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k=3

112-(3*(-3))=121

sqrt(pi) = 1.7724538509055159

im pretty sure she isnt thirsty u r 

This will have a max value where   the sin  = 1..this happens at pi/2.....this means that we need to find where   [2x - pi/3]  = pi/2

So......solving for x, we have that

2x - pi/3  = pi/2    add pi/3 to both sides

2x =  [ 5pi/6]      divide both sides by 2

x =  5pi / 12   .......and it will reach that max  at every  ± pi  rads from this value

To find out where it has a min....we need to find out  where the sin  = -1...this happens at  3pi/2....thus, we need to find out where

2x - pi/3  = 3pi/2    add pi/3 to both sides

2x  = 11pi/6     divide both sides by 2

x  = 11pi/12  ........and it wil,. again, have a min at every ±pi  rads from this value

See the graph, here :  https://www.desmos.com/calculator/ohrm0oeuul

atan(rise/run)

max{abs(2 sin(2 x - π/3) - 5) + 3} = 10 at x = -π/12 + n π for integer n

min{abs(2 sin(2 x - π/3) - 5) + 3} = 6 at x = -(7 π)/12 + n π for integer n

min{abs(2 sin(2 x - π/3) - 5) + 3} = 6 at x = (5 π)/12 + n π for integer n

what's 6=2(b-4)

\(6=2(b-4)\)        [ / 2   on both sides

\(b-4=3\)              [ +4   on both sides

\(b=7\)       !

Thanks to all!!!!.....

Note to EP......infinity + 1  is still just "infinity".......LOL!!!!!

BTW, GA.....I think there should be more "fingers"   on that cake than just one......!!!!

1) Bring it all to one side: 6x² - 11x = 0

2) Isolate one of the x's: x*(6x-11)=0

3)To become zero one of the factors must be zero: x = 0 or 6x-11 = 0

4)Solve: x = 0 or x = 11/6

what is the formula for volume?

Volume = mass divided by density

\(\LARGE V=\frac{m}{\delta}\)      !

400*75-150²=7500

7500/75=100

400-100*4=0=tasty

If you'd have to calculate it you would wanna calculate the derivative and see where that equals 0. 

(To calculate the derivative of an absolute value function you have to split it into two for when 2sin(2x - pi/3) - 5 > 0 and 2sin(2x - pi/3) - 5 < 0 (and add a minus before this one))

if you simply need those values, just plot it and you'll get minimum 6, maximum 10

A 'rad' is a radian, a means of measuring an angle.

There are  2 pi  radians in a circle.

Since there are also 360º  in a circle, there will be  pi  radians in one-half of a circle, allowing us to come up with this formula (with R representing radians and D representing degrees:

    D / 180  =  R / pi

It's the standard unit of meausurement for angles where the complete circle is 2pi rad. This makes dealing with goniometrics h**l of a lot easier!

https://en.wikipedia.org/wiki/Radian

Now comes the answer.

First approuch (Theoritical approuch)

Well we have the law of cosine that states: a² = b²+c² - 2bc*cos(A) (where A is the angle across the side a) 

We can manipulate this formula to the form of \(A = acos(\frac{(a²-b²-c²)}{-2bc}{})\)

So if we fill in our formula we'll get: \(A = acos(\frac{10²-4²-5²)}{-2*4*5}{})\)

We'd get \(A = acos(-1.475)\), which has no solution

Second approuch (Visual approuch)

You could look at the function \(f(x) = \sqrt{4² + 5² - 2*4*5*cos(x)}\)(where f(x) would be your third side and x would be the angle between the 4- and 5 side)

If you look at the plot of this function you'll see that it never reaches f(x) = 10

Third approuch (intuitional approuch)

A triangle has  three sides connected to eachother on their ends -> The sum of two sides must be bigger than or equal to the third side, else there would be no way to connect them to the ends of that side. 4+5 = 9 -> 9 < 10 thus the triangle would be impossible. 

Hope this helped!

[ sqrt(2) / (-2) ] ^-4  =  [ (-2) / sqrt(2) ] ⁴  =  [ 2 / sqrt(2) ] ⁴  =  [ sqrt(2) ] ⁴  =  { [ sqrt(2) ] ² } ²  =  2²  =  4