Help Needed: Solving x and Simplifying Equations

  • MHB
  • Thread starter bigpoppapump
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    Simplifying
In summary, the conversation revolved around two math problems that the person was having trouble with and a word problem that they needed help converting into an equation. With the help of others, they were able to solve the math problems and were given guidance on how to approach the word problem. The equation to model the current in the circuit was also provided.
  • #1
bigpoppapump
5
0
having trouble with the following, if anyone could provide assistance it would be appreciated.

Solve for x:

1619175324265.png


and

Simplify the following:
1619175453718.png
 

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  • #2
Beer soaked request follows.
bigpoppapump said:
having trouble with the following, if anyone could provide assistance it would be appreciated.

Solve for x:

View attachment 11112

and

Simplify the following:
View attachment 11113
Please show us what you have tried and exactly where you are stuck.

We can't help you if we don't where you are stuck.
 
  • #3
https://mathhelpboards.com/attachments/1619175324265-png.11112/
change $\sin^2{x}$ to $(1-\cos^2{x})$ and solve the resulting quadratic equation for $\cos{x}$https://mathhelpboards.com/attachments/1619175453718-png.11113/

change the cosecant and cotangent to factors in terms of sine & cosine, then simplify
 
  • #4
skeeter said:
https://mathhelpboards.com/attachments/1619175324265-png.11112/
change $\sin^2{x}$ to $(1-\cos^2{x})$ and solve the resulting quadratic equation for $\cos{x}$https://mathhelpboards.com/attachments/1619175453718-png.11113/

change the cosecant and cotangent to factors in terms of sine & cosine, then simplify
Thank you. This helps, I was stuck but I have a good idea on how to solve both of these. Will work on it tonight.
 
  • #5
I have managed to solved these problems with confidence which is great. Thanks for your guidance.

I have a word problem that I’m finding it difficult to convert into an equation. Could some direction be given so I can then run with it and complete.

The question is...
An electrical circuit runs at 50Hz at 0.5amps. Due to a lag in the switch, the first maximum current is reached at 6milliseconds. Assuming no variation, find an equation to model the current in this circuit using time in milliseconds.
 
  • #6
frequency is the reciprocal of period (time to complete one cycle of AC)

$T = \dfrac{1}{50} = 0.02 \text{ sec } = 20 \text{ milliseconds}$

current flow (with no lag) as a function of time in milliseconds ...

$A = 0.5 \sin\left(\dfrac{\pi}{10} \cdot t \right)$

For that period, the sinusoidal graph of current would peak at $\dfrac{T}{4} = 5 \text{ milliseconds}$

Due to the lag, there is a 1 millisecond horizontal shift in the graph ...

In future, please start a new problem with a new thread.
 
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Related to Help Needed: Solving x and Simplifying Equations

1. What is the difference between solving and simplifying equations?

Solving an equation means finding the value of the variable that makes the equation true. Simplifying an equation means reducing it to its simplest form by combining like terms and using algebraic rules.

2. How do I know when to use which method?

The method you use depends on the type of equation you are working with. If the equation has only one variable, you can solve it by isolating the variable on one side of the equation. If the equation has multiple variables, you may need to simplify it first before solving.

3. What are the common mistakes to avoid when solving and simplifying equations?

Some common mistakes to avoid include forgetting to distribute negative signs, not following the correct order of operations, and making errors in simplifying fractions. It is important to double check your work and use parentheses when necessary.

4. Can equations have more than one solution?

Yes, equations can have more than one solution. This is known as having infinite solutions. It means that any value you plug in for the variable will make the equation true.

5. How can I check if my solution is correct?

You can check your solution by plugging it back into the original equation and seeing if it makes the equation true. Another way is to graph the equation and see if the point representing your solution lies on the graph.

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