Samuel H.

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

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

Thomas Calculus 12

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

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

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

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

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

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

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