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Naya [18.7K]
2 years ago
8

Polynomial function f(x) has only 3 real roots. It has a root at −3 and a double root at 4. It has a y-intercept of 24. Which eq

uation represents f(x) ?
Mathematics
1 answer:
Oduvanchick [21]2 years ago
7 0

Answer:

f(x) = (1/2) (x + 3)(x - 4)^2

Step-by-step explanation:

f(x) = C(x + 3)(x - 4)^2

y-intercept = f(0) = C(3)(-4)^2 = 48C = 24, so C = 1/2

f(x) = (1/2) (x + 3)(x - 4)^2

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Answer:

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Step-by-step explanation:

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While playing baseball, sofia takes note of the extreme vectors for which she bats. what is the angle between her two extreme ba
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The angle between the two extreme vectors of Sofia bats is 74.60 degrees.

In this question,

The angle between two vectors will be deferred by a single point, which is called as the shortest angle at which we have to turn around one of the vectors to the position of co-directional with another vector.

The extreme vectors of Sofia bats are  \vec u = < -8, 12 > and \vec v = < -8, 12 >

The angle between the vectors is

\theta = cos^{-1} \frac{\vec u.\vec v}{||\vec u|| ||\vec v||}

The dot product is calculated as

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The magnitude can be calculated as

||\vec u|| = \sqrt{(-8 )^{2} +(12)^{2} }

⇒ \sqrt{64+144}

⇒ \sqrt{208}

||\vec v|| = \sqrt{(13 )^{2} +(15)^{2} }

⇒ \sqrt{169+225}

⇒ \sqrt{394}

Thus the angle between the vectors is

\theta = cos^{-1} \frac{76}{(\sqrt{208} )(\sqrt{394} )}

⇒ \theta = cos^{-1} \frac{76}{\sqrt{81952} }

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⇒ \theta = cos^{-1} (0.2654)

⇒ \theta=74.60

Hence we can conclude that the angle between the two extreme vectors of Sofia bats is 74.60 degrees.

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