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Blizzard [7]
3 years ago
13

An entrepreneur estimates that the total profit (profit = total revenue minus total cost) from his proposed company will be give

n by the function P(x) = x3 – 4x2 + 3x – 12, where P is in hundreds of dollars and x is the number of years elapsed after the company starts operations. In how many years (x) will the company break even (no profit, no loss)?
Mathematics
1 answer:
EastWind [94]3 years ago
4 0
P ( x ) = x³ - 4 x² + 3 x - 12 = 
= x² ( x - 4 ) +3 ( x - 4 ) = ( x - 4 ) · ( x² + 3 ) 
x - 4 = 0,  x = 4
x² + 3 = 0,  x² = - 3 ( there is no real solution )
Answer: In 4 years the company will break even.
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If arc XV = 80° and arc YX = 120°, what is the measure of ?YUV?
kramer

Answer:

The measure of angle YUV is 40°

Step-by-step explanation:

Consider the diagram of this question is attached below,

Where, Tangent line UV and secant XY intersect outside the circle at U,

Since,

\widehat{XV}+\widehat{XY}+\widehat{VY}=360^{\circ}

We have,

\widehat{XV}=80^{\circ}, \widehat{XY}=120^{\circ}

\implies 80^{\circ}+120^{\circ}+\widehat{VY}=360^{\circ}

200^{\circ}+\widehat{VY}=360^{\circ}

\widehat{VY}=360^{\circ}-200^{\circ}=160^{\circ}

Since, the measure of intercepted angle outside the circle is half of the difference of measure of intercepted arcs,

\implies m\angle YUV = \frac{\widehat{VY}-\widehat{XV}}{2}

=\frac{160^{\circ}-80^{\circ}}{2}

=\frac{80^{\circ}}{2}

=40^{\circ}

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