samarahjimerson
11.07.2019 •
Mathematics
An architect is designing a new building. he makes a model of the building such that the area of the rectangular base is 12x2 - 11x - 5 and the length is 3x + 1. the completed model will be in the shape of a rectangular prism where the volume is given by the polynomial 24x3 - 58x2 + 23x + 15. determine the width and height of the model in terms of x. fill in the values of m and b to complete the expressions. type the width on the first line and the height on the second line
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Ответ:
Since, the area of the rectangular base =
We have to determine the width if length is (3x+1)
Let us split the middle terms of the given equation to find its factors.
Taking common from first, second and third, fourth terms.
= 3x(4x-5)+1(4x-5)
= (3x+1) (4x-5)
Since, (3x+1) is the length of the rectangular base.
Therefore, the width of the rectangular base is (4x-5) units.
Now, Volume of the rectangular prism is given by the polynomial
We have to find width and height.
Let x = -
in the given equation of volume.
We get as,
-135+135=0
Hence, (3x+1) is a factor of the given volume polynomial.
Now, performing long division of the given polynomial by (3x+1),
we get factors as (4x-5) and (2x-3).
So, the width is (4x-5) units and height is (2x-3) units.
Ответ:
The general formula for the area of a rectangle is as follows, where l represents the length, and w represents the width.
The area of the rectangular base of the model is given by the polynomial 12x2 - 11x - 5. Since the length of the base is 3x + 1, use long division to find the width of the base as follows.
So, the width of the model's base is 4x - 5.
The general formula for the volume of a rectangular prism is as follows, where B represents the area of the base and h represents the height.
The volume of the completed model is given by the polynomial 24x3 - 58x2 + 23x + 15. Since the area of the base of the model is 12x2 - 11x - 5, use long division to find the height of the model as follows.
So, the height of the model is 2x - 3.
Step-by-step explanation:
Ответ:
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Step-by-step explanation:
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