CPhill

Area  = LW  = 28

Perimeter  =  2(W + L)

So  we have this

28  = LW    (1)

22 = 2(W + L)     divide by 2  on both sides

11= L + W      subtract  W  from both sides

11 - W  =   L      (2)

Sub (2)  into (1)  for L   and we have that

28 = (11 - W) * W        simplify

28 = 11W  - W^2        rearrange as

W^2  - 11W  +  28  =  0    factor

(W -7) ( W - 4)  = 0

Setting each factor to 0  and solving for  W  will give us the dimensions

W =  7    or W  = 4

So....the dimensions  are  7 ft  x  4  ft

Look at the graph.....go  over to  40  on the x axis and  then  go up until  you hit the line

Notice that  the value we reach  is a little more than 150 but less than 175

Thus....the only answer that makes sense is  "about 155"

Do you see this  ????

The first two are correct

For the third  one, each spin is independent...the outcome of any spin does not depend on any previous outcome...each spin has 1/5  of a chance of landing in any one area

I don't believe  that  this  has  any unique answer

Here are three such triangles  [ many more are possible ]

Annual compounding

5000( 1+.084)^(3.5)  ≈ $6630.90

Monthly compounding

5000(1 + .084/12)^(12 * 3.5)  ≈ $6702.05

4sin x - 1  =  0

4 sin x  =  1          divide both sides by  4

sin x  =  1/4

Using  the sine inverse to find x

arcsin (1/4)  = x   ≈ .253  rads     (1st quadrant angle)

Also  x is a second quadrant angle

x =  pi - .253  ≈  2.89 rads

log _b 5 = 1.609         log _b 8  =  2.079

Note that

log _b 5 + log _b 8  = log _b (5*8)  =  log_b 40

1.609   +   2.079  =  log _b 40

3.688  = log _b 40

(1/2)log x  - log (5y)  + log (7z)   =

We are using three properties here

a log b = log b^a

log a + log b=  log (ab)

log a + logb - log c  =    log [(ab)/c ]

So.....

log x^(1/2)  - log (5y) + log (7z)  =

log x^(1/2) + log (7z)  - log (5y)  =

log  √x  + log (7z) - log (5y)   =

log  [  ( 7z√x ) / ( 5y) ]

Very impressive, jfan  !!!!!

The circumference  of  the cone will be  (3/4) * 2 pi  r  =(6/4) pi* 1  =  (6/4) pi  = (3/2) pi

We can find  the radius  if the  cone as

(3/2)pi  =  2 pi * r     divide out pi

(3/2)  = 2 r       divide both sides by  2

(3/4) =  r

The orginal radius  will be  the slant height of the cone

And  the height of the cone  =  sqrt [  slant height^2  -  radius of cone ^2]  =

sqrt  [ 1^2  - (3/4)^2 ]  =

sqrt [ 1  - 9/16] =

sqrt [ 7/16] =

sqrt [7]   / 4