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6840

The answer is 4,568,867,856,654

42695598626

Let the general formula for the temperature decrease be :

t(h)  = (-0.65 / 100) h      where t is the temperature decrease at some height, h  ........so we have....

t(2800) = (-0.65/100)(2800)  = -18.2 degrees

So........

10 - 18.2   = -8.2 degrees at 2800 ft

This also might be :

e^5x - e^-5x    ....if so......we can factor out the e^-5x  and be left with :

e^-5x (e^10x  - 1 )

Whether this is "simpler" than the original expression is debatable.....!!!

Yep...it's a right triangle......look at the graph, here......https://www.desmos.com/calculator/qym7gvot6w

The distance from (3, 5) to the other two points = sqrt(2)

And the distance between the other two points = 2  = the hypotenuse

The volume of what??  A sphere, a cylinder, a cube......etc.  ???

2/3 * 535 = about 357 members of Congress

If you want to factor this, remember, we need to take any common factors out, first.  So we have :

2x^2+8x+6  =

2(x^2 +4x + 3) =

2 (x + 1) (x + 3)

And that's it.....!!!

(A)  Sample Space :

HHH

HHT

HTT

TTT

TTH

THH

THT

HTH

(B)  This is a compound event.....tossing one coin is a simple event........tossing two or more is a compound event

Yes you are right.

It is my experience that even very sophisticated calcs can't handle roots of negative numbers. 

I think Alan went into more detail on this once before. Maybe he will comment later. :/

Thanx Melody...uhm, just one thing more please, I am batteling a bit to see (understand) the reasoning behind getting the factors (x-1) and (x-4)..I will still try to figure it out, but was wondering if you would be so kind to just take me through that?..If your'e busy or there is a reason why you cannot, (don't want to I mean), I will understand, no hard feelings?

You are so stupid it's 4.

x^-8=sqrt(20000)

x^8=141.4213

x=141.4213^1/8

x=1.8570

Minimize the objective function  150x + 50y  where x is the number of packages ordered from Jungle and y is the numer of packages ordered from OHagan

And each package ordered from both companies supplies 5 mystery novels......and we must have at least 2500 of these....so, the constraint becomes :

5x + 5y >= 2500  →  x + y >= 500

And each package from Jungle supplies 10 romance novels and each package from OHagan supplies 5 romance novels.....and we need at least 3500 of these....so we have

10x + 5y >= 3500  →  2x + y >= 700

Further....at least 75% of the the packages must come from OHagan....in other words, out of every 4 ordered, at least 3 must come from OHagan......put another way, we have

3x <=  y

Look at the following graph :   https://www.desmos.com/calculator/6hdrqjgy2o

Since mins and maxes occur only at the corner point of a feasible region, the only point that "works" here occurs at (140, 420)..........

Thus.........  150(140) + 50(420) = $42000 is the minimum cost by ordering 140 packages from Jungle and 420 packages from OHagan....

x^-8=sqrt(20000)

How do i solve it?

\(\small{ \begin{array}{rcll} x^{-8} &=& \sqrt{20000} \\ x^{-8} &=& 20000^{\frac12} \qquad | \qquad ()^{\frac{1}{-8}}\\ x^{\frac{-8}{-8}} &=& 20000^{\frac{1}{-8\cdot 2}} \\ x &=& 20000^{\frac{1}{-16}} \\ x &=& \frac{1}{20000^{\frac{1}{16}}} \\ x &=& 0.5384998979 \end{array} }\)

[6.2*10^5 ]-[2.6*10^4]-[1.9*10^2]

\(\small{ \begin{array}{rcll} && 6.2\cdot 10^5 \\ &-& 2.6\cdot 10^4 \\ &-& 1.9\cdot 10^2 \\ && &=& 620000 - 26000 - 190\\ && &=& 593810 \\ && &=& 5.9381 \cdot 10^5 \end{array} }\)

Okay super I understand, but what about \({(-1)}^{1/3}\). 

I think that will be \(\sqrt[3]{-1}\)

You can say (-1)*(-1)*(-1) = -1, but it still says error?

You can get superscript and subscript formats using the ribbon.

But Heurka and I both use LaTex to write our math speak in.

The Latex gateway is in the ribbon too.

If you decide you want to have a look at LaTex there is a rather messy thread on it in the sticky notes.  Some of our youngest members have learned it in the past but it does take a little effort. :)

420 packages from O'Hagan and 140 packages from Jungle would seem to get you 2800 mystery novels and 3500 romances at a total cost of 42000 dollars.

nb.

420/(420+140) = 0.75

No problem Melody. Thank you very much indeed for this solution. Also Heureka, Thank you, thank you and again..a big thank you. wow!. Just something, how do you get the squares to show "normal", as opposed to the "^" character?..

100/5*4+4³      using the order of operations, we have

20 * 4 + 64   =

80 + 64  =

144

The answer is 144

Sorry for confusing you guest.  That was a small mistype.  It was =0 not =1

I have fixed it in my answer.  My answer is correct.  :))

I like Heureka's answer better though.

Thanks Heureka :))      

Hi, I have this problem solved to this:

(x^2-5x+2)^2-(x^2-5x)=8

\(\small{ \begin{array}{rcll} (x^2-5x+2)^2-(x^2-5x)&=& 8 \qquad & |\qquad \text{we substitute } z = x^2-5x \\ \\ \hline \\ (z+2)^2 - z &=& 8 \\ z^2+4z+4-z &=& 8 \\ z^2 +3z - 4 &=& 0 \qquad & |\qquad \text{factorisation }\\ (z-1)(z+4) &=& 0 \\ z = 1 &\text{or}& z = -4\\ \\ \hline \\ x^2-5x &=& z \qquad & |\qquad z = -4 \\ x^2-5x &=& -4 \\ x^2-5x+4 &=& 0 \qquad & |\qquad \text{factorisation }\\ (x-1)(x-4) &=& 0 \\ x = 1 &\text{or}& x = 4\\ \\ \hline \\ x^2-5x &=& z \qquad & |\qquad z = 1 \\ x^2-5x &=& 1 \\ x^2-5x-1 &=& 0\\ \boxed{~ \begin{array}{rcll} ax^2+bx+c &=& 0\\ x &=& {-b \pm \sqrt{b^2-4ac} \over 2a} \end{array} ~}\\ x^2-5x-1 &=& 0 \qquad & |\qquad a=1 \quad b=-5 \quad c=-1\\ x &=& {5 \pm \sqrt{25-4 \cdot (-1)} \over 2}\\ x &=& {5 \pm \sqrt{29} \over 2}\\ x = {5 + \sqrt{29} \over 2} &\text{or}& x = {5 - \sqrt{29} \over 2} \\ x = 5.1925824036 &\text{or}& x = -0.1925824036 \\ \end{array} }\)