I don't remember how they want you to do this in eighth grade, but I'm doing my sixth year of university and getting my Ph.D in Muon - catalyzed nuclear fusion. The equations we do are a bit harder but you can apply the process, called anti-derivative asymptote completion. Basically, you just want to find the least prime derivative of n and find its critical point. Now, here's where it gets tough. to find the least prime derivative (pD) of n you need to factor its hyperbolic value, done like so:
5n+1=5n-1
∑5n=1=∑/1(5n-1)
|R(gamma)5n=1^cos(-1)
pD(n)≈1.65 (I'm rounding this to the second decimal to keep this equation from getting out of hand, that's why you see the ≈ instead of =}
Now that we have the prime derivative, we simply need to multiply it the the inverse of the anti - integral of beta, which is actually so close to pi (π) in this question that we can substitute that instead.
x=1.65(π)
x=5.18 (again, I'm rounding to the second decimal here)
So there you go, hope I helped. Even if didn't learn this stuff, at least you can impress your teacher by showing him this. It's also very interesting that the anti - integral of beta (n) is so close to pi, you might want to ask your teacher about that, it's due to an interesting property of sub - hypocycloids, one of which is 5.25349856.
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I don't remember how they want you to do this in eighth grade, but I'm doing my sixth year of university and getting my Ph.D in Muon - catalyzed nuclear fusion. The equations we do are a bit harder but you can apply the process, called anti-derivative asymptote completion. Basically, you just want to find the least prime derivative of n and find its critical point. Now, here's where it gets tough. to find the least prime derivative (pD) of n you need to factor its hyperbolic value, done like so:
5n+1=5n-1
∑5n=1=∑/1(5n-1)
|R(gamma)5n=1^cos(-1)
pD(n)≈1.65 (I'm rounding this to the second decimal to keep this equation from getting out of hand, that's why you see the ≈ instead of =}
Now that we have the prime derivative, we simply need to multiply it the the inverse of the anti - integral of beta, which is actually so close to pi (π) in this question that we can substitute that instead.
x=1.65(π)
x=5.18 (again, I'm rounding to the second decimal here)
So there you go, hope I helped. Even if didn't learn this stuff, at least you can impress your teacher by showing him this. It's also very interesting that the anti - integral of beta (n) is so close to pi, you might want to ask your teacher about that, it's due to an interesting property of sub - hypocycloids, one of which is 5.25349856.