sinh(x-3)=4
2007-07-25 21:39:05 · 5 answers · asked by babam11218716 1 in Science & Mathematics ➔ Mathematics
sinh(x) = (1/2)(e^x - e^-x)
sinh(x-3) = (1/2)(e^(x-3) - e^-(x-3))
(1/2)(e^(x-3) - e^(-x-3)) = 4
(e^(x-3) - e^-(x-3)) = 8
Let y = e^(x-3)
Then e^-(x-3) = 1/y
y - 1/y = 8
y^2 - 1 = 8y
y^2 - 8y - 1 = 0
y = [8±sqrt(64+4)]/2
= [8±sqrt(68)]/2
= 4±sqrt(17)
y = e^(x-3)
y must be positive
Therefore
y = 4+sqrt(17)
= 4+sqrt(17)
(x-3) = ln(4+sqrt(17))
x = 3 + ln(4+sqrt(17))
≈ 5.095
2007-07-25 21:53:36 · answer #1 · answered by gudspeling 7 · 0⤊ 1⤋
sinh-1 4+3
2007-07-25 22:37:23 · answer #2 · answered by Anonymous · 0⤊ 1⤋
x=7
2007-07-25 21:42:03 · answer #3 · answered by josh r 1 · 0⤊ 3⤋
x = 3 + arcsinh 4 â 5.095.
To get exact values, we have
(e^(x-3) - e^(-(x-3))) / 2 = 4
so e^(x-3) - e^(-(x-3)) = 8
Let u = e^(x-3), then e^(-(x-3)) = 1/u and we have
u - 1/u = 8
<=> u^2 - 8u - 1 = 0
<=> u = (8 ± â68) / 2
Since u > 0 we must have u = (8 + â68) / 2 = 4 + â17.
So x-3 = ln u
=> x = 3 + ln (4 + â17)).
2007-07-25 21:48:23 · answer #4 · answered by Scarlet Manuka 7 · 1⤊ 1⤋
(x-3)=4
+3---+3
x=7
2007-07-25 21:54:22 · answer #5 · answered by Phill 4 · 0⤊ 2⤋