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Degree: Mathematics (Masters) - Oxford, St John's College University

About Me I am a Mathematics student at Oxford University, and have a real interest in helping those who are in a similar position to my own a few years ago. I am passionate about science and mathematics, and believe that a firm understanding of the basics is absolutely essential for mastering these subjects at higher level, and also provides fascinating insight on the world! Academic Qualifications I achieved 100% at GCSE and A Level Maths, and also over 99% in A Level Further Maths. In 2014 I sat and passed the MAT paper. Lessons During lessons, I can teach to any syllabus, and am very willing to explain whatever you find most useful, while ensuring that all necessary material is covered. I encourage two-way learning, and will provide opportunity for you to explain topics to me and to submit work for marking and feedback. I like to use several teaching methods, and believe that content should be demonstated with clear, relevant examples. Contact Me! You can send me a message through "WebMail", or book a "Meet the Tutor Session", using this website. Please let me know which exam and board you would like help with, as well as any specific topics.

#### Subjects offered

SubjectQualificationPrices
Further Mathematics A Level £30 /hr
Maths A Level £30 /hr

#### Qualifications

MathsA-levelA2A*
Further MathsA-levelA2A*
PhysicsA-levelA2A*
ChemistryA-levelA2A*
 CRB/DBS Standard No CRB/DBS Enhanced No

#### Ratings and reviews

5from 135 customer reviews

Ismaeel (Student) June 15 2017

Helped provide me with tips for C3.

Ismaeel (Student) June 3 2017

Helped show me multiple ways to answer a question.

Ismaeel (Student) April 25 2017

He helped me with a difficult topic.

Shenal (Student) April 6 2017

Good session learnt a lot!
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### [FP2] Solve: 3 cosh x - 4 sinh x = 7

First write cosh and sinh as exponentials, from their respective definitions: sinh x = 1/2 (ex  - e-x) cosh x = 1/2 (ex  + e-x​) So:   3 * 1/2 (ex  + e-x​) - 4 * 1/2 (ex  - e-x) = 7 Multiply by 2:  3 * (ex  + e-x​) - 4 * (ex  - e-x) = 14 Expanding gives:   3 * ex  + 3 * e-x  - 4 * ex + 4 * e...

First write cosh and sinh as exponentials, from their respective definitions:

sinh x = 1/2 (e - e-x)

cosh x = 1/2 (e + e-x​)

So:   3 * 1/2 (e + e-x​) - 4 * 1/2 (e - e-x) = 7

Multiply by 2:  3 * (e + e-x​) - 4 * (e - e-x) = 14

Expanding gives:   3 * e + 3 * e-x  - 4 * e+ 4 * e-x = 14

Collecting terms:   -ex + 7 * e-x = 14

So:   ex - 7 * e-x + 14 = 0

Since ex is not 0, we can multiply by it:

ex * ex - 7 * e-x *e+ 14 * ex = 0

e2x - 7 + 14 * ex = 0

This is a quadratic in ex, and we can use the quadratic formula to obtain:

ex = -7 +- 2 root 14

But ex > 0, so we discount the negative root:

ex = -7 + 2 root 14

x = ln ( -7 + 2 root 14)

Which can easily be checked with a calculator.

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2 years ago

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