ElectricPavlov

Find two convenient points    -2,1    And   0,-3      Calculate slope as  (  y1-y2)/(x1-x2) = - 2

y = -2x + b        Sub in one point to calc b

1 = -2(-2) + b       b= -3

y= -2x -3

1/6 - 1/8 = 1/x    Solve for x

4/24  - 3/24=1/x

x = 24 hrs

(X+5)(x-1)= x^2+(a^2-5a+b+4)x + b       So b= -5      You can take it from here! 

128  = 2⁷

1/64  = 2^-6

(2⁷)^x+2  = (2^-6)^x     Equate the exponents

7x+14= -6x

x = -14/13

Rate x time = distance    (Or amount burned)

rate1   =   1candle/6hr= 1/6

rate 2 =   1 candle/ 4 hours = 1/4

amount remaining after x hours = 1 candle - rate * x

1- 1/6 *x  = 2 (1- 1/4 * x)

1- 1/6 x = 2 - 1/2 x

1= 2/6 x 

x = 3 hours

  ( I couldn't find the other posted answer)

3 hrs  x  1/6 =   1/2  Burned  =  1/2 left

3 hrs x1/4 = 3/4       Burned   = 1/4 left 

This has been posted before.... try a search to find the answer....

 As long as we are making a Wish List of filters....

toss out all questions that have a link to the actual question

toss out all postings that have multiple independent questions or links  !!  

Divide both sides by sin to get

Cot-1 = sqrt 2

arccot(1+sqrt2)=acot(2.414213562373095) = 22.5^o

Betsy must have one quarter and 4 nickels ( for Andrew to have a multiple of her quarters)

Andrew has 2 quarters and 2 nickels = 60 cents

X = Apple price

she paid 100% of x.  Plus 3% of x.     Or. 1.03x

1.03x = 19.16.   Divvied both sides by 1.03

x= 19.16/1.03=......