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Mathematics

1 answer:

AfilCa [17]2 years ago

6 0

Answer:

The polynomial will be P(x) = - 5 (x + 2)²(x - 3)

Step-by-step explanation:

The degree of the polynomial P(x) is 3 and it has zeros at x = - 2 with multiplicity 2 and at x = 3 with multiplicity 1.

Therefore, (x + 2)² and (x - 3) are the factors of the equation.

Let the polynomial is

P(x) = a(x + 2)²(x - 3) ........... (1)

Now, the polynomial passes through the point (2,80).

So, from equation (1) we gat,

80 = a(4)²(-1)

⇒ a = - 5

Therefore, the polynomial will be P(x) = - 5 (x + 2)²(x - 3) (Answer)

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A meter stick casts a shadow 2.4 m long at the same time a flagpole casts a shadow 9.7 m long. How tall is the flagpole

Luda [366]

The first thing we are going to do is draw a diagram of the situation to help us to solve the situation.
We an draw tow similar triangle between the length of the shadows and the height of the stick and the pole.
Since <span>meter stick has a length of 1 meter, the height of our smaller triangle is 1 meter. Let </span> $h$ be height of of the pole. Since both triangles are similiar we can establish a proportion between their corresponding sides and solve for $h$ :
$\frac{h}{1} = \frac{9.7}{2.4}$
$h=\frac{9.7}{2.4}$
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We can conclude that the pole is 4.04 meters tall.