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y = (ln(x) )^x      take the ln of both sides

ln(y)  =  ln [ln(x)]^x

ln (y)  = x ln [ln (x) ]     now.....differentiate both sides

y' / y   = ln [ln (x) ]   +  x [  (1/x) / ln(x) ]    simplify

y' / y = ln [ ln (x) ] + 1/ [ln (x) ]    multiply both sides by y

y' = y [ ln [ln (x)  + 1/ [ln (x) ]      and substitute  [  ln(x) ]^x   for y

y'  = [ln (x)]^x [ ln [ln(x)] +  1 / ln (x) ]

Ordering of functions  from  slowest growing to fastest growing  as x  →  infinity

 e^(x/2)        e^x       [ln (x)]^x         x^x

It's not a solution to (b) or (d)......

For a table you can just plot the points and graph them out, if the line is straight that means it's linear. If it curves in any shape or form (not straight) then it's non-linear.

For equations it's all about the LEADING TERM (Or the term with the highest power) if the leading term is just an x or y without any powers attached to them then you've got yourself a linear equation. However if the leading term has a power associated with itself then it's going to be non-linear.

Here are some examples:

(x - 2) = y     LINEAR

x^2 + 6 = 4y    NON-LINEAR

(x + 6)^3 = y    NON- LINEAR

9001x (ITS OVER 9000) + 420y = 1   LINEAR

Hope this helped. 

Nice, fiora....!!!!

33 1/3% ≈ 33.3333333333333% ≈ 1/3

Now to reitterate your question, it's asking what is 1/3 of 15. I'm sure you can handle this.

For this kind of problem, I recomend you write the function out. I'll demonsrate for you:

Since she earns $35 that's a constant (meaning no variable goes with it) and $8 for every item that she sells (let the # items equal x since $8 is the coeffecient of the # of items she sells). y of course will be her total earnings. Using this information you should obtain the equation:

$35 + $8x = y

Now use the "coordinates" to plug in solutions for x and y.

Hope I helped you understand the concept. c:

The linear function we are dealing with is :

y = 8x + 35

So....just put the first value for each ordered pair into the equation for x and see if it produces the second value of the ordered pair....if it does, that point is on the graph...

For instance....for the point (7, 91) we have

y = 8(7) + 35  =  56 + 35  =   91.......so this point is on the graph......

Possible derivation:
d/dx(log^x(x))
Express log^x(x) as a power of e: log^x(x) = e^(log(log^x(x))) = e^(x log(log(x))):
  =  d/dx(e^(x log(log(x))))
Using the chain rule, d/dx(e^(x log(log(x)))) = ( de^u)/( du) ( du)/( dx), where u = x log(log(x)) and ( d)/( du)(e^u) = e^u:
  =  (d/dx(x log(log(x)))) e^(x log(log(x)))
Express e^(x log(log(x))) as a power of log(x): e^(x log(log(x))) = e^(log(log^x(x))) = log^x(x):
  =  log(x)^x d/dx(x log(log(x)))
Use the product rule, d/dx(u v) = v ( du)/( dx)+u ( dv)/( dx), where u = x and v = log(log(x)):
  =  log(log(x)) d/dx(x)+x d/dx(log(log(x))) log^x(x)
The derivative of x is 1:
  =  log^x(x) (x (d/dx(log(log(x))))+1 log(log(x)))
Using the chain rule, d/dx(log(log(x))) = ( dlog(u))/( du) ( du)/( dx), where u = log(x) and ( d)/( du)(log(u)) = 1/u:
  =  log^x(x) (log(log(x))+(d/dx(log(x)))/(log(x)) x)
The derivative of log(x) is 1/x:
  =  log^x(x) (log(log(x))+(1/x x)/(log(x)))
Simplify the expression:
Answer: |   =  log^x(x) (1/(log(x))+log(log(x)))

x=t+1     t=x-1  \(\frac{dt}{dx}=1\)

y=3t+2    \(\frac{dy}{dt}=3\)

applying chain rule we have

\(\frac{dy}{dx}=\frac{dy}{dt}*\frac{dt}{dx}=3\)

what are the 6 answers of (-1) to the 1/6th power.

It doesn't have 6 roots!. 1/6th power means the "sixth root of -1" or:  ⁶√-1

It does have a decimal approx., which is this:

0.8660254037844386467... + 0.5 i

Nevermind I realize now that there was information given that I missed that would be used to find the pressure.

It is a solution to all of them except "b".

How do you say:16.6666666666666667=16 2/3-It is called "sixteen and two-thirds."

a)  To show that v₀ sqrt(2) / 32 x [sin(2A) - cos(2A) - 1]  equals  v₀ sqrt(2) / 16 x cos(A) x [sin(A) - cos(A)]

      --->              v₀ sqrt(2) / 16 x (1/2)[sin(2A) - cos(2A) - 1]  equals v₀ sqrt(2) / 16 x cos(A) x [sin(A) - cos(A)]

      --->              (1/2)[sin(2A) - cos(2A) - 1]  equals    cos(A) x [sin(A) - cos(A)]          

      --->  But:  sin(2A)  =  2sin(A)cos(A)   and  cos(2A)  =  2cos²(A) - 1

      --->  Left side:          

                       (1/2)[2sin(A)cos(A) - (2cos²(A) - 1) - 1]

                                =  (1/2)[2sin(A)cos(A) - 2cos²(A) + 1 - 1]

                                =  (1/2)[2sin(A)cos(A) - 2cos²(A)]

                                =  sin(A)cos(A) - cos²(A)

                                =  cos(A)[sin(A) - cos(A)    <--- which equals the right side.

b)  sin(2A) + cos(2A )  =  0

     --->   sin(2A)  =  -cos(2A)             (now divide both sides by cos(2A):

     --->   sin(2A) / cos(2A)  =  -1

     --->   tan(2A)  =  -1

     --->  2A  =  135°

     --->     A  =  67.5°

c)  Place these values into the equation, and you will find the maximum distance is 0.586 feet (approx).

To have two boys on the team you must choose one of the 8 boys (out of 19 total persons) followed by choosing one of the 7 remaining boys (out of 18 remaining persons):

The probability of getting two boys:  8/19 x 7/18  =  56/342.

To have two girls on the team you must choose one of the 11 girls (out of 19 total persons) followed by choosing one of the 10 remaining girls (out of 18 remaining persons);

The probability of getting two girls:  11/19 x 10/18  =  110/342,

The probability of getting either two boys or two girls is found by adding these independent probabilities together:

     56/342 + 110/342  =  166/342  =  83/171.

0 is not prime either since it has no factors. It also cannot divide itself because it creates a mathematical error.

What is the probability that a class of 24 people win a 10-number lottery with 2-number combination?

The probability of winning the lottery by selecting 2 numbers out of 10 for 1 ticket is:

10C2=45, or 1 in 45 chances. The fact that 1 ticket is shared between 24 people is not going to change the odds of winning the first prize. It is just they will have to divide the proceeds of the winning ticket among 24 people.

Well if you need to move at least two bottles during your three moves then here is my order of moves:

Some symbols to simplify things

Upside down = Ω

Rightside up = Σ

You start off with...

 Ω Σ Ω 

FIRST MOVE: In this move I'll make the right side up upside down:

Ω Ω Ω

SECOND MOVE: In this move I'll now move ANOTHER bottle rightside up since we need to move more than ONE bottle:

Σ Ω Ω

ΤΗΙRD MOVE: I can just flip the bottle (Σ) back to being upside down (Ω):

Ω Ω Ω

I think I did this correctly, someone tell me if I did something wrong. The instructions were a bit wonky to read.

Hope this helped c:

Alright Guest, in order to solve this problem you need to get rid of that mixed number, in order do so, do as what follows:

You start off with:

7 x 1 \(\frac{3}{5}\)

Let's ignore the seven for now and focus on that mixed number: 

\(\frac{3}{5}\)

1 3/5

Now what you want to do is multiply the denominator (5) by the whole number (1) and add that answer to the numerator, WHILE KEEPING IT AS A FRACTION if done correctly you should get:

8/5

Now put that seven back into play:

7 x 8/5

If you'd like you can think of the seven as 7/1 multiply the numerators by the numerators and multiply the denominators by the denominators.

7/1 x 8/5

After multiplying, you should obtain the solution of:

56/5

Suppose ln x = 9, ln y = 3, and ln z = 27. Evaluate.

ln(xyz)

Since you have already given the ln of x, y, z as:9, 3, 27 that means that the ln(xyz)=9+3+27=39!!, because: x=e^9, y=e^3 and z=e^27.

The second part isn't clear the way you have written down.

What about the number \(0?\)

\(\frac{8}{\frac{1}{4}}\)

\(8\times\frac{4}{1}\)

\(\frac{8}{1}\times\frac{4}{1}\)

\(\frac{32}{1}\)

\(32\)

\(\frac{dy}{dx};\)  \(x=t+1;\)  \(y=3t+2\)

\(\frac{d\times(3t+2)}{d\times(t+1)}\)

\(\frac{1\times(3t+2)}{1\times(t+1)}\)

\(\frac{3t+2}{t+1}\)

Good job guest! +5