mathematics
1 answer:
galben [10]3 years ago
5 0
Answer is in the attachment below. Please open it up in a new window to see it in full.

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Evaluate the expression for x=5 and y= 3
kenny6666 [7]

I will use the positive / negative property of the absolute value to split the equation into two cases, and I will use the fact that the "minus" sign in the negative case indicates "the opposite sign", not "a negative number".

For example, if I have x = –6, then "–x " indicates "the opposite of x" or, in this case, –(–6) = +6, a positive number. The "minus" sign in "–x" just indicates that I am changing the sign on x. It does not indicate a negative number. This distinction is crucial!

Whatever the value of x might be, taking the absolute value of x makes it positive. Since x might originally have been positive and might originally have been negative, I must acknowledge this fact when I remove the absolute-value bars. I do this by splitting the equation into two cases. For this exercise, these cases are as follows:

a. If the value of x was non-negative (that is, if it was positive or zero) to start with, then I can bring that value out of the absolute-value bars without changing its sign, giving me the equation x = 3.

b. If the value of x was negative to start with, then I can bring that value out of the absolute-value bars by changing the sign on x, giving me the equation –x = 3, which solves as x = –3.

The theory can be encapsulated in a main equation called the standard model Lagrangian (named after the 18th-century French mathematician and astronomer Joseph Louis Lagrange), which was chosen by theoretical physicist Lance Dixon of the SLAC National Accelerator Laboratory in California as his favorite formula.

"It has successfully described all elementary particles and forces that we've observed in the laboratory to date — except gravity," Dixon told LiveScience. "That includes, of course, the recently discovered Higgs(like) boson, phi in the formula. It is fully self-consistent with quantum mechanics and special relativity."

The first line is traditionally called forces. That Tensor quantity indicates electromagnetism and both nuclear forces. Importantly, that term does this in a way that preserves certain symmetries. They are called gauge symmetries, and even though they are hard to explain, they are very important in physics. You’ll hear more about them later.

The second line is what I might call motion. It is the reason why electrons and quarks can move. It is also what allows the forces to interact with matter.

The third line is called the Yukawa coupling. It gives mass to things like quarks and electrons. It actually used to look different. That ϕ didn’t used to be there. It was added because it was the only way to have mass while preserving gauge symmetry.

The last line is called the Higgs sector. If you’ve heard of the Higgs boson, it’s the same guy. This term is responsible for ‘spontaneous symmetry breaking’. This means that even though the universe does indeed have gauge symmetry, that symmetry can often be obscured at low temperatures. This explains the masses we observe for particles.


5 0
3 years ago
What's 300000+49498383837?
tatuchka [14]
49498683837. To work these questions out, use column addition, it is a quick and simple way to add large numbers.

8 0
3 years ago
Read 2 more answers
What is the value of this -3 2/3 ÷ 1/3​
mihalych1998 [28]

Answer:

-11

Step-by-step explanation:

Convert -3 2/3 to -11/3

-11/3÷1/3

Dividing by 1/3 is the same as multipling by 3

so the equation becomes

(-11/3)(3)

=-11

8 0
3 years ago
Read 2 more answers
PLEASE HELP MEH IM NEED THIS NOW PLEZZ<br><br> What is x ? -2x + 3 &lt; 5
algol13

Answer: x>-1

Step-by-step explanation: I know this because I solved this equation. I know that is not a good explanation but I know it is right.

8 0
3 years ago
Read 2 more answers
How do u guys solved this?
TEA [102]

Answer:

3 boxes

Step-by-step explanation:

First, we need to find the area of the whole square, so we can find out how much to subtract from. We can easily do this by multiplying 16 by 16, since it is a square.

16*16=256 square feet.

Now, we just need to find the area of the circular rug, and subtract it from 256 to find the area not covered by the rug that needs to be tiled. Since the sides of the rug touch each side of the floor, than the diameter will be the same as the side length of the square. Thus, the diameter is 16.

Now we can use the equation <em>A=pir^2 </em>or <em>Area=pi*radius squared</em> to find the area of the circle. The radius is halve of the diameter, so divide 16 by 2 to get the radius, or 8. Now all we have to do is square 8 and multiply it by 3.14.

8^2=64

Now multiply.

64*3.14=200.96.

The area of the circle is 200.96, so subtract 200.96 from 256.

256-200.96=55.04.

So they will need 3 boxes to cover the area left.

Hope this helps!

3 0
3 years ago
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