# Simultaneous equation for two unknowns

• Apr 13th 2010, 11:37 PM
alis88
Simultaneous equation for two unknowns
Hello

Please could someone rearrange and show the steps for solving simultaneous equations for 2 unknowns, please? The unknowns are r and theta.

Equation 1 is

IB = (2r^2 / (17 x 10^3) x Na) (21 - 11sin^2 theta)

Equation 2 is

IB* = (r^2 / (5 x 10^3) x Na) (21 - 8sin^2 theta)

Thank you very much.

Kind regards,

A
• Apr 13th 2010, 11:51 PM
sa-ri-ga-ma
What is IB, IB* and Na?
• Apr 13th 2010, 11:55 PM
alis88
IB = 2.841 x 10^-47

IB* = 5.45 x 10^-47

NA = 6.022 x 10^23
• Apr 14th 2010, 12:07 AM
sa-ri-ga-ma
IB = (2r^2 / (17 x 10^3) x Na) (21 - 11sin^2 theta)

Equation 2 is

IB* = (r^2 / (5 x 10^3) x Na) (21 - 8sin^2 theta)

IB/IB* = 2*5*(21 - 11sin^2 theta)/17(21 - 8sin^2 theta)
IB17(21 - 8sin^2 theta) = IB*2*5*(21 - 11sin^2 theta)
Substitute the values of IB and IB* and solve for sinθ and then θ. Using this value of θ, find the value of r.
• Apr 14th 2010, 12:14 AM
alis88
BRLLIANT- thank you so much, very clear and well-written!
• Apr 14th 2010, 12:24 AM
alis88
Do you know how to rearrange for theta? So far I have:

2.841 x 10^-47 x 17 x (21 – 8sin^2θ) = 5.45 x 10^-47 x 2 x 5 x (21 – 11 sin^2θ)

4.8297 x 10^-46 x (21 – 8sin^2θ) = 5.45 x 10^-46 x (21 – 11 sin^2θ)

0.88611 x (21 - (8sin^2) x θ) = 21 - (11sin^2) x θ
• Apr 14th 2010, 01:02 AM
sa-ri-ga-ma
Quote:

Originally Posted by alis88
Do you know how to rearrange for theta? So far I have:

2.841 x 10^-47 x 17 x (21 – 8sin^2θ) = 5.45 x 10^-47 x 2 x 5 x (21 – 11 sin^2θ)

4.8297 x 10^-46 x (21 – 8sin^2θ) = 5.45 x 10^-46 x (21 – 11 sin^2θ)

0.88611 x (21 - (8sin^2) x θ) = 21 - (11sin^2) x θ

11sin^2(θ) - 0.88611*8sin^2(θ) = 21 - 0.88611 x 21
sin^2θ(11 - 8*0.88611) = 21(1 - 0.88611)
Now proceed.
• Apr 14th 2010, 07:03 AM
alis88
I've found theta and it equals 51.

Please may you help rearrange the equation for r? I am not very good at handling sin^2. Thank you, and sorry for my slowness.
• Apr 14th 2010, 07:13 AM
sa-ri-ga-ma
Quote:

Originally Posted by alis88
I've found theta and it equals 51.

Please may you help rearrange the equation for r? I am not very good at handling sin^2. Thank you, and sorry for my slowness.

IB = (2r^2 / (17 x 10^3) x Na) [21 - 11sin^2(θ)]
Substitute the values of IB, Na and sin^2(51) and solve for r.
Find sin(51) in the calculator and square it.
• Apr 14th 2010, 08:09 AM
alis88
r = 1.540 x 10^-10

did you get the same? x