Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.
A collection of integers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix, are the integers. In addition to several mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.
In computer graphics, where they have been used to describe picture rotations and other transformations, matrices have vital uses as well.
Thus, Not all square matrices can be diagonalized. If there are just two eigenvectors (up to multiplication by a constant), then the matrix cannot be diagonalized.
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Does someone mind helping me with this problem? Thank you!
Answer: the answer is 180 km.
Step-by-step explanation:
Answer:
180 km
Step-by-step explanation:
1 cm to 20 km
9cm=20 times 9
180 kilometers
Express the ratio below in its simplest form.
4.5
:
3
1/2
Answer:
9 : 7
Step-by-step explanation:
given the ratio
4.5 : 3 [tex]\frac{1}{2}[/tex] , that is in decimal form
4.5 : 3.5 ( multiply both parts by 10 to clear the decimal )
= 45 : 35 ( divide both parts by 5 )
= 9 : 7 ← in simplest form
Answer:
9:7
Step-by-step explanation:
Convert all the numbers to either decimal or fraction. The operation becomes simple.
Simplifying after converting to decimal
Convert 3 1/2 to decimal 3 1/2 = 3 + 1/2
1/2 = 0.5
3 + 1/2 = 3 + 0.5 = 3.4
Ratio 4.5:3.5 = 4.5/3.5
Divide by 5 to give
[tex]\dfrac{4.5 /5 }{3.5/5} = 0.9/0.7\\\\[/tex]
Multiply both numerator and denominator by 10
0.9 x 10 = 9
0.7 x 10 = 7
So the ratio becomes 9/7 = 9:7
Simplifying after converting to fraction
4.5 = 4 + 0.5
0.5 = 1/2
5.5 = 4 + 1/2 = 4 1/2
Convert to mixed fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2
Convert 3 1/2 to fraction
3 1/2 = (3 x 2 + 1)/2 = 7/2
So 4.5 : 3 1/2 = 9/2 : 7/2
Multiplying by 2 we get the same answer: 9:7
Choose whichever approach you feel comfortable with
Find parametric equations for the line that is tangent to the given curve at the given parameter value. r(t) = (2t^2) i + (3t + 4) j + (2t^3) k, t = t_0 = 3 What is the standard parameterization for the tangent line? x= y= z =
The standard parameterization for the tangent line is x = 12t + 18 , y = 3t + 13 , z = 54t + 54
Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.
Given that,
Given that, t = t0 = 3, I + (3t + 4) j + (2t 3) k
In order to get the tangent line to the curve at t=3, (x, y, z) = 18, 13, and 54,
r'(t) = 4t, 3, > and r'(t=3) = 12, 3, 54>. (18, 13, 54)
finally,
x = 12t + 18
y = 3t + 13
z = 54t + 54
The tangent line's usual parameterization is as follows:
x=12t+18, y=3t+13, and z=54t+54
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Find mqn
Please help me
70 degrees is the measure of MQN from the provided figure.
Solving angles in a line geometry.A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
From the given figure, we are to determine the measure of angle <MQN. Applying the sum of angles on a straight line:
<MQN + 80 +30 = 180
<MQN + 110 = 180
<MQN = 180 - 110
<MQN = 70 degrees
Hence the measure of <MQN from the given figure is 70 degrees.
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Kevin run a woodhop. Every day the woodhop i open he earn money in ale and pend money on upplie. After cot, how much more money did Kevin make on Saturday than on Monday?
After cost, the more money did Kevin make on Saturday than on Monday is $376.89.
The amount of Spends on monday is,
Sales = $397.35
Supply cost = $108.72
So the profit he is earning is
$397.35 - $108.72 = $288.63
The amount of Spends on Saturday is,
Sales = $914.06
Supply cost = $248.54
So the profit he is earning is
$914.06- $248.54= $665.52
Money did Kevin make on Saturday than on Monday is,
Money from saturday - money from monday
= $665.52 - $288.63
= $376.89
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Any profits generated are returned to the company's owners, who can decide whether to keep the money for themselves, pay dividends to shareholders, or reinvest it in the company.
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On January 22 in 1943, the town of Spearfish, South Dakota, set the record for the world’s fastest temperature change. At 7:30 a.m., the temperature was -4°F. By 7:32 a.m., the temperature was 45°F. By 9:00 a.m. the same day, the temperature was 54 °F. By 9:27 a.m., the temperature was -4 °F. How many degrees did the temperature change each minute from 9:00 to 9:27?
From 9:00 a.m. to 9:27 a.m., the temperature changed from 54°F to -4°F, a change of 58°F. This change took 27 minutes.
The temperature change per minute was 58°F / 27 minutes = 2.15°F per minute.
Arts and Crafts An arts and craft supply store has a large crate that
contains brass, silver, and copper beads. Several friends take turns
pushing their hands into the beads, grabbing one, recording the bead
type, and placing the bead back into the crate. They then repeat the
process. The table shows the count for each bead type. Write a
probability model for choosing a bead.
Dlhrann-
Enter your
The probability of p(copper)=0.28
Probability model for choosing a bead?Probability is a measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. Probability is a fundamental concept in mathematics, statistics, and science that is used to quantify uncertainty and forecast the likelihood of future events based on available data. Probability is a measure of the likelihood or chance that an event will occur, expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
Given
Total Beads =112+96+192=400
Placing the bead back to the crate
so the total beads are always 400
copper:112
p(copper)=112/400=0.28
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your friend measured the distance between her town and the state capital on the map. Her measurement was 4 1/2 inches. Based on your friend's measurement ,what is the actual distance (in miles) between her town and the state capital ?
The actual distance (in miles) between her town and the state capital is 90 miles.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, a map of the state where your friend lives has the scale 1/2 in : 2 mi.
Now, 10 ÷ 1/2
= 10×2
= 20
Her measurement was 4 1/2 =9/2 inches.
Now, 20×9/2
= 90 miles
Therefore, the actual distance (in miles) between her town and the state capital is 90 miles.
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"Your question is incomplete, probably the complete question/missing part is:"
A map of the state where your friend lives has the scale 1/2 in : 2 mi.
Your friend measured the distance between her town and the state capital on the map. Her measurement was 4 1/2 inches. Based on your friend's measurement ,what is the actual distance (in miles) between her town and the state capital?
what’s the square root of 50, 147,96 and -8 square root 16
convert the given system to an augmented matrix. 2x1 x2 = 2 −x1 − x2 − x3 = 6. Find all solutions by reducing the system to echelon form and back substituting. (If there are an infinite number of solutions use s1
as your parameter
The solution to the system is x1 = -4, x2 = 10.
What is the solution to the system?
A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitute solutions to the system. (5, 4) is a solution of the first equation, but not the second.
The given system can be converted to an augmented matrix as follows:
[ 2 1 | 2 ]
[-1 -1 -1 | 6 ]
To find all solutions, we will reduce the system to echelon form and back substitute.
Step 1: Echelon Form
We can perform row operations to reduce the matrix to echelon form:
[ 2 1 | 2 ] R1 = R1 * 1/2
[-1 -1 -1 | 6 ]
[ 1 1/2 | 1 ] R2 = R2 + R1
[ 0 -3/2 -1 | 5 ]
Step 2: Reduced Row Echelon Form
Next, we can perform additional row operations to reduce the matrix to a reduced row echelon form:
[ 1 1/2 | 1 ] R2 = R2 * 2
[ 0 1 | 10 ]
The reduced row echelon form of the matrix represents the system of equations in a simplified form and the solution to the system can be obtained by back substituting.
Step 3: Back Substituting
x2 = 10
x1 = 1 - 1/2 x2 = 1 - 1/2 * 10 = 1 - 5 = -4
Therefore, the solution to the system is x1 = -4, x2 = 10.
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If Jon can paint the equivalent of 5/12 of a fence in an hour, how many minute will it take for them to complete the job?
Answer:
25 minutes
Step-by-step explanation:
5/12×60 minutes
5×60=300
300/12
Answer =25
Find the exact length of line segment PQ
The exact length of line segment PQ is 22.4.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
Given;
p(x,y)=(17,4)
m(x,y)=(-2,16)
Now,
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
D^2= (-2-17)^2+(16-4)^2
D^2=361+144
D^2= 505
D=22.4
Therefore, the distance will be 22.4
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a few months ago, mike and dez started a dog walking business. for each dog that they have agreed to walk, they recorded the total time (in hours) they walked that dog over a one-week period. these values are given below. use the calculator to draw a histogram for these values using 5 classes. 1.6,4.0,4.7,1.6,2.5,2.2,0.6,2.0,3.0,2.6 what percentage of their dogs are walked at least 1.5 hours but under 4.2 hours per week? (round your answer to the nearest percent.)
You can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.
How you can create a histogram?Determine the range of the data: 0.6 to 4.7.
Divide the range by the number of classes (5) to find the class width: (4.7 - 0.6) / 5 = 0.76.
Determine the lower limits of each class by starting at the minimum value (0.6) and adding the class width repeatedly: 0.6, 1.36, 2.12, 2.88, 3.64, 4.4.
Count the number of data values that fall into each class and record it in a table.
Draw a bar for each class using the lower limit of the class as the x-axis value and the height of the bar equal to the number of data values in the class.
After creating the histogram, you can easily find the percentage of dogs that are walked at least 1.5 hours but under 4.2 hours per week by counting the number of data values in the appropriate class and dividing by the total number of data values, then multiplying by 100.
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Geometry 1 find the measure of the angle
Answer:
46
Step-by-step explanation:
draw a line at 96° & make it parallel to bottom line
which will slice 96° into 2 angles
lower half is 180-130=50
top half is 96-50=46
angle 4r equals to top half
solve the initial-value problem answer: xy = y x^2 sinx, y(pi/3) = 0
The value of the constant in the function is c = -√3π²/6(3-π).
A differential equation is an equation that relates an unknown function and one or more of its derivatives. The equation dy/dx = f(x) is a simple example of a differential equation. Solving this equation means finding a function y with a derivative f. Therefore, the solutions of dy/dx are the antiderivatives of f. If F is one antiderivative of f, every function of the form y = f(x) + c is a solution of that differential equation.
Initial-value problems arise in many applications. Next we consider a problem in which a driver applies the brakes in a car. We are interested in how long it takes for the car to stop. Recall that the velocity function v(t) is the derivative of a position function s(t), and the acceleration a(t) is the derivative of the velocity function. In earlier examples in the text, we could calculate the velocity from the position and then compute the acceleration from the velocity. In the next example, we work the other way around. Given an acceleration function, we calculate the velocity function. We then use the velocity function to determine the position function.
The given equation is xy = y + x² sinx
⇒ xy - y = x² sinx
⇒ y(x-1) = x² sinx
⇒ y = x² sinx/(x-1) +c
Also, y(π/3) = 0
Put x = π/3 in above equation:
y(π/3) = (π/3) ² sin(π/3) /((π/3)-1) + c = 0
After solving the above equation, we get c = -√3π²/6(3-π)
Thus, the value of the constant in the function is c = -√3π²/6(3-π).
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Can someone help me on this?
find mean in the above distribution
The mean in the above distribution is 1.84
How to find mean in the above distributionFrom the question, we have the following parameters that can be used in our computation:
The figure
The mean value is then calculated as
Mean = SUm of the product of children and familes/Sum of families
So, we have
Mean = (0 * 23 + 1 * 19 + 2 * 29 + 3 * 9 + 4 * 20)/(23 + 19 + 29 + 9 + 20)
Evaluate
Mean = 1.84
Hence, the mean is 1.84
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Question Solve for x. x+27=−12 Enter your answer in the box. please answer Fast
Answer:
x = -39
-39 + 27 = -12
Step-by-step explanation:
Hope it helps! =D
Answer:
Here you have
Step-by-step explanation:
x + 27 = -12
x= -12 - 27
x= - 39
What are the measures of angles AB and C show your work and explain your answers? I really only need the answer to C please :) this is my first post so giving as much as I can to people who answer. PLEASE ANSWER SOON
The measure of angles becomes:
∠a = 30°
∠b = 60°
∠c = 105°
What is triangle?Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
∠a and 30° are vertical angles and vertical angles are equal
∠a = 30°
We have a triangle with a, b and a right angle. Triangles have angles that add to 180°.
∠a + ∠b + 90° = 180°
30° + ∠b + 90° =180°
120° + ∠b = 180
∠b = 180° - 120°
∠b = 60°
Angle c and 70 form a straight line and straight lines are 180 degrees
∠c + 75° = 180°
∠c = 180° - 75°
∠c = 105°
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Susie's mom is keeping track of how many pieces of candy Susie and her four brothers are eating. The information is graphed below. At what rate is the amount of candy changing? A. -75 pieces of candy per day B. 90 pieces of candy per day C. -90 pieces of candy per day D. 75 pieces of candy per day
The rate of change for a graph passing through (0, 0) and (2, -180) is -90 pieces of candy per day
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change and b is the y intercept
Let y represent the total pieces of candy remaining after x days. Let us assume that the graph passes through (0, 0) and (2, -180). Hence:
[tex]Slope(rate\ of\ change) = \frac{y_2-y_1}{x_2-x_1}\\ \\substituting:\\\\slope=\frac{-180-0}{2-0} =-90[/tex]
The rate of change is -90 pieces of candy per day
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4. Janet hiked 2.5 miles in one hour.
How far did she hike in kilometers?
A 0.6 km
B
1.6 km
C 4.0 km
D 4.2 km
Janet hiked a distance of 2.5 miles which is equivalent to 4 km
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on
Speed is the ratio of total distance to total time travelled. It is given by the equation:
Speed = distance / time
Janet hiked 2.5 miles in one hour. Hence:
Speed = distance / time = 2.5 miles / one hour = 2.5 miles per hour
1 mile = 1.609 km
2.5 miles = 2.5 miles * 1.609 km per mile = 4 km
Janet hiked 4 km
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Find the simple interest when $500 is invested at 6% for 3 years.
Given:-
[tex] \rm Principal = \bold { 500}[/tex][tex] \rm \: Time = \bold{ 3 year}[/tex][tex] \rm \: Interest \: rate = \bold 6 \%[/tex][tex] \: [/tex]
To find:-
[tex] \rm{simple \: interest = \bold {?}}[/tex][tex] \: [/tex]
By using formula:-
[tex] \pmb{\boxed{ \rm{Simple \: interest = \bold { \frac{Principal × Time × Rate}{100} }}}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{SI = \frac{PTR}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{500 \times 3 \times 6}{100} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{5 \cancel{00} \times 3 \times 6}{1 \cancel{00}} }[/tex][tex] \: [/tex]
[tex] \rm{SI = \frac{5 \times 3 \times 6}{1} }[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \rm \bold{{ \red{SI =90}}}}}[/tex][tex] \: [/tex]
hope it helps!:)
What is the value of sin^2-cos^2?
The of sin^2-cos^2 = [tex]Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]
Sin equals cos where?The sine of the angle is the ratio of the hypotenuse, or the angle's opposite, to the perpendicular in a right-angled triangle. Sinus is defined as Sinus = Perpendicular / Hypotenuse.
Sin 180 has a value of 0 precisely. One of the fundamental trigonometric functions is sine, which may be used to calculate the angle or sides of a right-angled triangle. Another name for it is trigonometric ratio.
If theta is an angle, then sine theta is the ratio of a right triangle's hypotenuse to its perpendicular.
trigonometric double angle formulas,
[tex]Sin 2x = 2 sin x cos x[/tex] ————(i)
And,
[tex]Cos 2x = Cos2x - Sin2x[/tex]
[tex]= 2 cos2x - 1 [Since Sin2 x + Cos2 x = 1][/tex] ————(ii)
[tex]= 1 - 2Sin2x[/tex] ————(iii)
Now, multiply equation I by (ii) or (ii) by equation I to obtain the value of Sin 2x Cos 2x (i)
Think about equation I and (ii),
[tex]Sin 2x = 2 sin x cos x[/tex]
And,
[tex]Cos 2x = 2 cos2x - 1[/tex]
Simplifying the above equation, then we get
[tex]Sin 2x Cos 2x = 2 Sin x Cos x (2 cos2x - 1)= 4 Sin x Cos3 x - 2 Sin x Cos x= 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]
Think about equation I and (iii),
[tex]Sin 2x = 2 sin x cos xCos 2x = 1 - 2 Sin2x[/tex]
Simplifying the above equation, then we get
[tex]Sin 2x Cos 2x = 2 Sin x Cos x (1 - 2 Sin2x)= 2 Sin x Cos x - 4 Sin3 x Cos x= 2 Cos x (Sin x - 2 Sin3 x)So,Sin 2x Cos 2x = 2 Cos x (2 Sin x Cos2 x - Sin x)[/tex]
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How much does a customer pay for an article marked at $50.00 if a sales tax of 6% is charged?
Answer:
Howdy so if you buy an item to which 6% tax is added, you pay 106% of the price. The price of the item is $50, you pay 50(1.06) = $53.
(−5/6x−7/12)−(−1/3x−1/4) . the slashes are fractions PLS ANSWER FAST
Answer:
That's what I got, not sure but I tried so I hope it helps.
Which of the following functions are solutions of the differential equation y′′+2y′+1y=0 ?
A. y(x)=−x
B. y(x)=e^-x
C. y(x)=xe^x
D. y(x)=e^x
E. y(x)=xe^−x
F. y(x)=−e^x
G. y(x)=0
Option (B) and (E) functions are solutions of the differential equation y′′+2y′+1y=0.
What is differential equation?An equation known as a differential equation describes the derivative or derivatives of an unknown function. Because they are equations involving a function and its derivatives (where the variable is a function rather than a number) (the functions obtained by differentiating it). Save this response. Common differential equations are used in everyday life to compute the flow of electricity, the motion of an item back and forth like a pendulum, and to illustrate the principles of thermodynamics. Additionally, in medical terminology, they are employed to graphically monitor the progression of illnesses.
Given that,
y′′+2y′+1y = 0
A.E = m² + 2m + 1 = 0
or, (m + 1)² = 0
or, m = ± 1
y = (c₁ + c₂x)e⁻ˣ
y = c₁e⁻ˣ + c₂xe⁻ˣ
Thus, option (B) and (E) are solutions of the differential equation:
y′′+2y +1y = 0.
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A university student completed courses worth 3 credits and some courses worth 4
credits. The student earned a total of 54 credits after completing 15 courses. How
many courses worth 4 credits did the student complete?
2078/08/20, A machine was valued Rs.20,000 whereas its original value was Rs. 17,500.
it is an accountancy question..please answer fast
The depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units is 15000.
How to calculate the depreciationCost of machine = Rs. 1,70,000; Scrap value = Rs. 20,000;
Depreciation in production during the first year = 6,000 units;
Production units during the life of the machine = 60,000 units
Depreciation rate per unit = (Rs. 1,70,000 - Rs. 20,000)/ 60,000 units
= Rs. 2.5
Depreciation of first year = 6,000 * Rs. 2.5 = Rs. 15,000
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Complete question
If the original cost of a machine is Rs. 170,000, estimated scrap value Rs. 20,000, what is the depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units.
What is the value of v?
Answer:
39°
Step-by-step explanation:
Information we need to know
The triangle is a SAS triangleTwo of the angles are equalAngles in a triangle add up to 180°As we know, one of the angles in this triangle is 39° this means that the angle opposite it would also be 39°! This is because as the triangle is SAS v and the given 39 has to be equal
Have a lovely day :)
Answer:
39°
Step-by-step explanation:
Triangle HJI is an isosceles triangle.
In isosceles triangles the base angles are congruent which means their measures are equal.
So the measure of m∠HIJ = 39°
let n ≥ 9. how many trees are there on vertex set [n] in which at least one vertex has degree n − 3?
n−4 out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex], [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.
Now, According to the question:
It is easy to show that a tree with n ≥ 9 can have at most one vertex of degree n - 3. It is [tex]v_0[/tex].
Now, there are n - 1 - (n - 3) = 2 vertices that are not adjacent to [tex]v_0[/tex], it is also
[tex]v_n_-_1[/tex] and [tex]v_n[/tex]
Then a desired tree can be of 3 possible forms:
1. n - 4 out of n - 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 2 and is adjacent to both [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_n_-_1[/tex] has degree 2 and is adjacent to [tex]v_k[/tex] and [tex]v_n.v_n[/tex] is a leaf.
2. n − 5 out of the n − 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_j[/tex] and [tex]v_k[/tex]. [tex]v_j[/tex]has degree 2 and is adjacent to [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_k[/tex] also has degree 2 and is adjacent to[tex]v_0[/tex] and [tex]v_n[/tex]. [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.
3. n−4 out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex], [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.
It is then easy to computer the number of trees in each form and sum them up.
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