CPhill

$1500*(1+0.08)^35  ≈ $ 22178.02

Area to the right of z = 1.42  =

1 - area of the curve to the left of 1.42  =

1  - 0.92219616  =

0.07780384

Because of symmetry, we could have also calculated the area to the left of z = -1.42

I believe Whitespy made a small error...

tan (x)  =  5/20

tan (x)  =  1/4        use the arctan to find x

arctan (1/4)  =  14.04°

If you mean writing as a single log .......

(log 2)(log 4)   =

(log 2) (log 2^2 ) =

(log 2 )  *  [ 2 ( log 2)  ]

2 (log 2)^2

The first  is using  degrees......the second, radians

The leg of a right triangle is equal to 1/5 the sum of other sides. The triangle has a perimeter of 1. What is the triangle's area? Thank you.

Let the sides be  a, b and c      where a and b are the legs and c is the hypotenuse

Let  a  =  ( b + c) / 5     so    5a   = b + c

And since the perimeter   =  1, we have that

a +  b + c  =  1                

a +  5a   = 1

6a  =  1    →   a  =  1/6 units

And we have that  5(1/6)=  b + c   →  5/6  = b + c  →  c = (5/6) - b

So.....using the Pythagorean Theorem, we have that

a^2 + b^2  =  c^2

(1/6)^2  + b^2   = [ (5/6)  - b ] ^2

(1/36) + b^2   =  b^2  - (10/6)b + 25/36    simplify

(1/36)    = 25/36 - (5/3)b      rearrange as

(5/3)b   =   25/36  -  1/36

(5/3)b  =  24/36

(5/3)b  =  2/3

5b =  2

b = 2/5 

So.......the area  = (1/2)(product of the legs) =  (1/2)(a)(b)   =  (1/2)(1/6)(2/5)   =  1/30 units^2

The sum of this inifnite series  =

4 / ( 1 - 3/a)        where  4  is the first term  and  (3/a)  is the common ratio

Simplifying this, we have

4a /  [ a - 3]

Note.........that  since a is positive, the first value of a that produces a perfect square is when a  = 4

4(4) / [ 4 - 3 ]  =  16 / 1    =  16    which is a perfect square

Since the two triangles created are similar, each dimension of the larger triangle created will be  (17/8)  that of the smaller triangle

Call h the height of the smaller triangle......so its   area  =  (1/2)*8*h  =  4h  (1)

And the area of the larger triangle  = (1/2)* 17 * (17/8) h   =   (289 / 16)h    (2)

So  the area  of the trapezoid  =  (2) - (1)   =  (289/16) h - 4h   =  [ 289 - 64 ] / 16 * h =

[225 / 16] h

So.....the ratio of the smaller triangle to the trapezoid  =  [4h] /  ( [ 225/ 16] h )  =  64 / 225

Just as Melody found....!!!!

There are 60 seconds in a minute.......30  and above, round up to next minute, else, round down

So......

48°16'

Melody did......a long time ago......in the Mesozoic Era......you can tell by her picture....