simple algebra questions, make it pdf

Math-UA.009. Written Homework

MATH-UA-009 — Algebra, Trigonometry and Functions

Professor Ross Flek

Name:

NetID:

Homework Assignment #9

Due Date: December 4th, 2023, 11:59 PM

• This homework should be submitted via Gradescope by 23:59 on the date

listed above. You can find instructions on how to submit to Gradescope on

our Campuswire channel.

• There are three main ways you might want to write up your work.

– Write on this pdf using a tablet

– Print this worksheet and write in the space provided

– Write your answers on paper, clearly numbering each question and part.

∗ If using either of the last two options, you can use an app such as

OfficeLens to take pictures of your work with your phone and convert

them into a single pdf file. Gradescope will only allow pdf files to be

uploaded.

• You must show all work. You may receive zero or reduced points for

insufficient work. Your work must be neatly organised and written.

You may receive zero or reduced points for incoherent work.

• If you are writing your answers on anything other than this sheet, you should

only have one question per page. You can have parts a), b) and c) on the

page for example, but problems 1) and 2) should be on separate pages.

• When uploading to Gradescope, you must match each question to the

page that your answer appears on. If you do not you will be docked a

significant portion of your score.

• When appropriate put a box or circle around your final answer.

• The problems on this assignment will be graded on correctness and completeness.

• These problems are designed to be done without a calculator. Whilst there is

nothing stopping you using a calculator when working through this assignment,

be aware of the fact that you are not permitted to use calculators on exams

so you might want to practice without one.

1

Math-UA.009. Written Homework

1. (6 points) Evaluate the following.

(a) (1 point) log7 (710 ) =

(b) (1 point) log3

1

27

=

1

(c) (1 point) log4

=

2

(d) (1 point) log4 (8) =

(e) (1 point) 5log5 (27)

(f) (1 point) eln(1/π)

2

Math-UA.009. Written Homework

2. (10 points) Expand the following completely. Your final results should have

no exponents or radicals.

(a) (2 points) ln (x2 y)

(b) (2 points) log7

2 !

x

y

3 2

xy

(c) (2 points) log2

z

(d) (2 points) log5

!

√ p

x 3 y2

z4

r

(e) (2 points) log4

3 2

4 x y

z4

!

3

Math-UA.009. Written Homework

3. (9 points) Combine the following into a single logarithm.

(a) (2 points) log2 (A) + log2 (B) − 2 log2 (C)

(b) (2 points) 4 log6 (y) −

1

log6 (z)

4

(c) (2 points) 4 log2 (x) −

1

log2 (x2 + 1)

3

(d) (3 points) log10 (5) + 2 log10 (x) + 3 log10 (x2 + 5)

4

Math-UA.009. Written Homework

4. (4 points) Solve the following basic equations for x.

(a) (1 point) log4 (x) = 3

(b) (1 point) ln (x) = −1

(c) (1 point) logx (16) = 4

(d) (1 point) log8 (x) =

1

3

5

Math-UA.009. Written Homework

5. (12 points) Solve the following equations for x

(a) (3 points) log5 (x) + log5 (x + 1) = log5 (20)

(b) (3 points) log13 (x) + log13 (x − 1) = log13 (4x)

(c) (3 points) log10 (x) + log10 (x − 3) = 1

(d) (3 points) log3 (x + 15) − log3 (x − 1) = 2

6

Math-UA.009. Written Homework

6. (4 points) Solve the following for x.

2

(a) (1 point) 8x = 83x+10

(b) (1 point) 51−x = 25

(c) (2 points) 9x = 272+x

7

Math-UA.009. Written Homework

7. (6 points) Graph the oriented angle in standard position. Classify each angle

according to which Quadrant its terminal side lies in.

(a) (1 point)

π

3

(b) (1 point) −

(c) (1 point)

π

6

7π

6

8

Math-UA.009. Written Homework

(d) (1 point) −

(e) (1 point)

11π

3

7π

2

(f) (1 point) −

15π

4

9

Math-UA.009. Written Homework

8. (12 points) Find the terminal point on the unit circle determined by the following real numbers t:

(a) (2 points) t =

5π

4

(b) (2 points) t =

4π

3

(c) (2 points) t =

5π

6

(d) (2 points) t = −

π

4

(e) (2 points) t = −

π

2

(f) (2 points) t = −π

10

Math-UA.009. Written Homework

9. (2 points) Find the area of a sector of a circle with central angle of 45◦ if the

radius of the circle is 4 m. Leave your answer in terms of π.

11