CPhill

Sum    1 + 2 + 3 + ....+  385    =     [ 385] [386] / 2  =   74305

Sum  of  first n odds  =  [ ( odd integer + 1 )  / 2 ] ^2  =  ( [ 915 + 1 ] .2 )^2  =

( 916 / 2)^2  =  458^2  = 209764 

 [ 1 - sin^2 (x) ] / cot^2 (x)  =

[ cos ^2 (x) ] /  [ cos^2 (x) / sin^2(x) ]

sin^2 (x) =   sqrt (3)  / 3         take both roots

sin (x)  =   ± sqrt ( 1/ √ 3) 

So.....      arcsin (  sqrt ( 1/ √ 3)  )  ≈  0.8631       and    pi - 0.8631 ≈  2.2785

And   arcsin ( -  sqrt ( 1/ √ 3)  )  ≈   5.4201    and   pi + 0.8631  ≈  4.0047

The first answer is correct

10 years ago  he was  t - 10  years old....so.....

His current age   =   3 times his age 10 years ago

t  =   3 ( t - 10)

(6,1)   (5,4)

Find the slope

[ 4 - 1 ] / [ 5 - 6 ]   =   3 / -1  =  -3

So....using  (6, 1)  we have

y =  -3 (x - 6)  + 1      simplify

y =  -3x +  18  + 1

y = -3x +  19         add 3x to both sides

In standard form we have    3x + y  =  19

(6, -7)  =  (x, y)

In polar coordinates we will have    (x , y)  =  ( r , θ)

r =  sqrt ( x^2 + y^2)         θ =  arctan (y /x)   ....this is in rads

r = sqrt ( 6^2 +  (-7)^2 )  =  sqrt (36 + 49)  =  sqrt ( 85)

θ =  arctan (y /x)   =    arctan ( -7/6)  ≈  -0.862 

So   (6, -7)   =   ( sqrt (85), -0.862 )   in  polar form

See if you can do the second one....

3 + |1+p| = 12

subtract 3 from both sides

l 1 + p l  = 9

We really have these two equations......

1 + p   = 9                    and          1 + p  = -9

subtract 1 from both sides

p  = 8                  and                  p   = -10

And those are the two solutions

Ah....thanks, hectictar.... I was in a rush.....!!!!

5(41  - x) +  -7(y + x)      x = -2 and y  = -4

5 ( 41 - - 2)  +  -7 ( -2 + -4)  =

5 (43)  +   - 7 (-6)  =

215  + 42   =  

257

(4)7/8 + 7(5/12 + 1/8) - 10    =                     get a common denominator of 24 within the parentheses

28/8   + 7 ( 10/24 + 3/24)  - 10  =

7/2  + 7 ( 13 / 24)  - 10  =

7 / 2  +   91 / 24    - 10  =                    common denominator  = 24

84 / 24  +   91 / 24  -  240 / 24  =

175 / 24  -  240 / 24  =

-65 / 24  

Jenny has six basketball teams, each team needs new shoes for an upcoming tournament, and she spent 630 dollars on all the shoes thus far. Each pair of shoes cost 6 times more than last year’s pairs of shoes.

How much did last year’s shoes cost?

Last year's shoes must have 1/6 the cost of this year's....so   ...     (1/6) * (630)  =   [600 + 30] / 6 =

600/ 6  +  30 / 6    =

100 +  5  =

$105

12.5 km  =  12500 m  per hour

So

11250 / 12500   * 60 minutes  =   54 minutes

Here's one possibility.......connect the "vertices" of this figure.....this will form an equilateral triangle with sides = 4 units

And the area bounded by one side of this triangle and one side of the figure will be =

[ (1/2) (4)^2 [pi]/3   -   16 sqrt (3) / 4 ] =   [ (8/3)pi  - 4sqrt (3) ] 

And since there are three of these areas, the sum of these =  [8pi - 12 sqrt (3) ]     (1)

And the area formed formed by the equilateral triangle is   (4)^2 sqrt (3) / 4  =  4sqrt (3)    (2)

So......the area of the figure shown  =   (2)  - (1)  =    4sqrt (3)  - [ 8pi  - 12sqrt (3) ]  =  [16sqrt (3) - 8pi] square units

So   a = 16, b = 3  and c = -8  ....so a + b + c  = 11

Thanks to hectictar for catching my error....!!!!