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
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insufficient work. Your work must be neatly organised and written.
You may receive zero or reduced points for incoherent work.
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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.
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• 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
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