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Thank you! :)

24 hours in a day.....so......

Ounces leaked in a day  =    24 * 13   = 312 oz

Ounces in a gallon  =    128

Gallons leaked per day  =   312 / 128  = 2.4375  gallons

​5 ​​√​ 243 =

​5​​√​ [ 81 * 3 ]  =

5 ​​*√ 81 * ​​√ 3  =

5 * 9  * ​​√ 3  =

45 ​​√ 3

so it a thing 

GhOsty: He/she may have meant:

243^(1/5) = 3

2+ 1/2 : 3 + 1/2  =  n : 2

2 + 1/2  =   5/2

3+ 1/2 =   7/2

So

(5/2) / (7/2)  =  n / 2

5 / 7  =   n / 2           cross-multiply

10  =  7n              divide both sides by 7 

10 / 7   =  n

About 77.94

Um... you use the keyboard?

2 1/2 : 3 1/2 = n : 2

(2 1/2) / (3 1/2)  x  2=1 3/7, so that:

2 1/2 : 3/12 = 1 3/7 : 2

The hypotenuse of a triangle is the longest side. But the triangle has to be a right triangle.

B.

If the number of watering holes doubles, then the life spans of desert animals will double.

\((a+0.077)/2=0.0048\)

Times both sides by 2

\(a+0.077=0.0096\)

minus 0.077 from both sides

\(a=0.0096-0.077\)

\(a=-0.0674\)

Nice! Not how I did it, but nice. (I didn't know this theorem existed )

You have got to be kidding!

 Do you really expect Helperid to take your useless blarney and do anything with it? It doesn’t even make good fertilizer.  

Heureka gave helperid two bunches of fine bananas. Helperid is too lazy to peel them.

If he does decide to do anything –like posting an attempt at a solution, he needs to hurry, this post will auto-lock in less than 48 hours.

You could have posted this link

Thanks Alan, :)

A compound's empirical formula tells you the smallest whole number ratio that exists between the elements that make up a compound.

In your case, the unknown compound has an empirical formula of C2H4O, which means that it contains carbon, C, hydrogen, H, and oxygen, O, in a 2:4:1 ratio.

In other words, one mole of this compound will contain carbon, hydrogen, and oxygen in a 2:4:1 mole ratio.

All you have to do now is determine the mass of the empirical formula and compare it with the molar mass of the compound. You will have

2×12.011 g mol−1+4×1.00794 g mol−1+1×15.9994 g mol−1=44.053 g mol−1

The molar mass of the compound essentially tells you the mass of one mole of the compound. This means that you will have

44.053g mol−1×n=88g mol−1

Rearrange to get

n=88 / 44.053=1.9976≈2

Therefore, the molecular formula of the compound, which tells you the exact number of atoms of each element present in one molecule of the compound, will be:

(C2H4O)2 =C4H8O2

People like math because they are fanatics, putting math above everything else. (actually thats not a bad thing...)

But math is a part of school, therefore you have to be a fanatic to like math.

-(a-15)

-(1)(a-15)

-a=-1*a

15=-15*-1

-a+15

(Thing to get here, -(blank) = -(1)(blank))

if i needed 80 people to go to the zoo, $6 for an adult and $3 for children and $336 was made,

how many children and adults when to the zoo?

Let x = adults
Let y = children

\(\begin{array}{|rcll|} \hline & 6x + 3y &=& 336 \quad & | \quad : 3 \\ (1) & 2x + y &=& 112 \\ (2) & x + y &=& 80 \\\\ \hline (1)-(2): & (2x + y) - (x + y) &=& 112-80 \\ & 2x + y - x - y &=& 112-80 \\ &\mathbf{x} &\mathbf{=}& \mathbf{32} \\\\ & x + y &=& 80 \\ & 32 + y &=& 80 \\ & y &=& 80 - 32 \\ &\mathbf{y} &\mathbf{=}& \mathbf{48} \\ \hline \end{array}\)

32 adults and 48 children went to the zoo.

I assume a is meant to be:  a = 2i - 6j + k

with b = -3j - 2k

To add them you just add corresponding coefficients of i, j and k to get:

c = 2i - 9j - k

To get the unit vector in this direction divide each coefficient by the size of c

|c| = sqrt(2² + (-9)² + (-1)²)  → sqrt(86) 

c = (2i - 9j - k)/sqrt(86)

.

37*10^-1

Determinant of a matrix

 3  -5  -2  2

-4   7   4  4

 4  -9  -3  7

 2  -6  -3  2

1.  tridiagonal matrix, e. g. Gauß
\(\begin{pmatrix} 3 & -5 & -2 & 2 \\ 0 & \frac{1}{3} & 1\ \frac{1}{3} & 6\ \frac{2}{3} \\ 0 & 0 & 9 & 51 \\ 0 & 0 & 0 & 3 \\ \end{pmatrix} \)

2.  Determinant: multiply the diagonally elements

The determinant of this matrix is \(3 \cdot \frac{1}{3}\cdot 9\cdot 3 = \mathbf{27 }\)

I will not answer your question, however i will give you questions that can help you with solving part C of your question:

1. Derivate the function\(f(x)=\sqrt[x]{x}={x}^{\frac{1}{x}}\)

2. When does the derivative equal 0? What is the function's maximum and minimum values? (The function doesn't necessarily have maximum values or mininum values!)

3. Where is the function defined? What is the function's image when x is between 0 and 1?

What about when x is greater than 1?

Good luck!

If you need help just ask for it

~blarney master~

How would I solve this?

((x-2)/(2x)+(1)/(x+2))/((3)/(2)-(6)/(x^(2)+2x))

\(\begin{array}{|rcll|} \hline && \mathbf{\dfrac{ \dfrac{x-2}{2x} + \dfrac{1}{x+2} } { \dfrac{3}{2}- \dfrac{6} {x^{2}+2x} } } \quad & | \quad x^{2}+2x = x(x+2) \\\\ &=& \dfrac{ \dfrac{x-2}{2x} + \dfrac{1}{x+2} } { \dfrac{3}{2}- \dfrac{6} {x(x+2)} } \\\\ &=& \dfrac{ \dfrac{(x-2)(x+2) + 1\cdot 2x}{2x(x+2)} } { \dfrac{3x(x+2)-2\cdot 6}{2x(x+2)} } \\\\ &=& \dfrac{\left[~(x-2)(x+2) + 1\cdot 2x ~\right]}{2x(x+2)} \cdot \dfrac{2x(x+2)} {\left[~ 3x(x+2)-2\cdot 6 ~\right] } \\\\ &=& \dfrac{(x-2)(x+2) + 1\cdot 2x} {3x(x+2)-2\cdot 6} \\\\ &=& \dfrac{(x-2)(x+2) + 2x} {3x(x+2)-12} \\\\ &=& \dfrac{x^2-4 + 2x } {3x^2+6x-12} \\\\ &=& \dfrac{1}{3} \cdot \dfrac{\left(x^2+2x-4\right)} {\left(x^2+2x-4\right)} \\\\ &\mathbf{=}& \mathbf{ \dfrac{1}{3}} \\ \hline \end{array}\)