CPhill

Note that Everest  has the greatest positive value associated with it

So....it's the highest

a₁  =  3.8  = the first term

a₂₀ = 113.2  =the 20th term

So......

To find the common difference, d,  we have

a₂₀   =   a₁  + d ( 20 - 1)            filling in the blanks we have

113.2 =  3.8 + d (19)      subtract 3.8 from both sides

109.4  = d (19)    divide both sides by 19

d = 547/95   

For the second part...."d"  tells us  that the  number of carets (in millions)  is increasing by  547/95 ≈ 5.8 million carets per year  

Look at the first table.....which mountain has the largest positive associated with it  ???

s =  [ 15 + 18 + 21] / 2   =  54 / 2  =  27

Area =  √ [ 27  (27 - 15) (27 - 18) ( 27 - 21 ) ]  =

√[ 27 * 12 * 9 * 6 ] =

√ 27  * √12 * √9 * √6  =

3√3 * 2√3  * 3 * √6  =

18 * √3 * √3 * √6  =

18 * 3 * √6  =

54√6

No....Mariana's Trench

It  has the greatest negative value

I don't believe that I explained this very well

A better   method  is to just take the absolute value  of each negative

The one with the greatest absolute value  will be the deepest

abs (-11,033)  = 11,033

abs (-8,600) = 8600

abs (-10,882) = 10,882

abs (-7,725) = 7,725

Since 11,033  is the greatest absolute value.....the Marianas Trench is the  deepest

Hope that helped   !!!

Since the two gears are connected by a chain, the smaller gear will have the same linear velocity as the larger chain

The linear velocity per miunute is  60 * 17pi/6  =   170 pi    inches per minute

So.......to find the radius of the smaller  chain we have

170 pi  =  radius *  (radians per minute)

170 pi = radius  * ( 34pi/3  )         divide out pi

170  = rradius * (34/3)        multiply both sides by 3/34

170 (3/34)  =  radius  =  15  in

Note that the white sectors comprise 4/16  = 1/4  of the area of the  circle

So... 4 * ( 3pi/28  )  =  12pi/28  =  3pi/7  =  the area of the circle in square inches

Area =  pi * radius^2

So

3pi/7 = pi * radius^2            divide out  pi

3/7  = radius^2                 take the positive root

 √[ 3/7]  = radius ≈  0.65 in

Take the  greatest negative value  in the first table

Which is it???

Hint : remember that   -3  is a greater negative value than - 2

Let me know if you get stuck

Thx, MathsLlama  !!!

sec A  =  r  / x

r =  sqrt  [ (-6)^2  + 3^2 ]  = sqrt  [ 36 + 9 ] =  sqrt [45 ]  = 3sqrt (5)

So

sec A  =   3sqrt (5) / -6    =    - sqrt (5) / 2