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Samuel Hannah

University of Nottingham

Biography

I am a mathematics student at the University of Nottingham. I love using mathematics to solve problems in physics, especially those in the realm of black holes and quantum mechanics. I love how you can use techniques such as differential equations and statistical analysis, some of the core techniques in maths, to solve extremely complicated problems in other areas.

Education

MS Mathematics
University of Nottingham

Topics Covered

Derivatives
Differentiation
Differential Equations
Systems of Equations and Inequalities
Solve Linear Inequalities
Geometry Basics
Geometric Proof
Congruent Triangles
Equations and Inequalities
Complex Numbers
Linear Equations and Inequalities
Quadratic Equations
Polar Coordinates
Introduction to Conic Section

Samuel's Textbook Answer Videos

06:00
Thomas Calculus

You are planning to close off a corner of the first quadrant with a line segment 20 units long running from $(a, 0)$ to $(0, b)$ . Show that the area of the triangle enclosed by the segment is largest when
$a=b_{\text { . }}$

Chapter 4: Applications of Derivatives
Section 5: Applied Optimization
Samuel Hannah
00:51
Geometry A Common Core Curriculum

In Exercises $3-6,$ place the $\quad$ gure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Explain the advantages of your placement.
(See Example 1.)
a right triangle with leg lengths of 3 units and 2 units

Chapter 5: Congruent Triangles
Section 8: Coordinate Proofs
Samuel Hannah
00:58
Geometry A Common Core Curriculum

In Exercises $3-6,$ place the $\quad$ gure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Explain the advantages of your placement.
(See Example 1.)
an isosceles right triangle with leg length $\mathrm{p}$

Chapter 5: Congruent Triangles
Section 8: Coordinate Proofs
Samuel Hannah
01:52
Geometry A Common Core Curriculum

In Exercises $9-12,$ place the $\quad$ gure in a coordinate plane and 1 nd the indicated length.
a right triangle with leg lengths of 7 and 9 units;
Find the length of the hypotenuse.

Chapter 5: Congruent Triangles
Section 8: Coordinate Proofs
Samuel Hannah
02:01
Geometry A Common Core Curriculum

In Exercises $9-12,$ place the $\quad$ gure in a coordinate plane and 1 nd the indicated length.
a rectangle with a length of 5 units and a width of 4 units; Find the length of the diagonal.

Chapter 5: Congruent Triangles
Section 8: Coordinate Proofs
Samuel Hannah
03:34
Geometry A Common Core Curriculum

In Exercises 15 and $16,$ ind the coordinates of any unlabeled vertices. Then nd the indicated length(s).
Find ON and MN.

Chapter 5: Congruent Triangles
Section 8: Coordinate Proofs
Samuel Hannah
1 2 3 4 5 ... 25

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