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Considering the question, we can select
any value for a and b
13. Choose any value for π
to synthetic division divide 2x3 β x2 + x + 4 by (x +k) by
synthetic division
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Steps |
Outcomes
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Step
1 |
Coefficient
of the numerator polynom |
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Step 2 |
Finding the zeros of the denominator as x = -2 and then
writing the problem in the synthetic format. |
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Step
3 |
Carrying
down the leading coefficient unchanged and then below the division symbol. |
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Step 4 |
Multiply the carry down value by the zero of the denominators
and then the results are added to the next column. |
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Step5
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Adding
down to the column |
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Step 6 |
Multiplying the carry down values and then adding the results
in the next column as (-5)(-2)=10 and then adding to the next column it give
1 +10 = 11 |
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Step
7 |
Multiplying
the next carry down values with the zero and then adding to next column as
11(-2) = -22. Adding down to the
column as 8-22=-14 |
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Step 8 |
The last carry down value of the synthetic division is
remainder that is -14 therefore the results of the polynomial synthetic
division becomes |
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14. Give three examples of
system of linear equations that has
a. Unique solution
b. No solution
c. Infinitely many solutions
a.
A linear system of the equations can consider as to be consistent if
there is at least one solution and if there is no solution then it will be
inconsistent. For the consistent linear system there are two conditions that
the equation hold unique solution and have infinite number of solutions. The
system of linear equations cannot have exactly three solutions, but two
equations are linear and two unknown variables are there that intersect at a single
point.
Solving the equations
simultaneously give the solution of the system and if the system has an
infinite number of solutions it will be based on t = 0,
t = 4, t =-2
Solution gives
The linear equation
with the unique solution such as 
and 
will have a unique solution as both lines will
interest at a single point. The lines are neither parallel nor coincident.
b.
The
linear equations that represent two y
= 4x + 2 and y
= 4x + 5 are two equations that have same slope
and different points for the y- axis. These lines are parallel to each other
and never cross. Since these two lines are parallel and they will never
intersect each other therefore system has no solutions.
c.
The
complex linear equations have infinite number of solutions such as
15. Give example of
a. Arithmetic progression with
common different 3.
b. Geometric sequence with first term 1.
16. Choose any value for π
> 1 to solve the following problem
Medical research indicates that
the risk of having a car accident increases exponentially as the concentration
of alcohol in the blood increases.
This is modelled using π
(π₯)
= π(3π₯) Where π
(π₯)
is the risk and π₯ is the alcohol blood
concentration.
(a)
If the alcohol blood concentration is
0.06 , find the risk of having a car accident.
Recent research suggest that the
relative risk R for having an accident while driving the car can be measured by
the modeled equation as
Now consider the
concentration of alcohol in the blood as 0.06 that is x and we can measure the
value of R by solving the equation for k if we suppose the value of k greater
then 1.
Suppose
(b) If the risk of having a car
accident is 5, what should be the alcohol blood concentration?
At the risk level 5,
the concentration of alcohol in the blood will be 0.833.
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