Math 120 B, Spring 2018Final Exam

Wednesday, June 6, 2018

Name:

UW email address:

Problem 1 12Problem 2 12Problem 3 12Problem 4 10Problem 5 12Problem 6 12

Total 70

• There are 6 problems spanning 6 pages (your last nonempty page should be numbered as 6).Please make sure your exam contains all these questions.

• You are allowed to use a TI-30x IIS Calculator and one double sided hand-written 8.5 by 11inch page of notes.

• You must show your work on all problems (unless explicitly instructed otherwise). The cor-rect answer with no supporting work may result in no credit. Put a box around your FINALANSWER for each problem and cross out any work that you don’t want to be graded. Giveexact answers wherever possible.

• Any student found engaging in academic misconduct will receive a score of 0 on this exam.

• You have 110 minutes to complete the exam. Budget your time wisely. Do not spend too muchtime on an individual problem unless you are done with all the rest.

GOOD LUCK!

1. (12 pts.) All parts are independent.

(a) Write the equation of the line perpendicular to 2x+3y�1 = 0 that passes through the point(2, 3).

(b) Write an equation for the lower semicircle of radius 2 centered at (4,3).

(c) Find a linear-to-linear rational function whose graph passes through the point (2,3) and hashorizontal asymptote y = 2 and vertical asymptote x = �4.

1

2 351 0 3y I 2x y x

slope of perpg 3 x 2

Cx 4ft Cy35 43 y312 4 Cx 45

y 3 14 45y 3 4 45

y 1127 nov as y A A 2was C 4

ye2 134

3 222143 3 13 18 4

13 14

fix2 144

2. (12 pts.) The parts are independent.

(a) Find a formula for the inverse of the function f(x) =2x+ 4

x� 3.

(b) Solve the equation:

ln

✓2x

x� 5

◆= 3.

(c) Solve the equation:3 · 43x+7 = 1

2

ya213 yx 31 2 4 yx 31 2 4

Ky 2 3yt43yt4_

So f 63 1 Y 2

x 2

but 3 e3 2x e3 5

x.ee e32

O

3.43 7 1 listen 43 74

3 7 ln4 his

3xt73

ln4

2. (12 pts.) You are given the functions g(x) = 2x�4 and f(x) =

(5�

p9� (x� 3)2, 3 x 6

2� (x� 3)2, x 3.

(a) Write a multipart rule for the function g(f(x))

(b) Write a multipart rule for the function f(g(x))

(c) Solve the equation f(g(x)) = 3

2

g gas2 5 37 4 3 Execs

z 2 Cx 3712 4 xE3

pregame5 9 52 3 E ex 4 6

2 2 4 35 2 4 E3

5 FF EE2 2 75 x EZz

5 0 77 3

a 912 772 22

12 712 5 2 7 155

x 71152

x 7t bee 7 EICE2 2 712 3 as 2

2 7 1 no Sol

4. (10 pts.) You are standing on flat ground some distance away from a skyscraper. Climbingup the skyscraper, 150 feet from the top, is a gorilla. From where you stand, you measure theangle of elevation from the ground to the gorilla, and you find it to be 70�. Then you measurethe angle of elevation from the ground to the top of the skyscraper. It’s 75�. How tall is theskyscraper?

4

5. (12 pts.) [Autumn 2016] Essun is running 3 meters per second clockwise around a circulartrack. From her starting point, it takes her 9 seconds to reach the northernmost point of thetrack, and then an additional 13 seconds to reach the easternmost point of the track. After 2minutes, how far east is Essun from the westernmost point of the track?

5

f

I I E ransradius31 5 786rads pm

Initial angle

Iz g Iz do 22126

After Zurin

ex26 120 9817

26so x coovd 8

cos 9 17

18.58

Distance east 7t 18.58

43.4 ft

6. (12 pts.) Stanley checked the concentration of glucose in his blood several times during the daytoday and found out that it was at its lowest level of 65 mg/dl at 8 am and at its highest levelof 125 mg/dl at 2pm. Assume that the concentration of glucose in Stanley’s blood is modeledby a sinusoidal function and that there was no other highest or lowest value between 8 am and2 pm.

(a) Determine a sinusoidal function that gives Stanley’s blood glucose today, t hours aftermidnight.

(b) Stanley feels dizzy when his blood glucose is below 80 mg/dl. For how long did Stanleyfeel dizzy today, in the time interval between 6 am and 11 pm?Hint: drawing a graph of the function in part (a) can help.

6

As maxtfin 65 30

D wagtails 1252652 95

By 1,4 8 6 as 13 122pm

x of Max By 14 11

pct 30 sin t 11 95

i i i30 sin 2 t u t 95 80

sin 72Ct n I2 t 117 2 Kats in II t u f Uca ft 11 12k t 12kt102 1 11 2 kata sinCf t Il 2kmen tft 11 12kt Gt 1Sol's 10 22 6,18 t 12kt 18

Total 8 hours