MYTUTOR SUBJECT ANSWERS

1133 views

[FP2] Solve: 3 cosh x - 4 sinh x = 7

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.

William U. A Level Physics tutor, GCSE Physics tutor, A Level Maths t...

2 years ago

Answered by William, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

423 SUBJECT SPECIALISTS

£20 /hr

Scott E.

Degree: Computer Science (Bachelors) - Warwick University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Computing

“Maths and Computer Science lover. With a patient, thorough and friendly teaching style.”

£20 /hr

Paul D.

Degree: PhD in Mathematical Physics: Noncommutative Geometry and Quantum Gravity (Doctorate) - Nottingham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I'm a Mathematics Physics PhD student, studying at The University of Nottingham. I'm an avid rock climber and live for the great outdoors.”

MyTutor guarantee

£20 /hr

Tinashe M.

Degree: Chemical Engineering MEng (Integrated Masters) - Newcastle University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“I love maths, chemistry and biology and my passion for these subjects is something that will help teach students.”

MyTutor guarantee

About the author

William U.

Currently unavailable: for new students

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

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“About MeI 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 aboutscience and mathematics, and believe that a firm underst...”

You may also like...

Other A Level Maths questions

Differentiate expressions of form Ax^b where A and b are constants and x is a variable

Show that the derivative of ln(x) = 1/x

The line L has equation y = 5 - 2x. (a) Show that the point P (3, -1) lies on L. (b) Find an equation of the line perpendicular to L that passes through P.

When given an equation in parametric form, how can you figure out dy/dx?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok