one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.
What is eigenvalue?
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.
a) -4
b) 1
c) 1
Step-by-step explanation:
a) The matrix A is given by:
[tex]A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\[/tex]
where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:
[tex]A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right][/tex]
and by taking the determinant:[tex]\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}[/tex]
and the roots of this polynomial is:
[tex]\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}[/tex]
hence, the real eigenvalue of the matrix A is -4.
b) The multiplicity of the eigenvalue is 1.
c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)
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Complete Quetion
The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.
the volume of a cube with length x is V(x)=x^3. The volume of the sphere with radius 1/2x is shown in the graph. Over the interval [1,2], which volume is increasing faster?
Answer:
The volume of the cube is increasing faster.
The volume of the cube with length : [x] is increasing faster.
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 the volume of a cube with length [x] is V(x) = x³. The volume of the sphere with radius (1/2)x is shown in the graph.
We have the volume of the cube with length : [x] is -
V{C} = x³
Volume of the sphere with radius : (1/2)x is
V{S} = (4/3)πr³ = (4/3)π(x/2)³ = πx³/6
V{S} = πx³/6
Refer to the graph of the function attached of both the function. It can be seen that the function of the volume of the cube with length [x] is increasing faster.
Therefore, the volume of the cube with length : [x] is increasing faster.
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The sum of two (2) prime numbers is 85. What is the product of these two prime numbers?
Answer: 166
Step-by-step explanation:
The sum of two odd numbers is an even number.
85 is odd, and so is the sum of an odd number and an even number.
2×83=166
7.
Which is a factored form of 8x³ + 27? (1 point)
O (2x+3)(2x+3)(2x + 3)
O (2x+3)(4x² - 6x +9)
○ (2x − 3)(4x² + 6x + 9)
O(2x-9)(4x² + 18x +81)
Answer:
B) (2x + 3)(4x² - 6x + 9)-----------------------------------
Given sum of cubes, use identity a³ + b³ = (a + b)(a² - ab + b²):
8x³ + 27 = (2x)³ + 3³ = (2x + 3)((2x)² - (2x)(3) + 3²) = (2x + 3)(4x² - 6x + 9)The matching choice is B.
Answer:
B) (2x + 3)(4x² - 6x + 9)
Step-by-step explanation:
Given expression:
[tex]8x^3+27[/tex]
Rewrite 8 as 2³ and 27 as 3³:
[tex]\implies 2^3x^3+3^3[/tex]
[tex]\textsf{Apply exponent rule} \quad a^nc^n=(ac)^n:[/tex]
[tex]\implies (2x)^3+3^3[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Sum of Cubes Formula}\\\\$a^3+b^3=(a+b)(a^2-ab+b^2)\\\end{minipage}}[/tex]
Therefore:
a = 2xb = 3Using the Sum of Cubes formula:
[tex]\begin{aligned}\implies (2x)^2+3^3&=(2x+3)((2x)^2-2x(3)+3^2)\\&=(2x+3)(4x^2-6x+9)\end{aligned}[/tex]
Im so confused on this like i think it was y=-5/3x but i dont know
Answer:
Below
Step-by-step explanation:
Slope , m, is calculated (y1-y2) / ( x1-x2) =
Using the first two points : (-5-0) / (-3 -0) = 5/3
slope = 5/3
22. What are the values of w and x in the triangle below? Round the answers to the nearest tenth.
(1 point)
The values of x and w on the triangle are given as follows:
w = 14.4, x = 11.2.
How to obtain the values of x and w?The values of x and w are obtained applying the trigonometric ratios, as the triangle is a right triangle.
The three trigonometric ratios are given as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For the angle of 48º, we have that:
The adjacent side is w.The opposite side is of 16.Hence:
tan(48º) = 16/w
w = 16/tan(48º)
w = 14.4.
For the angle of 32º, we have that:
The adjacent side is 14.4 + x.The opposite side is of 16.Hence:
tan(32º) = 16/(14.4 + x)
tan(32º)(14.4 + x) = 16
x = (16 - 14.4tan(32º))/tan(32º)
x = 11.2.
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3x+9-7=c+10+x
-4x+9=2x+10
A grocery store has small bags of apples for $5 each and large bags for $8 each. If you buy 15 bags and spend $93, how many of each size bag did you buy?
Answer:
There are 9 small $5 bags and 6 large $8 bags
Step-by-step explanation:
9 x 5 = 45
6 x 8 = 48
45 + 48 = 93
Question 4
A seller at a farmer's market sells trays of large eggs and extra large eggs.
They sold a total of 75 trays of eggs in the past month.
•
They sold twice as many trays of large eggs as extra large eggs.
4.1. If they sold x trays of large eggs and y trays of extra large eggs, write
down two linear equations for the results above.
Answer:
They would have sold 8.2 eggs
Step-by-step explanation:
^
30. Choose all equations that are true.
48 X 1,000 = 4,800
48 x 1024,800
48 X 104
480,000
48 X 10³ = 4,800.00
48 X 10³ = 48,000
Answer: 1, 3
Step-by-step explanation:
2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of which type of reaction?
The reaction described by 2 h subscript 2 end subscript o plus 2 k open parentheses s close parentheses rightwards arrow 2 k o h open parentheses l close parentheses plus 2 h subscript 2 end subscript open parentheses g close parentheses is an example of oxidation - reduction reaction
What is Redox reaction?Any chemical process in which a participating chemical species' oxidation number changes is known as an oxidation-reduction reaction, often known as a redox reaction. The phrase refers to a broad range of procedures.
The equation of the reaction is written as
2H₂O + 2K → 2KOH + 2H₂
The reducing agent here is Potassium which is K it transformed from Potassium to Potassium Hydroxide. Potassium is electron donor
The oxidizing agent is water which ended up as Hydrogen molecule
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the probability that a restaurant passes its health department inspection is 0.94. the owners of 58 restaurants are surveyed to see if their restaurants passed inspection.
For each binomial experiment described, find
A. the mean
B. the variance
C. the standard deviation
The mean , standard deviation, and the variance of each binomial experiment using given probability and sample of restaurant owners surveyed is equal to 54.52 , 1.808, 3.2712 respectively.
As given in the question,
Let success be defined by health department inspection is passed by restaurant
Probability of success rate 'p' = 0.94
Value of ' 1 - p ' = 1 - 0.94
= 0.06
Number of owners of restaurant which are surveyed 'n' = 58
For the given binomial experiments calculation of the following distributions are:
Mean 'μ' = np
= 58 × 0.94
= 54.52
Standard deviation 'σ' = √ np (1 - p)
= √ 58 × 0.94 × 0.06
= √3.2712
= 1.808
Variance 'σ²' = np( 1 - p )
= 58 × 0.94 × 0.06
= 3.2712
Therefore, the mean , standard deviation , and the variance from the given probability and sample size is equal to 54.52 , 1.808, 3.2712 respectively.
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What Is The Order?
For The Variable Expressions
Answer:
I think it’s 4/n and 4 divided by n. Sorry if it’s wrong!
Step-by-step explanation:
In Jillian's garden, there are 3 rows of carrots, 2 rows of string beans, and 1 row of peas.There are 8 plants in each row. How many plants are in the gradenn?
Consider the relation below
Is it a function?
Is the relation a one to one function?
Is the inverse of the relation below itself of function ?
the standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. a standard dartboard is 18 inches in diameter. suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left. brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor. does brian's dart land on the dartboard? drag the choices into the boxes to correctly complete the statements.
The question is an illustration of equation of circles.
The equation of the dartboard circle is: [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.
Given that,
h = 5 feet 8 inches ---- the height at which the dartboard was hung
d = 18 inches in diameter ---- the diameter of the dartboard
B = 12 feet --- the bull's eye
D = 11.5 feet , 5 feet --- Brian's dart
Equation of the circle
First, we convert all units to feet
This is done by dividing inches units by 12
h = 5 feet 8 inches
h = 5 ft + 8/12 ft
h = 5 ft + 2/3 ft
Take LCM
h = [tex]\frac{15+2}{3}[/tex] ft
h = [tex]\frac{17}{3}[/tex] ft
d = 18 inches
d = [tex]\frac{18}{12}[/tex] ft
d = [tex]\frac{3}{2}[/tex] ft
Divide by 2 to calculate radius
r = [tex]\frac{3}{2*2}[/tex] ft
r = [tex]\frac{3}{4}[/tex] ft
To find the equation of a circle when you know the radius and centre, use the formula as [tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex] , where represents the centre of the circle, and is the radius.
The equation of the circle is represented as:
[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]
In this case:
a = B = 12 feet -- the distance between the bull's eye and the wall
b = h = [tex]\frac{17}{3}[/tex] ft ---- the height at which the dartboard was hung
So, we have:
[tex](x-a)^{2} +(y-b)^{2} =r^{2}[/tex]
[tex](x-12)^{2} +(y-\frac{17}{3}) ^{2} = (\frac{3}{4}) ^{2}[/tex]
Evaluate the exponents
[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Hence, the equation of the circle is:
[tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Does Brian’s dart land on the dartboard?
Yes her dart lands on the dartboard because
D = 11.5 feet , 5 feet is within the circumference of the dartboard
Therefore,
The question is an illustration of equation of circles.
The equation of the dartboard circle is: [tex](x-12)^{2}+(y-\frac{17}{3}) ^{2} =\frac{9}{16}[/tex]
Brian's dart lands on the dartboard because D = 11.5 feet , 5 feet is within the circumference of the dartboard.
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Can Someone Explain Sin Cos and Tan to me, My finals are coming up and I do not understand anything about them
Sine and cosine are the fundamental trigonometric functions associated to the sides of a right triangle and tangent is a derivate trigonometric function.
What are the sine, the cosine and the tangent of an angle?
Let be a right triangle, whose features are introduced in the figure attached below. The side with measure y is the side opposite to the angle θ, whereas the side with measure x is the side adjacent to the angle θ. The side with measure r represents the hypotenuse of the right triangle, which can be found by means of Pythagorean theorem:
r = √(x² + y²)
Trigonometric functions are trascendent functions that relates two sides of the right triangle. There are two fundamental trigonometric functions and four derivate trigonometric functions:
Fundamental
sin θ = y / r = (Opposite side) / (Hypotenuse)
cos θ = x / r = (Adjacent side) / (Hypotenuse)
Derivate
tan θ = sin θ / cos θ = y / x = (Opposite side) / (Adjacent side)
cot θ = 1 / tan θ = cos θ / sin θ = x / y = (Adjacent side) / (Opposite side)
sec θ = 1 / cos θ = r / x = (Hypotenuse) / (Adjacent side)
csc θ = 1 / sin θ = r / y = (Hypotenuse) / (Opposite side)
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Plsss help me with this !!
convert 0.55 as a fraction.
Answer: 11 / 20
Step-by-step explanation:
Rename 4/5 and 5/7 using the least common denominator.
helpppp me please!!!
Answer:
Step-by-step explanation:
17-8=9 but if 18-7=11 then 19-8=7
An investor invested a total of $2900in two mutual funds. One fund earned a 8% profit while the other earned a 6% profit. If the investor's total profit was $194, how much was invested in each mutual fund?
The amount invested at 8% and 6% is 1000 and 1900 respectively.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, The person invested $2900 in two mutual funds and the total profit is $194.
Let the amount invested at 8% is x, then the amount invested at 6% is:
2900-x
Since the total profit is $194, it follows:
8% of x + 6% of (2900 - x) = 194
8x/100 + 6(2900 - x)/100 = 194
8x + 17400 - 6x = 19400
2x = 19400 - 17400
2x = 2000
x = 1000
The amount invested at 6% is:
2900 - 1000
= 1900
Hence, the amount invested at 8% and 6% is 1000 and 1900 respectively.
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7. Charlie went to Juarez, Mexico, on a shopping trip.
He bought silver rings at $5 each and bracelets at $8
each. If he bought a total of 19 items and spent $131,
how many bracelets and rings did he buy?
if 15 and 9 are two members of a
Pythagorean triple, what is the third
member?
Answer: 12
Step-by-step explanation:
hope this helps
Write down the inequality shown on the
number line below.
For the given number line the inequality equation would be -10 < x ≤ 20.
What is inequality?
In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
In the given number line, a hollow circle represents that the number is excluded and solid circle represents that the number is included in the range
and the range lies between -10 to 2.
Let's take a variable to describe the relationship,
By using inequality we can prepare the inequality equation as
-10 < x ≤ 20
Hence, for the given number line the inequality equation would be -10 < x ≤ 20.
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Which of the following choices correctly names the figure below?
Heather works as a waitress at her family's restaurant she works every 2 hours every morning during the breakfast shift and returns to work each evening for the dinner shift in the last 4 days she worked 28 hours if Heather works the same number of hours each evening how many hours did she work during each dinner shift?
Heather worked 5 hours every evening during each dinner shift.
What is a Linear Equation?Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
A nonlinear equation is an equation whose highest power of the variables is not 1 and the graph is not a straight line.
Let morning shift = m
evening shift = e
Representing the word problem in an equation;
4(m + e) = 28
Diving both sides by 4
m + e = 7
but she always works 2 hours in th morning shift
2 + e = 7
e = 7 - 2
e = 5
Therefore she worked 5 hours in the evening shift for 4 days.
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determine if law of sines or law on cosines is the best choice substitute the values into the appropriate formula and solve
Answer:
Hi again, use the sine rule for length. answer: 82.42
Step-by-step explanation:
You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period. How many hours x of television must you watch in the eighth week to meet your goal?
Television Viewing
Week....... Hours Watched
1 .......................1
2 .....................1.5
3 .....................0.5
4 .......................3
5 ......................1.5
6 ........................2
7 .......................0.5
There are 2 hours of television must you watch in the eighth week to meet your goal.
What is television?
The transmission of audio and video data electronically between a source and a recipient.
The primary use of television is to transmit shows for entertainment, information, and education. Television is a system for transmitting visual images and sound that are reproduced on screens.
Given: You want to limit the amount of television you watch to an average of at most 1.5 hours per week during an 8-week period.
Suppose x is the hours of watching television in the 8th week.
Let the average of watching television per week is 1.5.
⇒
[tex]\frac{1 + 1.5 + 0.5 + 3 + 1.5 + 2 + 0.5 + x}{8} = 1.5\\ \frac{10+x}{8}=1.5 \\10+x = 12\\x = 12-10\\x = 2[/tex]
Hence, there are 2 hours of television must you watch in the eighth week to meet your goal.
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Alex has $600 in her checking account. She wants to spend a part of this money on a computer.
She wants to have at least $250 left in her checking account after buying the computer. Write an
inequality that can be used to find t, the amount of money in dollars that Alex can spend on the
computer, and solve for t.
Answer: $350 = t
Step-by-step explanation:
might help); 600-250 = t
t + 250 ≤ 600 INEQUALITY
Answer: $350.
Explanation: if you do [tex]600 -250[/tex] you will end up with $350
the capacity of an elevator is either 20 children or 15 adults. if 17 children are currently in the elevator, how many adults can still get in?
Two more adults can board the elevator if there are 17 children present inside.
Explain the concept of capacity of an elevator?The point when 20 children or 15 adults can enter an elevator is considered the elevator's capacity. The number of adults who can still enter the elevator when there are 17 children inside must be determined.A linear equation can be created to resolve the aforementioned issue.The number of adults who can still enter will be determined by the linear equation solution.
let
c is equal to a child's weight.a is equal to 1 adult's weight.20c = 15a ; 5 divided by both sides
4c = 3a
Another 3 kids can enter the elevator if there are already 17 in it.
The fact that;
3c = 9/4 a
3c = 9/4 a
3c = 2.25 a
3c = 2 a (no fraction)
Thus, two more adults can board the elevator if there are 17 children present inside.
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