F(x)=X over x^3-2x^2+5x why will this have no zeros
1 answer:
If you evaluate directly this function at x=0, you'll see that you have a zero denominator.
Nevertheless, the only way for a fraction to equal zero is to have a zero numerator, i.e.
So, this function can't have zeroes, because the only point that would annihilate the numerator would annihilate the denominator as well.
Moreover, we have
So, we can't even extend with continuity this function in such a way that
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Let's remember some angle pair rules:
-> Co-Interior angles add up to 180º.
-> Alternating angles are equal.
-> Corresponding angles are equal.
-> Vertically opposite angles are equal.
-> Angles on a straight line add up to 180º.
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Knowing that, and knowing Angle 6 = 102º, you can easily find any of the 7 angles.
I will skip angle 1 for now, you'll understand why.
Angle 2 and Angle 6 are Corresponding, so Angle 2 must be 102º.
Angle 3 is Vertically Opposite to Angle 2, so Angle 3 must be 102º.
Angle 4 is Co-Interior to Angle 6, so we calculate it this way:
Angle 4 must be 78º.
Angle 1 is Vertically Opposite to Angle 4, so it must be 78º.
Angle 5 is Alternating to Angle 4, so Angle 5 must be 78º.
Angle 7 and Angle 5 are On A Straight Line, so Angle 7 is calculated this way:
Angle 7 must be 102º.
Angle 8 is Vertically Opposite to Angle 5, so it must be 78º.
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I wrote some parts in bold so you can refer to the rules I wrote above.
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<u>In summary:</u>
Angles 1, 4, 5, and 8 = 78º
Angles 2, 3, 6 and 7 = 102º