Q:

What is the zero of the function d=70-2.4t

Accepted Solution

A:
Answer:  The "zero" is:  " 2 [tex]\frac{11}{12}[/tex] " ;  or, write as:  " 2.92 " ._____________________________________               →    " t = 2 [tex]\frac{11}{12}[/tex] " ;  or, write as:  " t = 2.92 " ._____________________________________Step-by-step explanation:_____________________________________Letting assume that this given function is supposed to be written as:  "distance as a function of time" ;  that is:            d(t) = 70 - (2.4)t ;   →  since distance, "d" is the dependent variable (cannot be "manipulated or controlled") and as such, belongs on the "y-axis"—as the "dependent variable" ;  whereas as time, "t" ; can be somewhat controlled (with respect to distance, at list as a starting point); and as such belongs on the "x-axis" as the "independent variable" .Since no "specific units" are given to us in the problem for Either "distance" or "time" ; we shall use the term "units" to describe their values.We have:  d(t) = 70 - (2.4)t ; Let us rearrange this: 70 - (2.4)t  ;   ↔   =  70  +  (- 2.4)t  ;  ↔   =  (-2.4)t  +  70 ; And rewrite the function:           →   d(t) = (-2.4)t + 70 ; To find the "zero" ; or "zeros" ; of this function; set "d(t)" equal to "zero" ; that is; "0" ; and solve for  the value(s) for "t" when "d(t)" = 0 :           →  0 = -2.4(t) + 70 ;  ↔    Rewrite as:           →  -2.4(t) + 70 = 0 ;  For simplicity;  let us multiply Each side of the equation by "10" ; to get rid of the decimal value:     10*[ (-2.4)t) + 70 ] = 10 * [0] ; From the left-hand side of the question:Note the "distributive property" of multiplication:     a(b + c) = ab + ac ; As such:    10* [-2.4(t) + 70 ] =     [10* -2.4(t)] + [10 * 70] =       -24t + 70 ; From the "right-hand side" of the equation:     10 * 0 = 0 . __________________________________So; we rewrite the equation as:   -24t + 70 = 0 ; __________________________________Solve for " t " ;    -24t + 70 = 0 ; Subtract "70" from Each Side of the equation;   -24t + 70 - 70 = 0 - 70 ;  to get:   -24t = -70 ; Now, let's multiply each side of the equation by "-1" ;        to get rid of the "negative values" ;   -1* (-24t) = -1(-70) ; to get:    24t = 70 ; Now, let's divide Each Side of the equation by "24" ; to isolate:  "t" ;  on one side of the equation; & to solve for "t" ;    24t / 24 = 70/24 ; to get:            t = 70/24 ; To simplify:  either:  1)  use calculator:  70 ÷ 24 = 2.916666666 ;                              →  round to:  2.92 ;                              →  t ≈ 2.92 ;  or:  " [tex]\frac{70}{24} =\frac{(70/2)}{(24/2)}=\frac{35}{12}[/tex] ; →  write as simplified improper fraction:  " t = [tex]\frac{35}{12}[/tex] " →  or:  write as mixed number:            →  " [tex]\frac{35}{12}[/tex] = 35 ÷ 12 =                               2 R 11                      12 ⟌35                           - 24                                1 1                      →  write as:  " 2[tex]\frac{11}{12}[/tex] " ;                                                                →  " t = 2 [tex]\frac{11}{12}[/tex] " ._____________________________________Hope this is helpful to you.         Wishing you the best!_____________________________________