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Because it's mostly air on the inside. 

They make it out of really light steel.

11 is to 5 as x is to 13 

11/5 = x/13 

5x = 143 

x = 143/5 = 28.6 

For this problem, there are 6 vowels and 20 consonants.

Each two letter "word" ust have at least one vowel. They can look like:

C-V     =     20 x 6   =  120

V-C     =     6 x 20   =  120

V-V     =      6 x 6    =  36

So, we can have  120 + 120 + 36  =  276  different "words".

Let each side ot the equilateral triangle be x.

Then, its perimeter is 3x.

The formula for the area of an equilateral triangle is:  Area  =  ( sqrt(3)/4 )·side².

For this triangle:  Area  =  ( sqrt(3)/4 )·x².

Since the perimeter of the equilateral triangle is 3x, the perimeter of the square must also be 3x.

Perimeter of the square = 4·side.

For this square:  3x = 4·side, so each side = (3/4)·x.

The formula for the area of a square is:  Area  =  side².

For this square:  Area  =  [ (3/4)·x ]²  =  (9/16)·x².

Ratio of the area of the equilateral triangle to the area of the square

     =     ( sqrt(3)/4 )·x²   /   (9/16)·x²      =     ( sqrt(3)/4 )   /   (9/16)  =  4·sqrt(3) / 9

A high cohesion means the intermolecular forces are high.....the particles stick together

 high adhesion means they also stick to other substances....

    a very sticky slow moving viscous blob is what you wind up with ~!

Nice :)

Since AC = BC, triangle(ABC) is an isosceles right triangle. Therefore, angle(B) is a 45^o angle.

This makes triangle(BDE) an isosceles right triangle, with BD = DE.

Triangle(AEC) is congruent to triangle(AED) by hypotenuse-side. 

This makes CE = ED. 

Since CE = 7, ED = 7.

Since BD = ED, BD = 7.

One way is via displacement....

    say you have a stone.....weight it

        then place it in a graduated cylinder partially full with water and not the change in volume on the cylinder ....that is the volume of the stone

                   then density =   weight/ volume

To get the circumference you just multiply the diameter by pi. So if your diameter is 4, then the circumferance is 4 pi

thank you cphill ! :)

Rearrange  as

  1             a^3

_____ + _______  =    7

a^3+ 7     a^3 + 7

1 + a^3

______  =     7             cross-multiply

a^3 + 7

1 + a^3  = 7 ( a^3 + 7)

a^3  + 1  =  7a^3  + 49       subtract   49, a^3  from both sides

-48  =  6 a^3       divide both sides by  6

-8  = a^3           take  the cube oot of both sides

-2  =  a

See the following image

Using symmetry  the top half of the  common area  can be found as follows :

Area of (1/4)circle  with a radius of 1 - Area of right triangle  with  legs of  1  =

(1/4) pi (1)^2  - (1/2)(1)^2  =

pi/4 -  1/2

So.....the  total  common area  =  2 (pi/4 - 1/2)  =  pi/2 - 1 units^2

That makes sense! Thank you so much! 

Complex number form:  x + yi.

The number i can be written in the complex number form of 0 -1i.

To rewrite this number into r·cis( theta ) form, use these two formulas:

  r  =  sqrt( x² + y² )     and     theta  =  tan^-1( y/x ).

For this problem:  x = 0   and  y = -1.

   r  =  sqrt( x² + y² )   =  sqrt( (0)² + (-1)² )  =  sqrt( 0 + 1 )  =  sqrt( 1 )  =  1

  theta  =  tan^-1( -1/ 0 )  =  undefined   --->   But, if you were to graph 0 - 1i, the point would be on the negative y-axis,

  therefore,  theta  = 270^o  (or, in radian form, 3pi/2).

r·cis( theta )  =  1·cis( 270^o )

Basically I know what r is which is 1 but as I try to get theta I get 0 degrees so because I applied arctan so I would add 180 degrees or 360 degrees which both are incorrect. The answer is 270 degrees, I'm just not sure where the 270 degrees is coming from. 

Could you please explain how you solved it? I got a different answer. Thanks

I appreciate you helping others solve problems but I really think you can do some of your problems by yourself. Think about the previous answers I gave you. What does cohesion mean what does adhesion mean?