Question

very simple: simplifying

Answer 1

can this be simplified any further?

Answer 2

\[t(r) = \frac{ 50 + 4r }{ r }\]

Answer 3

u can distribute r like this:
50/r+4r/r = 50/r + 4
but not much simplified.

Answer 4

thats it. its correct

Answer 5

so it'd be like \[t(r) = \frac{ 50 }{ r } + 4\]
?

Answer 6

yes

Answer 7

yup .

Answer 8

Thank you!!

Answer 9

welcome :)

Answer 10

Okay so I'm lost now... here's why

Answer 11

This equation is from this original word problem:

"r
is the distance in miles, and r is the rate in miles per hour.
a. Sydney drives 10 mi at a certain rate and then drives 20 mi at a rate 5 mi/h faster than the initial rate. Write expressions for the time along each part of the trip. Add these times to write an equation for the total time in terms of the initial rate, t total (r) ."

Answer 12

So I got the equation.. now question B asks me,

"Determine the reasonable domain and range and describe any discontinuities of
t total (r) . Graph ttotal (r) on your graphing calculator."

Answer 13

how do i graph it on the calculator? Do i just plug in y = (50/r)+4 ?

Answer 14

it will be discontinuous at zero

Answer 15

what do you mean?

Answer 16

at r=0 50/r becomes infinite, and infinite+4 is infinite, so discontinuous

Answer 17

physically you will take infinite time to travel

Answer 18

but what is the domain and range?

Answer 19

domain is (-infinity 0),(0 infinity)
range is (4, infinity)

Answer 20

I'm confused on how you wrote the domain, is it (-infinity 0, 0 infinity) ?

Answer 21

kind a ya. but you will exclude 0 and infinity, all elements are allowed in between them

Answer 22

thank you!

Answer 23

I still dont know how to graph the equation though.. which leaves me clueless for the next question :\

Answer 24

"At what rate, to the nearest mi/h, must Sydney drive if the entire 30 mi must be covered in about 45 min? Find the answer using the graph and using algebraic methods."

Answer 25

wait ill draw