# Sarah is driving. Her distance in km from Tempe after t hours of driving is given by: x = D(t) = 13 + 57ta. Determine a formula in terms of x for: t = D^-1(x)b. Compute D^-1(70)c. In the expression D^-1(x) :what quantity (distance or time) does the x represent?what quantity (distance or time) does the entire D^-1(x) represent?d. Which of the following statements best describes D^-1(x)? a) the ratio of Sarah's distance from Tempe (in km) to x hours of driving. b) the reciprocal of Sarah's distance from Tempe (in km) after x hours of driving. c) the number of hours of driving needed for Sarah to be x km from Tempe. d) Sarah's distance in km from Tempe after x hours of driving.

• Subject:

Mathematics
• Author:

brielle
• Created:

7 months ago

The solutions for your four question problem are:

a) t = D^-1(x) =  (1/57)*x -(13/57)

b) t = D^-1(x) =  1 h

c) D^-1(x) represents time.

d) The number of hours of driving needed for Sarah to be x km from Tempe. (option (c))

Step-by-step explanation:

a) Determine a formula in terms of x for: t = D^-1(x)

The distance in km from Tempe after t hours of driving is given by

x = D(t) = 13 + 57t.

We just need to find the value  t function of x

x = 13 + 57*t

x -13 =  57*t

57*t  = x -13

t = (1/57)*x -(13/57)

We can see the plots of both equation in the picture below.

b) Compute D^-1(70)

Once we find the expression for D^-1(x)

We substitute for x = 70 km

t = D^-1(x) =  (1/57)*x -(13/57)

t = D^-1(x) =  (1/57)*(70) -(13/57)

t = D^-1(x) =  (70/57) -(13/57)

t = D^-1(x) =  (1.228) -(0.228)

t = D^-1(x) = 1 h

c) In the expression D^-1(x) :  what quantity (distance or time) does the x represent?  what quantity (distance or time) does the entire D^-1(x) represent?

x represents Distance in both equations (D(t), and D^-1(x))

t represents Time in both equations (D(t), and D^-1(x))

Since t = D^-1(x),

D^-1(x) represents time.

d) Which of the following statements best describes D^-1(x)?

The number of hours of driving needed for Sarah to be x km from Tempe.

Since, t = D^-1(x), and t represents the amount of time elapsed since Sarah, parted from Tempe, the correct answer is option (c)

The expression for D^-1(x) can be found in the previous answers

t = D^-1(x) =  (1/57)*x -(13/57)

The input is x (distance) and the output is t (time) a. t = (x - 13)/57 b. t = 2.7 hrs c. x represents the distance in km from Tempe after t hours of driving. D^-1(x) represents the number of hours of driving needed for Sarah to be x km from Tempe. d. c) the number of hours of driving needed for Sarah to be x km from Tempe.

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