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2 years ago

(3x2 + 9x + 6) - (8x2 + 3x - 10) + (2x + 4)(3x - 7)

Mathematics

1 answer:

nika2105 [10]2 years ago

3 0

Answer:

Let's simplify step-by-step.

3x2+9x+6−(8x2+3x−10)+(2x+4)(3x−7)

Distribute:

=3x2+9x+6+−8x2+−3x+10+(2x)(3x)+(2x)(−7)+(4)(3x)+(4)(−7)

=3x2+9x+6+−8x2+−3x+10+6x2+−14x+12x+−28

Combine Like Terms:

=3x2+9x+6+−8x2+−3x+10+6x2+−14x+12x+−28

=(3x2+−8x2+6x2)+(9x+−3x+−14x+12x)+(6+10+−28)

=x2+4x+−12

Answer:

=x2+4x−12

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The maximum distance is the <u>diameter of the circle</u>, which is of 44 units.

The equation of a circle of <u>radius r and center</u> $(x_0,y_0)$ is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

The diameter is <u>twice the radius</u>, and is the <u>maximum distance</u> between two points inside a circle.

In this problem, the circular path is modeled by:

$x^2 + y^2 - 10x - 18y - 378 = 0$

We complete the squares to place it in the standard format, thus:

$x^2 - 10x + y^2 - 18y = 378$

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$(x - 5)^2 + (y - 9)^2 = 484$

Thus, the radius is:

$r^2 = 484 \rightarrow r = \sqrt{484} = 22$

Then, the diameter is:

$d = 2r = 2(22) = 44$

The maximum distance is the <u>diameter of the circle</u>, which is of 44 units.

A similar problem is given at brainly.com/question/24992361

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