CPhill

(–6, –2)     y = 2x– 4

The slope of the given line  = 2

So.....the line perpendicular to this one will have a negative reciprocal slope, i.e., -1/2

So....using the point-slope form, we have

y -  (-2)  = (-1/2) ( x - (-6) )     simplify

y + 2  = (-1/2) ( x + 6)

y  + 2  = (-1/2)x - 3     subtract 2 from both sides

y = (-1/2)x - 5

The cost per pound = 70 cents

However.....since only 74/100  of a typical apple is edible.....

The cost per edible pound   = .70 * 100 / 74 = about 94.6 cents

Very nice, Misaki....!!!!!

Shades....I'm going to show that (b) can be made to look like (a) where k is replaced by  k + 1

All you would need to do is to reverse the steps  [if you wanted to ]

3(3^k - 1)/2 + [ 3^(k+1)]   =

Note 3^(k +1)  = 3*3^k........also....split the first term into two fractions

[3*3^k ]/ 2   - 3/2   +    [3*3^k]  =    

Get a common denominator in the third fraction by multiplying by 2 on top/bottom

[3*3^k ]/ 2   - 3/2   +    2*[3*3^k]/2

Put everything over 2

(3*3^k  - 3  + 2*[3*3^k] ) / 2  =

[3*3^k - 3  + 6*3^k] / 2  =

Combine like terms

[9*3^k - 3] / 2  =       

Factor out a  3

3 [3*3^k -1] / 2  =

Note again, 3*3^k  =  3^(k + 1)

3 [ 3^(k + 1)  - 1] / 2

I assume that we are multiplying these terms together  ???? ......if so......

Notice that this can be written as :

6 ^  [ 1/2 + 1/4 + 1/8 + 1/16.......]

And the sum, S, of this series can be found thusly :

S  =  a / [ 1 - r)    where a is the first term  = 1/2    and r is the common ratio between successive terms = 1/2

So  we have

S = (1/2) / ( 1 - 1/2)  =  (1/2) /(1/2)  = 1

6 ^  [ 1/2 + 1/4 + 1/8 + 1/16.......]   =

6^ [1]  =

6

(cos x)/(sec x -1) - (cos x)/(sec x + 1) = 2 cos^3 x csc^2 x

Get a common denominator of  (secx + 1) (secx - 1)  on the left

[cosx (secx + 1) - cosx (secx -1)  ]   / [ (secx + 1) (secx -1)]

Simplify

[1 + cosx - 1 + cosx] / [sec^2 x - 1]     

Remember   [ tan2x + 1 = sec^x] ....  so....  [ sec^x - 1  = tan^2x]

[2cosx] / [tan^2x] =

[2cosx] / [ sin^2x / cos^2x]  =

[2cosx] [cos^2x / sin^2x ]  =

2cos^3x  * [ 1 / sin^2x]  =

2cos^3x * csc^2x

And the left = the right

This says that

cos x = (0.92307692)

So.......taking the cosine inverse, we have

arccos (0.92307692) = x =  about 22.6°

If this is supposed to be

4x^2  - y     we have

4(3)^2  -  8   =

4*9  - 8  =

36  - 8   =

28

3 * (1/2)^x   =

3* (2^-1)^x  =

3 * 2^(-x)

6x^2+11x-35

In the form    ax^2 + bx - c.......the axis of symmetry is given by :

x = -b/2a       where b = 11 and a = 2   .....  so we have...

x = -11/ (2*6)  =  -11/12

So, this vertical line represents the axis of symmetry.