[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) = 7Multiply by 2: 3 * (e + e-x​) - 4 * (e - e-x) = 14Expanding gives: 3 * e + 3 * e-x  - 4 * e+ 4 * e-x = 14Collecting terms: -ex + 7 * e-x = 14So:  ex - 7 * e-x + 14 = 0Since ex is not 0, we can multiply by it:ex * ex - 7 * e-x *e+ 14 * ex = 0e2x - 7 + 14 * ex = 0This is a quadratic in ex, and we can use the quadratic formula to obtain:ex = -7 +- 2 root 14But ex > 0, so we discount the negative root:ex = -7 + 2 root 14x = ln ( -7 + 2 root 14)Which can easily be checked with a calculator.

WU

Related Maths A Level answers

All answers ▸

Given that: y = 3x^2 + 6x^1/3 + (2x^3 - 7)/(3x^1/2), x > 0 Find dy/dx, give each term in its simplest form


use the substitution u=2+ln(x) to show that int(e,1(ln(x)/x(2+ln(x)^2))dx)=p+ln(q) , where p and q are rational numbers.


Find the derivative of sinx, use that to find the derivative of xsinx


How do you find the area between two lines?