Mastering Homework Equations: Tips and Strategies for Success

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To master homework equations, it's essential to correctly plug in points into each equation and ensure all components, like constants, are accounted for. Solving a system of two equations is necessary to find variables such as a and b. It's important to verify if specific points satisfy the given equations, confirming their validity. Additionally, recognizing that multiple solutions may exist can guide the problem-solving process. Engaging with hints and collaborative problem-solving can enhance understanding and lead to successful outcomes.
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Homework Statement



q2.jpg


Homework Equations




given2.jpg


The Attempt at a Solution



as2edited.jpg
 
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Remember the response I posted earlier:

1. Plug the points (x, y) into each equation properly.
2. You got rid of the 1 and didn't use it.
3. You'll need to solve a system of 2 equations to find a, b.
 


Thank you :smile:

Is this correct?
ans1.jpg
 


chemic_23 said:
Thank you :smile:

Is this correct?
ans1.jpg
Check it yourself! It clearly has center (0,0). Do (3, \sqrt{7}) and -\sqrt{3},3) satisfy that equation? That is, are
\frac{3^2}{30}+ \frac{(\sqrt{7})^2}{10}= 1
and
\frac{(\sqrt{3})^2}{30}+ \frac{3^2}{10}= 1 ?

And don't forget that you were told there were two possible answers. What is the other answer?
 
I really don't have an idea... can you give me a hint please? I tried to equate both equation but still I got the same answer...:confused:
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

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