You've been chosen to practice football with Odell! On the day of the practice, you leave your house at 3 AM, but due to heavy traffic, arrive at 5:23 AM. Odell noted that it took you \(x^4-2x^3+8x+127\) minutes to get to practice, for a positive integer You finish practice at 3 PM, and traffic is still quite nasty- taking you \(x^6-8x^3+x^2-2x+12\) minutes to get home. At what time do you arrive home?
+33616 Time taken in the morning is 143 minutes, so: \(x^4-2x^3+8x+127=143\)
Rewrite this as; \(x^4-2x^3+8x-16=0\)
This factors as: \((x-2)(x+2)(x^2-2x+4)\)
The only real positive solution is x = 2.
According to the equation you have for the return journey, time taken = \(2^6-8*2^3+2^2-2\times 2+12\rightarrow 12\) minutes!
This doesn't square with heavy traffic!! I think you might have written the second equation incorrectly.
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+425 Duration from 3 AM to 5.23 AM -> 2 h 23 min = 83 min
I use PhotoMath (best calculator)
Solving for x,
(x4 - 2x3 + 8x + 127 ) min = 83 min
Subtract 127.
x4 - 2x3 + 8x = -44
Expand the algebraic expression
x*x*x*x - 2*x*x*x + 8*x = -44
Simplify
Properties: Distributive property of subtraction/multiplication : (a-b)c = ac - bc
(x-2)x*x*x + 8*x = -44
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By using photo math, we found out that x could be one of the following:
x = -1.464914 ± 1.490055 i Option 1 + Option 2 -
x = 2.464914 ± 2.000378 i Option 3 + Option 4 -
Options 1 and 2 will yield -34 minutes - nonsense.
Options 3 and 4 yielded -470 minutes - nonsense too.
IDK if this makes sense...
+33616 Time taken in the morning is 143 minutes, so: \(x^4-2x^3+8x+127=143\)
Rewrite this as; \(x^4-2x^3+8x-16=0\)
This factors as: \((x-2)(x+2)(x^2-2x+4)\)
The only real positive solution is x = 2.
According to the equation you have for the return journey, time taken = \(2^6-8*2^3+2^2-2\times 2+12\rightarrow 12\) minutes!
This doesn't square with heavy traffic!! I think you might have written the second equation incorrectly.
.
