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Tema
7 days ago
8

Two buildings on opposites sides of a highway are 3x^3- x^2 + 7x +100 feet apart. One building is 2x^2 + 7x feet from the highwa

y. The other building is x^3 + 2x^2 - 18 feet from the highway. What is the standard form of the polynomial representing the width of the highway between the two building?
Mathematics
1 answer:
babunello [11.8K]7 days ago
3 0

Given:

Distance between two buildings = 3x^3- x^2 + 7x +100 feet apart.

Distance between highway and one building = 2x^2 + 7x feet.

Distance between highway and second building = x^3 + 2x^2 - 18 feet.

To find:

The standard form of the polynomial representing the width of the highway between the two building.

Solution:

We know that,

Width of the highway = Distance between two buildings - Distance of both buildings from highway.

Using the above formula, we get the polynomial for width (W) of the highway.

W=3x^3- x^2 + 7x +100-(2x^2 + 7x)-(x^3 + 2x^2 - 18)

W=3x^3- x^2 + 7x +100-2x^2-7x-x^3 -2x^2+18

Combining like terms, we get

W=(3x^3-x^3)+(- x^2 -2x^2-2x^2)+ (7x -7x)+(100 +18)

W=2x^3-5x^2+0+118

W=2x^3-5x^2+118

Thus, the width point highway is 2x^3-5x^2+118.

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