9. a) Determine real coefficients b and c so that polynomial P(x) = x2 + bx + c satisfies following P(1 - i) = 2+i.
Answers
In the given polynomial equation, P(x) = x2 + bx + c, the real coefficients b = -i/2
and c = i/2, such that P(1 - i) = 2+i.
Given: Polynomial is P(x) = x2 + bx + c; P(1 - i) = 2+i.
We need to find out the real coefficients b and c, such that the polynomial P(x) = x2 + bx + c satisfies the above equation.
Solution: It is given that P(x) = x2 + bx + c; P(1 - i) = 2+i.
Using the polynomial, we can calculate the value of P(1 - i):P(1 - i)
= (1 - i)2 + b(1 - i) + c
= 1 + 1 - 2i + b - bi + c
= 2 - i + b + c
Let's substitute P(1 - i) = 2+i and calculate the values of b and c:2 - i + b + c = 2 + i
The real part of the above equation is 2 + b + c = 2 => b + c = 0 ..............(1)The imaginary part of the above equation is -1 = i + b - c => b - c
= 0 - i => b = c - i..............(2)
From equation (1), we have b = -c.
Substituting in equation (2), we get: -c = c - i => 2c
= i => c = i/2.
Substituting the value of c in equation (1), we get: b = -i/2.
Therefore, the real coefficients b and c that satisfy the given polynomial equation P(x) = x2 + bx + c
and P(1 - i) = 2+i are b = -i/2 and c = i/2.
Answer: We have found the real coefficients b and c that satisfy the polynomial equation P(x) = x2 + bx + c and P(1 - i) = 2+i.
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Related Questions
If the cost of 7m is Rs. 1470, find the cost of 5m cloth
Answers
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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among the six who are taking the test for the first time. (a) What kind of a distribution does X have (name and values of all parameters)? nb(x;6, 18
8
)
h(x;6,8,18)
h(x;6, 18
8
)
b(x;6, 18
8
)
b(x;6,8,18)
nb(x;6,8,18)
(b) Compute P(X=2),P(X≤2), and P(X≥2). (Round your answers to four decimal places.) P(x=2)=1
P(x≤2)=1
P(x≥2)=
(c) Calculate the mean value and standard deviation of X. (Round your answers to three decimal places.) mean individuals standard deviation individuals
Answers
The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).
To compute the probabilities:
P(X = 2): nb(2;6, 8/18)
P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)
P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)
To calculate the mean value and standard deviation of X:
Mean (μ) = r * (1 - p) / p
Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))
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please answer it...... Question:
\(if 3 (X - 1) - 5 (x - 4) = 8 find the value of x -5 \times \frac{1}{2} \)
Answers
Answer:
.........................
![please answer it...... Question:[tex]if 3 (X - 1) - 5 (x - 4) = 8 find the value of x -5 \times \frac{1}{2}](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/OMj0GhpCU0jEbMQfVRnbp1fY7sheTS4D.jpeg)
does anything in the plot of the semimajor axis versus the period change when the eccentricity is changed?
Answers
Yes, the connection between the semimajor axis and an orbit's period varies as the eccentricity of the orbit changes.
What is eccentricity?In geometry, the eccentric definition is the distance from any point on a conic section to the focus divided by the perpendicular distance from that point to the nearest directrix. In general, eccentricity aids in determining the curvature of a form. The eccentricity grows as the curvature lowers.
Here,
In general, an orbit's period is proportional to the square root of the semimajor axis multiplied by three. This connection, however, is only valid for circular orbits with zero eccentricity. When the eccentricity is larger than zero, the period of the orbit is still determined by the magnitude of the semimajor axis, but it is also determined by the form of the orbit as given by the eccentricity. The relationship between the semimajor axis and the period in this situation is not as straightforward as a proportionate relationship.
As a result, modifying an orbit's eccentricity modifies the connection between the semimajor axis and the period.
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Chris’s bank allows him to have a negative balance in his checking account. Chris initially has $450 in his account. He then writes 3 checks each worth $200 as payments on his car. Write and evaluate an expression for the amount of money Chris has in his account after the three checks of $200 have been withdrawn from his account.
Answers
x=Money after withdrawals.
x=450-200(3)
x=450-600
x=-250
After making 3 $200 withdrawals from his account after initially starting with $450 he has a balance of negative $250 in his account.
in the big bucks lottery, the chances of winning a $10.00 prize is 1%. what is your best guess about how many people would win a $10.00 prize if 1,000 people each buy a single ticket to big bucks?
Answers
In the big bucks lottery, there are chances that 10 out of 1000 people will win the lottery.
If there are 1000 people in the Big Bucks lottery and there is a 1 percent chance of winning 10 dollars prize if all 1000 people buy the lottery ticket of 10 dollars. If every person buys 10 dollar lottery ticket, then the chances of winning people would be calculated as follows:
Total number of People = 1000
Chances of winning the lottery = 1%
How many people would win 10 dollar lottery = 1000 * 1%
= 1000 * 0.01
= 10 People.
So there are chances that 10 out of 1000 people will win the lottery.
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In 1902, the yearly attendance at a major league baseball park was 3.4 × 105 people. One hundred years later, the yearly attendance was 1.7 × 106 fans. How many times greater was the attendance in 2002 than in 1902?
Answers
Answer:
5 times greater hope this helps
On a Box and Whisker chart, a point that falls outside of the whisker but less than three interquartile ranges from the box edge is called an
Answers
On a Box and Whisker chart, a point that falls outside of the whisker but less than three interquartile ranges from the box edge is called an outlier.
Outliers are data points that significantly deviate from the majority of the data and may indicate unusual or extreme values. They are represented as individual points outside the whisker lines on the chart, indicating their deviation from the central distribution of the data.
Outliers can be important to identify as they can affect the overall interpretation and analysis of the data. Identifying outliers is important because they can indicate unusual or extreme values that may affect the overall analysis or interpretation of the data.
It is common to investigate and evaluate the reasons behind outliers to determine if they are genuine data points or if there were errors in measurement or data entry.
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HELP PLEASE!!!!!!!!!!!!
Answers
You can't, the only factor in both is 1
1(a^4 + 4b^4)
Hope this helps!
I need answer to this ,pls. If 3log1. 2 + 2 log 1/3√10 – log20 = log n
What is n?
Answers
The value of n in the expression is approximately equal to 269.33.
We have,
To find the value of n, we can simplify the given equation using logarithmic properties and then solve for n.
Using logarithmic properties:
3log₁.₂ + 2log₁/₃√10 - log₂₀ = log n
Applying the power rule of logarithms and converting the radicals to fractional exponents:
log₁.₂³ + log₁/₃(10)² - log₂₀ = log n
Simplifying the logarithmic expressions:
log₁.₂(8) + log₁/₃(100) - log₂₀ = log n
Converting the logarithmic expressions into the exponential form:
1.₂⁸ + 1/₃(100) - 20 = n
Simplifying the expression:
256 + 100/₃ - 20 = n
Evaluating the expression:
n = 256 + 33.33 - 20
n ≈ 269.33
Therefore,
The value of n in the expression is approximately equal to 269.33.
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The complete question:
If 3log₁.₂ + 2log₁/₃√10 - log₂₀ = log(n), what is the value of n?
find an equation of the plane passing through that is orthogonal to the planes xyz and xyz.
Answers
The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.
We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.
A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.
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Question correction:
Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0
Our company parking lot has cars, trucks, and motorcycles. The ratio of cars, trucks, and motorcycles is $4:3:2.$ If there are a total of $42$ cars and trucks, then how many motorcycles are there
Answers
There are 12 motorcycles in a company.
According to the statement
The ratio of cars, trucks, and motorcycles is 4:3:2.
The total number of cars and trucks is 42.
then
4x + 3x =42
7x = 42
x = 6.
now put these values in the ratio of vehicles.
Number of cars = 4*6 = 24
Number of truck = 3*6 = 18
Number of motorcycle = 2*6 = 12
So, There are 12 motorcycles in a company.
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find the value of given expression
\( \sqrt{200 - 4} \)
Answers
Answer:
1
Step-by-step explanation:
14 is answer I hope this help
what is the diameter of hemisphere with a volume of 841 cm^3 to the nearest tenth of a centimeter?
Answers
The rule of the volume of the hemisphere is
\(V=\frac{2}{3}\pi r^3\)r is the radius of it
Since the diameter of the hemisphere is double the radius, then we can find the radius then multiply it by 2 to find it
Since the volume of the hemisphere is 841 cm^3, then
Substitute V by 841
\(\begin{gathered} 841=\frac{2}{3}\pi(r^3) \\ 841=\frac{2}{3}\pi r^3 \end{gathered}\)Divide both sides by 2/3pi
\(\begin{gathered} \frac{841}{\frac{2}{3}\pi}=\frac{\frac{2}{3}\pi r^3}{\frac{2}{3}\pi} \\ \\ \frac{2523}{2\pi}=r^3 \end{gathered}\)Take cube root to both sides
\(\begin{gathered} \sqrt[3]{\frac{2523}{2\pi}}=\sqrt[3]{r^3} \\ 7.377555082=r \end{gathered}\)Multiply it by 2 to find the diameter, then round it to the nearest tenth
\(\begin{gathered} d=7.377555082\times2 \\ d=14.75511016 \\ d=14.8\text{ cm} \end{gathered}\)The diameter of the hemisphere is 14.8 cm
1. How can you find the decimal forms of 3/12 and 2/9 .
Answers
Answer:
3/12 as a decimal is 0.25
2/9 as a decimal is 0.2 reapeted
Answer:
Answer written below
Step-by-step explanation:
Divide 3 by 12 and 2 by 9 using long division solve like normal long division if your divisor is bigger than your dividend add a zero on top and add a zero to the dividend.
Decimal form of 3/12:0.25
Decimal form of 2/9:0.22223
Find the surface area of each cylinder. Round to the tenth place.
SA=
9m
15 m
sq. m.
Answers
The surface area of each cylinder would be = 777.15m²
How to calculate the surface area of the given cylinder?To calculate the surface area of the given cylinder, the formula that should be use will be written below. That is;
Surface area of cylinder = 2πr²+2πrh
Where;
radius = diameter/2 = 15/2 = 7.5m
height = 9m
Surface area= 2×3.14×7.5×7.5+2×3.14×7.5×9
= 353.25+ 423.9
= 777.15m²
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Find the center and radius of the circle whose equation is x
2
+3x+y
2
−2y−15=0. The center of the circle is ( The radius of the circldis Note: Your answers must be decimals.
Answers
The center of the circle is (-1.5, 1) and the radius of the circle is approximately 4.1533.
The given equation of the circle is:
x² + 3x + y² - 2y - 15 = 0.
Rearranging the given equation to get the standard form of the circle, we get
(x² + 3x) + (y² - 2y) = 15x² + 3x + y² - 2y + 1² - 1² = 16
Completing the square on x terms by adding (3/2)² = 2.25 to both sides, we get:
(x² + 3x + 2.25) + (y² - 2y) = 15 + 2.25 + 1² - 1²= 16.25
Completing the square on y terms by adding (-1)² = 1 to both sides, we get:
(x² + 3x + 2.25) + (y² - 2y + 1) = 16.25 + 1 = 17.25
Therefore, the standard form of the equation of the circle is:
(x + 1.5)² + (y - 1)² = 17.25
Comparing the given equation to the standard equation of a circle, we get that the center of the circle is (-1.5, 1) and the radius of the circle is √17.25/1 = √17.25 ≈ 4.1533 (rounded to four decimal places).Hence, the center of the circle is (-1.5, 1) and the radius of the circle is approximately 4.1533.
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The quadrilateral is a trapezoid. What is the value of x? if the top is 21 and the bottom is 27 and x is in the middleA) 4B) 5C) 48D) 25
Answers
The value of x for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.
Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.
From the given diagram, the expression below is true:
2(5x - 1) = 21 + 27
Expand
10x - 2 = 48
10x = 48 + 2
10x = 50
Divide both sides by 10
10x.10 = 50/10
x = 5
Hence the value of x is 5
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True
False
The objective function in the linear programming always consists of either maximizing or minimizing some value.
Answers
True, The objective function in linear programming is formulated to either maximize or minimize a specific value or quantity.
The goal of linear programming is to optimize this objective function by finding the optimal values for the decision variables within the given constraints. Whether it is maximizing profit, minimizing cost, maximizing production, or minimizing waste, the objective function is designed to achieve the desired optimization outcome.
The objective function in linear programming serves as the goal or target to be achieved. It can involve maximizing profits, minimizing costs, maximizing efficiency, minimizing waste, or any other measurable quantity. The objective function guides the optimization process by defining the objective to be pursued in the linear programming problem.
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how many 10-bit strings are there that contain exactly 4 ones?
Answers
By combinations, there are 210 10 bit strings which contains exactly 4 ones.
To find out how many 10-bit strings there are that contain exactly 4 ones, we can use the binomial coefficient formula.
The binomial coefficient formula is given by `C(n, k) = n! / (k! * (n-k)!)`,
where,
n is the total number of items, and k is the number of items
we want to choose from n. In this case, we want to choose 4 ones from 10 bits, so n = 10 and k = 4. Therefore, the number of 10-bit strings that contain exactly 4 ones is:
`C(10, 4) = 10! / (4! * (10-4)!) = 210`.
Hence, there are 210 10-bit strings that contain exactly 4 ones.
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solve for w and simplify the answer
Answers
Answer: w=20/3
Step-by-step explanation: start by multiplying -3/2 by 2 and multiply -10 by 2 as well. you would get -3w = -20. divide both sides by -3 and you’ll get 20/3.
HELPPP MEE PLSS!!!! Anything will do I just need a answer that matches this picture
Answers
help me no links please
Answers
Time (min) Distance (km)
2 6
6 18
8 24
15 45
HOPE IT HELPS YOU........
If IN =6x -5, LM=*+7, and MN = 3x + 20,
find MN.
Answers
The equivalent value of the length MN is 52/3 units long.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that LN = 6x - 5 , LM = 7 and MN = 3x + 20.
Now , we can write -
LM = LN + NM
(6x - 5) + (3x + 20) = 7
6x + 3x - 5 + 20 = 7
9x + 15 = 7
9x = 7 - 15
9x = - 8
x = -8/9
So -
MN = 3x + 20 = 3 x (-8/9) + 20
MN = 20 - 8/3
MN = (60 - 8)/3
MN = 52/3
Therefore, the equivalent value of the length MN is 52/3 units long.
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what is 12 divided by 4
Answers
Answer:
It is 3
Step-by-step explanation:
The equation 12 divided by 4 is 3
To make sure this is true 4 times 3 is 12
NEED ASAP 7TH GRADE MATH
Answers
Answer:
i think its the first one but im not completely sure...
Answer: b or c
Step-by-step explanation:
COLOR THEME
QQ ZOOM
1. Seth wrote an expression that is equivalent to 16 + 92. Which expression is
equivalent to the one Seth wrote?
A. (16 + 9)ᵗʷᵒ
B. 8ᵗʷᵒ + 9 • 2
C. 4ᵗʷᵒ + 81
D. 16 + 18
Answers
Answer:
the correct answer is A. Because it shows the equal qualifient of the answer
the line segment AB with endpoints A(5,-C²) and B(C,-3) has gradient C. What is the value of C?
Answers
To find the value of C, we can use the formula for the gradient (slope) of a line, which is the change in y divided by the change in x between two points on the line. In this case, the points are A(5, -C²) and B(C, -3).
The gradient (m) is given by:
m = (change in y) / (change in x)
Let's calculate the change in y and the change in x:
Change in y = y₂ - y₁
= (-3) - (-C²)
= -3 + C²
Change in x = x₂ - x₁
= C - 5
Now, using the gradient formula:
C = (change in y) / (change in x)
= (-3 + C²) / (C - 5)
We can solve this equation for C. Multiplying both sides by (C - 5) gives:
C(C - 5) = -3 + C²
C² - 5C = -3 + C²
-5C = -3
C = -3 / -5
C = 3/5
Therefore, the value of C is 3/5.
A recipe for bread uses 5 cups of white flour and 3 cups
of wheat flour. How many more cups of white flour than
wheat flour are used in the recipe? Write an equation and
complete the bar diagram to solve.
Answers
Please answer with the work shown
Answers
The perimeter first figure that is made of a square and equilateral triangle is 52 cm.
What exactly are squares?
A square is a two-dimensional planar shape with four equal sides and four 90-degree angles. The features of a rectangle are similar to those of a square, but the distinction is that a rectangle has just its opposing sides equal.
A square's most significant qualities are
The four inner angles are 90 degrees.The four sides of the square are congruent, or equal.The square's opposing sides are parallel.The diagonals of the square intersect at 90°.The square's two diagonals are equal to each other.The diagonal of a square is divided into two isosceles triangles.
Square area=(side)²
Square perimeter=4*side
Now,
For first figure given that
sides of square are 14 cm in length
and length of side of equilateral triangle are=5 cm
but for finding perimeter of the figure only 3 sides of square and 2 sides of triangle are needed.
So, perimeter=3*14+2*5
=42+10
=52 cm
hence,
The perimeter first figure 52 cm.
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