Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

In a certain state the maximum speed permitted on freeways is 65 mi/h and the minimum speed is 40 mi/h. The fine for violating these limits is 15 dollars for every mile per hour above the maximum speed or below the maximum speed. Express the amount of the fine $ F $ as a function of the driving speed $ x $ and graph $ F(x) $ for $ 0 \le x \le 100 $.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$F(x)=\left\{\begin{array}{ll}15(40-x) & \text { if } 0 \leq x<40 \\ 0 & \text { if } 40 \leq x \leq 65 \\ 15(x-65) & \text { if } x>65\end{array}\right.$

03:31

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Harvey Mudd College

Baylor University

University of Nottingham

Idaho State University

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

09:16

In a certain state the max…

02:18

permitted on freeways 65. …

04:22

05:23

Speeding Tickets In a cert…

03:14

02:24

01:56

The graph of $y=f(x)$ give…

01:31

02:19

03:58

Speed Limits The graph of …

Alright. So here we have common highway speeds, max speed, 65 men speed 40 MPH. And we're told that there's a fine of $15 per mile too high or too low, meeting above 65 Um or below 40. So basically we can kind of come up with a piecewise function to describe basically the the fee. So basically what's gonna happen is we're gonna need to fill this in so are fine is going to be made up of $0. You pay, you don't have to worry about any. I won't put units on your be easier basically zero fine. So long as your um your mph is in between 40 and 65. Life is good there. However, if you have, if you're under 40 or your Greater than 65 MPH, that's when you're gonna need to pay. So we need to come up with again, kind of these formulas uh for the police officers, I guess giving the fine. So so what we can do is basically just create a line with the data that we need. Okay, so let's do first below so here we are going to look at below 40 mph. Okay, So basically know that if we're at 40 mph or fine is zero. If we're at 39 MPH, we're going to have to pay $15. So let's get to make that into a line for a line, you need a point and a slope. So the slope is going to be rise over run. So if I take this minus this, I will get 15 minus zero Over 39 -40. So that's -15. So our slope is -15, which makes sense. We know we're paying $15 per mile um And so let's create our lines. So our line would be y equals we need a uh basically a point and a slope. So let's do this, Remind You that -Y0 equal slope X -X0. So let's just use the first point. So why zero Equals -15 X -40. So that's it then that is our function. Um why equals you can if you wanted to drive through by the minus sign, you get 15 40 minus x. So this will be 1540- ax. Alright, let's go now and do the above 65 mph. The equation, Same idea. We can like get a couple of points. Let's see if I'm at 65, no fine. Yay If I'm at 66 uh $15 fine. And of course, if I keep in implementing a mile, I keep implementing by 15. So our slope will do rise over run. So I get 15 -0/66 -65. And that will give me 15 slope is 15 will do why minus r point equal slope Times X -65. So there we have it. We have our second expression that we need And we'll put it right in there. 15 X -65. Okay, So there is our uh solution, so hopefully that makes sense. Have an amazing day.

View More Answers From This Book

Find Another Textbook

08:14

(15 points) bottle of coke at room temperature (72"F) is placed in &…

01:22

11,In how many ways can 7 out 0f 10 mice arranged In row for genetics experi…

00:12

Use Angle Bisector Theorem to solve for x8(Sx)o(3r+12)92 - 3…

02:30

3. Deterine the area of each of the following polygons on the Geoboard dot p…

01:32

figure drawn in quadrant is reflected over the x-axis and then rotated about…

01:21

Identify the type of data that would be used to describe a favorite baseball…

00:03

If the base of a pyramid and a prism are congruent, is it always true, somet…

01:42

Enter a number; if necessary rounded to two decimals: The sum of the measure…

01:19

The graph of a quadratic function with vertex (-2, ~4) is shown In the figur…