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Take ln of both sides of the equation to get

4x-1 = ln3        add one to both sides

4x = ln3 +1      divide by 4

x = (ln3+1)/4

The face has 6 cubes...there are 4 rows of 6 cubes   6 * 4 = 24 cubes

Second one:

 there are TWO faces that are  10 x 6        2 x (10 x 6)    in^2

 There are TWO faces that are  10 x 5       2 x (10 x 5)    in^2

  there ar TWO faces that are 5 x6       +  2 x (5 x 6)      in^2

Add the reds for your answer...

-6i (5+3i)     expand   (remember i = sqrt(-1)    so   i^2 = -1)

-30 i   -18 (i^2)

-18(-1) -30i

18-30i

Since they started with 800 and they triple every 8 hours, I think HOURS would be appropriate.

The last choice   2x^2 + 8x + 22 +  90/(x-4)

Here is my scrawled workings:

y = x^(x-1)     solve for 'x

log (y) = (x-1) log 3

log(y) /log 3 = (x-1)              Remember:   Switching log bases:   Logb(a) =  log(a) / log(b)

log3 (y) = x-1

log3(y) + 1 = x                    Now switch the y's and x's

y = log3(x) + 1

f'(x) = log3(x) + 1

In three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. A simple example of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron.   

( I had to look up that definition)

SO by definition

GC is the only one that fits....the others are parallel or intersect.

- pi/4   (7pi/4)

5 pi /4

ABCD would be the bottom as drawn....it is the face the box would sit on if you placed it on the ground in its present orientation.

Hey, thanks so much!

Surface area of a cyclinder = circumference x height     (if we are not counting the ends as surface area)

circumference = pi * d  = pi * 2r

SO surface area =  3.14   * 2 (5)   *  10     cm^2         I'll let you plug the numbers....

Let's find the longer leg of the larger triangle first ...this is also the hypotenuse of the smaller triangle

cos 30 = sqrt3 / 2 = adj / hyp = adj/16

adj = 16 sqrt3 / 2   = 8 sqrt3   = hypotenuse of smaller triangle

now for the smaller triangle

cos 30 = adj / hyp  = sqrt 3  / 2  =  adj / (8 sqrt 3)

adj = longer leg =  sqrt 3 / 2  *  8 sqrt 3 =   12 cm   

Thanks so much you guys!!

Uh... What’s a BUH-Jillion?

Uh... I don’t know. I don’t think.

Uh... no I haven’t tried.

I DON’T understand that complicated formula, it’s too hard, I don’t understand it. I need help just to log on and post these questions.

Uh... I didn’t get an answer because I haven’t tried.

Uh... I don’t know what the answers are. I haven’t tried. I’m waiting for CPhill to answer them.

Why are you so mean? Why are you a bully? Why are you being mean to me?

Thanx, CP.......once in a while I don't make an error!   Haha

Nice, EP  !!!!

Ok    -2x +3   gives the SLOPE of the parabola at any point x

We want the slope to be -3   (negative inverse of 1/3.....the slope of the line)

so   -2x+3 = -3    yields  x = 2 is where the tangent line is slope -3

Sustitute x= 2 into the ORIGINAL equation to find y = 2

Now find the line  given slope = -3   and point  3,2

y= mx+b

2= -3(3  ) + b       so b = 11

y = -3x + 11      (see graph)

Second one

The first four points form a parallelogram  with a width of 6   and a height of 4.....so its area  is

(6 * 4)   =  24 units^2

The last three points form a triangle with a base of 6  and a height of  2

So...its area is  (base * height) / 2  = 6 * 2  / 2    =    6 units^2

So.....the total area  is    (24 + 6)  =  30 units^2

Thanks, EP.....here's another approach  using the Law of Sines

x / sin 30  =  8 / sin 45

x sin (45)  =  8 sin 30

x (1/ √2 )  =  8  (1/2)

x / √2  =  4

x  = 4√2  ≈  5.66    ...   just as EP found  !!!

NVM.....EP has the correct answer!!!!

Hopefully Chris is doing the math and comes up with the same answer I calculated...here is my graph

Wow....you have posted a BUH-Jillion questions....and many are VERY SIMILAR !!!!

First of all, what do YOU think the answers are?   Have you TRIED to get an answer   ??   What did you get for an answer?

     volume of a cone = V = pi r^2 h/3      try that , then get back to me with what you find.

Second part..... What do YOU think the answers are for this one?  Have you tried?

Volume of a sphere is  4/3 pi r^3   =  4/3 (3.14) (4^3)       REMEMBER to use the RADIUS !!

= 267.9 cm^3   

The second one:

   You'll have to draw that one out....then break it into squares , rectangles and triangles to calculate the area

Then the last one:

V = 4/3 pi r^3    =  4/3  * 3.14  *  7.5^3  = 1766.25 in^3

Find two similar sides and express as a ratio:

WX/RS = 20/24 = 5/6

Let  B  and  H   be the dimensions of   DEF  

then  ABC  is   6/10  B     and    6/10  H

Area = 1/2 BH  for a triangle  so the ratios of the areas would be

     (1/2  6/10  B  6/10 H )  /    1/2  B H     the 1/2   the B's and the H's   'cancel out'

6/10 * 6/10 = 36/100 = 9/25 

Area for a square (or rectangle) is   L x W       Now scale by 6      (6L x 6W ) /  (L x W)  = 36 times bigger !