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2 answers:
Answer:
<h2>m∠EHF = m∠EDF = 55°</h2>Step-by-step explanation:
Look at the pictures.
(the picture 1)
Inscribed angle and central angle.
(the picture 2)
In a circle, central angle is two times larger than inscribed angle that intercept the same arc.
In a circle, inscribed angles that intercept the same arc are congruent.
We have the central angle C = 110°. The inscribed angle EHF is two times smaller than ∠C. Therefore m∠EHF = 110° : 2 = 55°.
The inscribed angles EHF and EDF that intercept the same arc. Therefore are congruent. m∠EHF = m∠EDF.
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Answer:
Between 1000 and 5000 snowboards will make the function AP(x) >0.
Step-by-step explanation:
Since x can only take possitive values, we have that AP(x) = P(x)/x > 0 if and only if P(x) > 0.
In order to find when P(x) > 0, we find the values from where it is 0 and then we use the Bolzano Theorem.
P(x) = R(x) - C(x) = -x²+10x - (4x+5) = -x²+6x - 5. the roots of P can be found using the quadratic formula:
Therefore, P(1) = P(5) = 0. Lets find intermediate values to apply Bolzano Theorem:
- P(0) = -5 < 0 ( P is negative in (-∞ , 1) )
- P(2) = -4+6*2-5 = 3 > 0 (P is positive in (1,5) )
- P(6) = -36+36-5 = -5 < 0 (P is negative in (5, +∞) )
The production levels that make AP(x) >0 are between 1000 and 5000 snowboards (because we take x by thousands)