Math  /  Algebra

QuestionLeila is walking. D(t)D(t), given below, is her distance in kilometers from Glen City after tt hours of walking. D(t)=12.84tD(t)=12.8-4 t
Complete the following statements.
Let D1D^{-1} be the inverse function of DD. Take xx to be an output of the function DD. That is, x=D(t)x=D(t) and t=D1(x)t=D^{-1}(x). (a) Which statement best describes D1(x)D^{-1}(x) ? The reciprocal of her distance from Glen City (in kilometers) after walking xx hours. The amount of time she has walked (in hours) when she is xx kilometers from Glen City. Her distance from Glen City (in kilometers) after she has walked xx hours. The ratio of the amount of time she has walked (in hours) to her distance from Glen City (in kilometers), xx. (b) D1(x)=D^{-1}(x)= \square \square (c) D1(8.4)=D^{-1}(8.4)= \square

Studdy Solution

STEP 1

1. D(t)=12.84t D(t) = 12.8 - 4t represents Leila's distance from Glen City after t t hours.
2. D1(x) D^{-1}(x) is the inverse function of D(t) D(t) .
3. We need to find the inverse function and evaluate it for specific values.

STEP 2

1. Interpret the meaning of the inverse function D1(x) D^{-1}(x) .
2. Calculate the inverse function D1(x) D^{-1}(x) .
3. Evaluate the inverse function at a specific value.

STEP 3

The inverse function D1(x) D^{-1}(x) represents the amount of time t t that has passed when Leila is x x kilometers from Glen City.
The correct statement is: "The amount of time she has walked (in hours) when she is x x kilometers from Glen City."

STEP 4

To find the inverse function, solve the equation D(t)=x D(t) = x for t t .
Given: D(t)=12.84t D(t) = 12.8 - 4t
Set D(t)=x D(t) = x : x=12.84t x = 12.8 - 4t
Solve for t t : 4t=12.8x 4t = 12.8 - x t=12.8x4 t = \frac{12.8 - x}{4}
Thus, the inverse function is: D1(x)=12.8x4 D^{-1}(x) = \frac{12.8 - x}{4}

STEP 5

Evaluate D1(8.4) D^{-1}(8.4) .
Substitute x=8.4 x = 8.4 into the inverse function: D1(8.4)=12.88.44 D^{-1}(8.4) = \frac{12.8 - 8.4}{4}
Calculate the result: D1(8.4)=4.44=1.1 D^{-1}(8.4) = \frac{4.4}{4} = 1.1
The solutions are: (a) "The amount of time she has walked (in hours) when she is x x kilometers from Glen City." (b) D1(x)=12.8x4 D^{-1}(x) = \frac{12.8 - x}{4} (c) D1(8.4)=1.1 D^{-1}(8.4) = 1.1

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord