Need a bit of help solving the following equations.
sqrt(5/8-(sqrt(5)/8))LH+cos (43pi/180)RH = 0
and
1/4(1+sqrt(5)LH+sin(43pi/180)RH-2g=0
What is the best way to start when trying to combine these equations?
Thanks
what do the LH and RH mean?
Just my variables, its to find tension in two strings. I made them LH and RH in my drawings.
I could have easily put T1 and T2 come to think of it...
I'll just use x and y, giving
√(5/8-(√5/8))x+cos(43°)y = 0
0.58778x + 0.73135y = 0
1/4(1+√5)x+sin(43°)y-2g=0
0.80902x + 0.68200y = 19.6
Now just solve by your favorite method (I suggest substitution).
Thanks steve, out of interest ive gotten a negative value for one. Since im looking for the tension in L and R strings. That doesnt seem right in which case ive made a mistake in getting to this point.
To combine these equations, you can follow these steps:
1. Simplify each equation separately to make them easier to work with.
2. Express both equations in terms of the same variables.
3. Set the two simplified equations equal to each other.
4. Solve the resulting equation for the unknown variable.
Let's go through these steps:
Equation 1: sqrt(5/8 - sqrt(5)/8)LH + cos(43pi/180)RH = 0
Step 1: Simplify the equation
- Simplify the expression inside the square root: 5/8 - sqrt(5)/8 = (5 - sqrt(5))/8
- So, the equation becomes: sqrt((5 - sqrt(5))/8)LH + cos(43pi/180)RH = 0
Equation 2: 1/4(1 + sqrt(5)LH + sin(43pi/180)RH) - 2g = 0
Step 1: Simplify the equation
- Distribute 1/4 to the terms inside the parentheses: 1/4 + (sqrt(5)/4)LH + (sin(43pi/180)/4)RH - 2g = 0
- Simplify the fraction: sin(43pi/180) is the same as sin(43 degrees), which can be approximated as 0.682
- So, the equation becomes: 1/4 + (sqrt(5)/4)LH + 0.682RH - 2g = 0
Step 2: Express both equations in terms of the same variables
- It seems LH and RH are common variables in both equations, so no changes are needed.
Step 3: Set the two simplified equations equal to each other
- Equate the expressions on the left-hand side of both equations: sqrt((5 - sqrt(5))/8)LH + cos(43pi/180)RH = 1/4 + (sqrt(5)/4)LH + 0.682RH - 2g
Step 4: Solve the resulting equation for the unknown variable
- Rearrange the equation to isolate the unknown variables, LH and RH, on one side:
sqrt((5 - sqrt(5))/8)LH - (sqrt(5)/4)LH + cos(43pi/180)RH - 0.682RH = 1/4 - 2g
- LH and RH should now be treated as common variables. To solve for them, you'll need additional information or constraints, as there are multiple variables in the equation.
Following these steps should help you combine the equations and move towards finding a solution. If you have further constraints or information, please provide them, and I'll be happy to assist you further.