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DochEvi [55]
1 year ago
12

Find the rational roots f(x) =3x3+ 2x2 + 3x + 6

Mathematics
1 answer:
Ann [662]1 year ago
4 0

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

<h3>How to determine the rational root of the function f(x)?</h3>

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

For a function P(x) such that

P(x) = ax^n +...... + b

The rational roots of the function p(x) are

Rational roots = ± Possible factors of b/Possible factors of a

In the function f(x), we have:

a = 3

b = 6

The factors of 3 and 6 are

a = 1 and 3

b = 1, 2, 3 and 6

So, we have:

Rational roots = ±(1, 2, 3, 6)/(1, 3)

Split the expression

Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3

Evaluate the quotient

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)

Remove the repetition

Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)

Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

The complete parameters are:

The function is given as:

f(x) = 3x^3 + 2x^2 + 3x + 6

The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)

Read more about rational roots at

brainly.com/question/17754398

#SPJ1

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What is the length of AB?
Xelga [282]

Answer:

<em>AB = 7.35 cm</em>

Step-by-step explanation:

From the attachment,

In ΔDEF,

DF = GH-(GD+FH) = 6 - (2+3) = 1 cm

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Applying Pythagoras theorem,

EF=\sqrt{DE^2-DF^2}=\sqrt{5^2-1^2}=\sqrt{24}=2\sqrt6

In ΔCDI,

DI = GH-(GD+IH) = 6 - (2+1.5) = 2.5 cm

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Applying Pythagoras theorem,

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AB = EF + CI = 2\sqrt6+\sqrt6=3\sqrt6=7.35\ cm

6 0
3 years ago
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For the scenarios presented in Problems 9–17, identify a problem worth studying and list the variables that affect the behavior
Nastasia [14]

Answer:

Problem: A company with a fleet of trucks faces increasing maintenance costs as the age and mileage of the trucks increase

Identify a problem worth studying : Yes, this problem is worth studying as it illustrate the classical optimization problem where to either minimize or maximize the outcome given some constraints. In this problem we need to maximize our profit by minimizing our maintenance cost give the age of trucks.

List the variables that affect the behavior you have identified: Lease expense, license, taxes, insurance, number of trucks, number of mechanics, type of fuel, maintenance and repair, labor, number of breakdowns, wait time to repair, loss of revenue and delay penalties, drivers retention and attrition, and number of customer reviews (negative and positive) the service.

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Which might be considered as constants initially: Assuming that our mechanics are full time employees, the labor cost can be considered constant. However, the parts and materials associated with the labor are not constant. And any one time cosmetic fixes can be considered constants such as a small paint job or seat cleaning.

Can you identify any sub models you would want to study in detail?: The sub model that I want to study in more detail is as follow:

Truck ownership cost=truck depreciation+truck Return on Investment (ROI)

As the truck depreciation is constant, the main focus will be on truck Return on Investment (ROI).

Truck Return on Investment (ROI)=(the gain from the truck−Cost of investment)/cost of investment.

Hence the detailed subsystem can be as follow:

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Step-by-step explanation:

The specific problem is selected above and it is worth analyzing and studying because is is similar to a classical optimization problem. This is because the desired output can be either maximized or minimized by adjusting the values of certain constraints such as maintenance cost, trucks parts and other necessary parameters.

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Dafna1 [17]
Measure B is 90 because 17x+=180/2
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