(1 point) Suppose that the trace of a 2 × 2 matrix A is tr(A)--16, and the determinant is det(A) smaller eigenvalue larger eigenvalue = 60 Find the eigenvalues of A
Answers
The trace and determinant of a matrix A are related to its eigenvalues, λ₁ (larger eigenvalue) and λ₂ (smaller eigenvalue), through the following formulas: tr(A) = λ₁ + λ₂, det(A) = λ₁ * λ₂
By factoring or using the quadratic formula, we find the eigenvalues: λ₁ = 10 (larger eigenvalue), λ₂ = 6 (smaller eigenvalue)
So the eigenvalues of matrix A are 10 and 6.
Sure, I can help you with that! To find the eigenvalues of a 2×2 matrix, we can use the characteristic equation:
det(A - λI) = 0
where λ is the eigenvalue and I is the identity matrix. In this case, we know that det(A) = (smaller eigenvalue)(larger eigenvalue) = 60, so we can use that to help us find the eigenvalues.
We also know that the trace of A is tr(A) = (sum of eigenvalues), and in this case we're told that tr(A) - 16. So we have:
λ1 + λ2 = tr(A) = 16
And we also have:
det(A - λI) = (smaller eigenvalue - λ)(larger eigenvalue - λ) = 0
Expanding this out, we get:
λ^2 - tr(A)λ + det(A) = 0
Substituting in our values for tr(A) and det(A), we get:
λ^2 - 16λ + 60 = 0
This quadratic equation can be factored as:
(λ - 6)(λ - 10) = 0
So the eigenvalues are λ1 = 6 and λ2 = 10. We can check that these values satisfy both equations:
6 + 10 = 16, and (6)(10) = 60
So our final answer is:
The eigenvalues of A are 6 and 10.
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Related Questions
Sadie stands on a platform that is 15 ft. above the pool surface. The pool has a depth of 12 ft.
a. What value can be used to represent the water's surface?
Answers
27 ft. can be used to represent the water's surface if the platform is 15 ft. above the pool surface and the pool has a depth of 12 ft.
As Sadie stands on a platform that is 15 ft. above the pool surface. The pool has a depth of 12 ft. then, and the total height of the water surface is, the total hight,
The total height = distance between pool surface to platform + the depth of the pool
∵ The total height = 15 ft. + 12 ft.= 27 ft.
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CAN SOMEONE HELP ME PLEASE:)<3
Answers
Answer: D. Cannot be determined
Step-by-step explanation: There are 3 postulates we can use for determining similar triangles.
There is Side Side Side (SSS) Postulate, which requires you have 2 sides of each triangle that are the same proportion as the other triangle. For example, in a triangle ABC, if 2 sides are 5 and 7, and in a triangle DEF, if 2 sides are 10 and 14, then the proportions 5/10 ( 1/2) and 7/14 (1/2) are equal. Thus these are similar triangles and the scale is 1/2.
There is Angle Angle (AA) postulate. If 2 angles are the same to another 2 angles in another triangle, then the two triangles are automatically similar.
The last is Side Angle Side (SAS), which requires you to have an angle that is congruent to another angle in a different triangle, and the angle is in between 2 sides that are proportionally equal to another triangle that also has the same angle in 2 sides. For example, if triangles ABC have angles A, B and C, and angle A is the same equal degrees to another angle in a triangle D, and both A and D are in between 2 sides (i.e DE and AB) that are proportionate (e.g DE and AB are proportionate.) The triangles are then similar.
None of these postulates can be applied to our given problem. Let's see why.
For Angle-Angle, we don't have 2 congruent angles. We have 2 right angles, but that's only 1 angle.
For Side Side Side, we don't have 2 sides given on each triangle, let alone proportionate ones.
For Side Angle Side, we don't even have 2 sides for each triangle given, so this cannot be used either.
[ 7 11] [12 4 5 ]
Find C =AB, if A = [2 9] B = [3 6 1]
[ 10 6]
Answers
The exercise involves finding the product C = AB, where matrix A is given by [2 9] and matrix B is given by [3 6 1]. We need to perform the matrix multiplication to obtain the resulting matrix C.
Let's calculate the matrix product C = AB step by step:
Matrix A has dimensions 2x1, and matrix B has dimensions 1x3. To perform the multiplication, the number of columns in A must match the number of rows in B.
In this case, both matrices satisfy this condition, so the product C = AB is defined.
Calculating AB:
AB = [23 + 912 26 + 94 21 + 95]
[103 + 612 106 + 64 101 + 65]
Simplifying the calculations:
AB = [6 + 108 12 + 36 2 + 45]
[30 + 72 60 + 24 10 + 30]
AB = [114 48 47]
[102 84 40]
Therefore, the product C = AB is:
C = [114 48 47]
[102 84 40]
In summary, the matrix product C = AB, where A = [2 9] and B = [3 6 1], is given by:
C = [114 48 47]
[102 84 40]
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On a strange railway line, there is just one infinitely long track, so overtaking is impossible. Any time a train catches up to the one in front of it, they link up to form a single train moving at the speed of the slower train. At first, there are three equally spaced trains, each moving at a different speed.
Answers
In the given scenario, where there is one infinitely long track and overtaking is impossible, the initial situation consists of three equally spaced trains, each moving at a different speed. The trains have the capability to link up when one catches up to the other, resulting in a single train moving at the speed of the slower train.
As the trains move, they will eventually reach a configuration where the fastest train catches up to the middle train. At this point, the fastest train will link up with the middle train, forming a single train moving at the speed of the middle train. The remaining train, which was initially the slowest, continues to move independently at its original speed. Over time, the process continues as the new single train formed by the fastest and middle trains catches up to the remaining train. Once again, they link up, forming a single train moving at the speed of the remaining train. This process repeats until all the trains eventually merge into a single train moving at the speed of the initially slowest train. In summary, on this strange railway line, where trains can only link up and cannot overtake, the initial configuration of three equally spaced trains results in a sequence of mergers where the trains progressively combine to form a single train moving at the speed of the initially slowest train.
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Please help! Quadratic equations!
Answers
Answer:
\(x^2 -2x - 35 =0\)
Step-by-step explanation:
Assume that the quadratic term of this equation has no coefficient. One can set the equation up in factored form using the given roots. Then expand the equation and simplify the equation to convert to standard form.
The equation in factored form is the following,
\((x+5)(x-7)=0\)
Expand, multiply every term in one of the parenthesis by every term in the other,
\((x+5)(x-7)=0\\\\(x)(x)+(5)(x)-(7)(x)+(-7)(5)=0\)
Simplify,
\(x^2 +5x -7x -35 =0\\\\x^2 -2x -35=0\)
find the measure of each angle
m angle QRT
and
m angle TRS
Answers
Combine like terms
13x - 2 = 180
Add 2
13x = 182
Divide by 13
x = 14
Solving QRT:
Plug in 14 for the x
3(14) + 5 = 47
QRT = 47°
Solving TRS:
Plug in 14 for the x
10(14) - 7 = 133
TRS = 133°
which functions have graphs that cross the x-axis at 0=pi/2?
A. y=sin0
B. y=cos0
C. y=tan0
D. y=sec0
E. y=csc0
F. y=cot0
Answers
Answer:
B. \(y=cos (\theta)\)
F. \(y=cot(\theta)\)
Step-by-step explanation:
If you look at the attached graph, it is simply a matter of checking each graph for the corresponding x-value, \(\frac{\pi}{2}\).
Two integers have a sum of -11 and a difference of 5. What are the two
integers?
(23 points!!)
Answers
Answer:
x = -3
y = -6
Step-by-step explanation:
x+y = -11
x-y = 5
x+y+x-y= -6
2x= -6
x = -3
y = -6
At the beginning of the year, the number of books owned by a library was 10,000. Since then, it has grown by 1% each month.
Which expressions represent the number of books, in thousands, owned by the library 5 years later if it continues to grow at that rate?
A) 10x ((1+0.01)^12)^5
B) 10x(1+0.01^12) ^60
C) 10x (1.01)^5
D) 10x(1.01)^60
E) 10x (0.01)^60
.
Answers
please help meeeeeeeeeeeeeeee
Answers
A satellite is 13,200 miles from the horizon of Earth. Earth's radius is about 4,000 miles. Find the approximate distance the satellite is from the Earth's surface.
Answers
The satellite is approximately 9,200 miles from the Earth's surface.
To find the approximate distance the satellite is from the Earth's surface, we can subtract the Earth's radius from the distance between the satellite and the horizon. The distance from the satellite to the horizon is the sum of the Earth's radius and the distance from the satellite to the Earth's surface.
Given that the satellite is 13,200 miles from the horizon and the Earth's radius is about 4,000 miles, we subtract the Earth's radius from the distance to the horizon:
13,200 miles - 4,000 miles = 9,200 miles.
Therefore, the approximate distance of the satellite from the Earth's surface is around 9,200 miles.
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PLSSSSSSSS HELPPPPPP ASAPPPPP
Answers
Ten minus tree times a number is no more than 61
Answers
Answer:
The inequality can be written as 10 - 3x ≤ 61. Solving for x, we have:
3x ≥ -51
x ≥ -17
Find the area of a triangle with a base of 17 in. and a height of 13 in.
Answers
Answer:110.5inches2
Step-by-step explanation:
to find the area of a triangle use the formula 1/2(base times height) where in this case base is 17 and height is 13. applying this formula= 1/2(17x13)=1/2(221)=110.5inches2
Can someone help me find the domain and range of this graph
Answers
Answer:
Domain = x - values
Range = y - values
Step-by-step explanation:
main points I'll use as examples for the rest on graph are: (-3,4) (1,2) and (1,6)
Domain: simple numbers here are {-3,1} dont repeat the same x value twice!
Range: {2,4,6}
Make sure values are in numerical order.
Find the rest by these three points! (Which are on graph)
Hope this helps, have a good day :)
Answer:
try 2
Step-by-step explanation:
because it an X-value and it on the graph
what is the common base for 5 to the power of 9 divided by 5 to the power of 6
Answers
A large population has mean 100 and standard deviation 16. What is the probability that the sample mean will be within plusminus 2 of the population mean if the sample size is n = 100? What is the probability that the sample mean will be within plusminus 2 of the population mean if the sample size is n = 400? What is the advantage of a larger sample size?
Answers
The probability that the sample mean will be within plus minus 2 of the population mean if the sample size is n = 100 between z-scores of 0 and 2.5 using a z-table.
The standard deviation of the sample distribution, commonly known as the standard error, can be computed using the formula given that the population mean is 100 and the standard deviation is 16:
Standard Error = Standard Deviation / sqrt(sample size)
Let's determine the likelihoods for sample sizes of n = 100 and n = 400:
For n = 100:
Standard Error = 16 / sqrt(100) = 16 / 10 = 1.6
We can determine the z-scores for the upper and lower boundaries to establish the likelihood that the sample mean will be within plus or minus 2 of the population mean:
Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error
Lower Bound z-score = (100 - 100) / 1.6
Lower Bound z-score = 0
Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error
Upper Bound z-score = (104 - 100) / 1.6
Upper Bound z-score = 4 / 1.6
Upper Bound z-score = 2.5
We can calculate the region under the normal distribution curve between z-scores of 0 and 2.5 using a z-table or statistical software. This shows the likelihood that the sample mean will be within +/- 2 standard deviations of the population mean.
For n = 400:
Standard Error = 16/√400
Standard Error = 16/20
Standard Error = 0.8
We determine the z-scores by following the same procedure as above:
Lower Bound z-score = (Sample Mean - Population Mean) / Standard Error
Lower Bound z-score = (100 - 100) / 0.8
Lower Bound z-score = 0
Upper Bound z-score = (Sample Mean - Population Mean) / Standard Error
Upper Bound z-score = (104 - 100) / 0.8
Upper Bound z-score = 4 / 0.8
Upper Bound z-score = 5
Once more, we may determine the region under the normal distribution curve between z-scores of 0 and 5 using a z-table or statistical software.
A larger sample size, like n = 400, has the benefit of a lower standard error. The sampling distribution of the sample mean will be more constrained and more closely resemble the population mean if the standard error is less.
As a result, there is a larger likelihood that the sample mean will be within +/- 2 of the population mean. In other words, the estimate of the population mean gets more accurate and dependable as the sample size grows.
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Which choice shows the graph of the solution set for the inequality p - 2 > 6?
(A
"10
"5
0
5
10
B)
10
5
0
5
10
"10
5
HHHO+++
5 10
0
*10
-5
HHHO++++
0 5 10
Answers
Answer:
p > 8
Step-by-step explanation:
p - 2 > 6
Add 2 to each side
p > 8
Isaak's father baked cookies from scratch. From a nutrition perspective, will these be
healthier than a box of cookies from a large company that Isaak purchases at the
grocery store?
(1 point)
O No, all cookies are very bad for you.
O Yes, anything homemade is very healthy.
O No, packaged cookies tend to be lower in fat and sugar.
O Yes, homemade cookies will not contain preservatives.
Answers
From a nutrition perspective, concerning the how healthy the cookies are, I will say D.Yes, homemade cookies will not contain preservatives.
What is the justification?Based on the given information, most of the home made cookies that is been made by the large companies are been preserved with preseratives because it is been produced in a large quantities which can be delivered to different regions and this implies that it may take somne days because it will be sold completely.
However too much of preservatives is not too good for our health, hence from nutrition perspective home made can be considered to be more healthy.
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if x is a discrete uniform random variable ranging from one to eight, find p(x < 6).
Answers
The probability that x is less than 6 is 5/8.
If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.
To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:
p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)
Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:
p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)
Simplifying, we get:
p(x < 6) = 5/8
Therefore, the probability that x is less than 6 is 5/8.
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Help pls
Which point on the number line represents the rational
number-2 3/5?
23 ?
A
B
C
D
Answers
Answer:
c
Step-by-step explanation:
C is 3/5 of the way down on section -2
Answer:
Its A
Step-by-step explanation:
I just answered on edge
A store buys sweaters for eight dollars and sells them for $26 how many sweaters does the store need to sell to make a profit of $990? HELP!!!!
Answers
Answer:
h
Step-by-step explanation:
here scrooll down for answer
no <3
just kidding multiply those and tada u'll get your answer
Answer:
38-39 just divide it c'mon seriously
HELP ME !!!!!!!!!!!!
Answers
Need help with #6
Find the missing angles
Answers
Answer:
p = 95
q = 95
r = 85
s = 85
Step-by-step explanation:
85 deg & p are same-side int angles & are supplementary.
p = 180 - 85 = 95
p & q are vertical & congruent.
q = 95
p & s are supplenmentary.
s = 85
s & r are alt int angles & congruent.
r = 85
On number 3 i need to find the following:
DF=
JH=
GJ=
m
m
please help and explain
Answers
Answer:
DF= 16m
JH= 14m
GJ= 19m
Step-by-step explanation:
turn the triangles until they overlap each other
since they are congruent, the measure of one angle will be the same for the other one
Answer:
DF= 16m JH= 14m GJ = 19m
Step-by-step explanation:
We know the two figures are equal to each other. So to find the missing sides just refer to the other figure with the included side.
another advantage of using anova is that it ________ so the significant differences can be located and interpreted easily.
Answers
Another advantage of using Anova is that it arranges the means so the significant differences can be located and interpreted easily.
The ANOVA test is a type of statistical test used to determine whether there is a statistically significant difference between two or more categorical groups by testing mean differences using variance.
Another important part of the ANOVA is the splitting of the independent variables into two or more groups.
The assumptions for the ANOVA test are the same as those for general parametric tests.
ANOVA can only be performed if there is no relationship between subjects in each sample. Sample size for different groups/levels must be the same.ANOVA can only be performed if the dependent variable is normally distributed.the population variances of must be equal (that is, homoscedasticity). Homogeneity of variance means that the variability of results is similar across populations.Advantages of ANOVA:
The z-test can only be used to compare two population means, whereas the ANOVA test can be used to compare three or more population means.When there are two different treatments/factors affecting the dependent variable, the Two Way ANOVA test can be used to analyze the effect of each treatment.To learn more about ANOVA test , refer:
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17.0938 in decimal expanded form
Answers
cuanto es la tercera parte de 15,000
Answers
Answer:
5,000.
¡Espero que ayude!
Step-by-step explanation:
292. evaluate ∬s(x y z)ds, where s is the surface defined parametrically by r(u, v) = (2u v)i (u − 2v)j (u 3v)k for 0 ≤ u ≤ 1, and 0 ≤ v ≤ 2.
Answers
the integral is:∬s(x y z)ds = (4/3 - 24/5 + 2/7 - 2/9) = -6/45
∬s(x y z)ds = ∬r(u,v)(2u v)(u − 2v)(u 3v)dudv
= ∫0^1∫0^2 (4uv^2 - 8uv^3 + u^2v^4 -2u^2v^5)dudv
= (4/3 - 24/5 + 2/7 - 2/9) = -6/45
We can evaluate the integral by first rewriting it in terms of parametric equations.
The surface s is defined parametrically by r(u,v) = (2u v)i (u − 2v)j (u 3v)k for 0 ≤ u ≤ 1, and 0 ≤ v ≤ 2.
Therefore, the integral can be written as ∬s(x y z)ds = ∬r(u,v)(2u v)(u − 2v)(u 3v)dudv.
Next, we can evaluate the integral by using double integrals.
We can evaluate the integral by first evaluating the inner integral with respect to v, and then evaluating the outer integral with respect to u.
The inner integral with respect to v is:
∫0^2 (4uv^2 - 8uv^3 + u^2v^4 -2u^2v^5)dv
= (4/3 - 24/5 + 2/7 - 2/9)
The outer integral with respect to u is:
∫0^1 (4/3 - 24/5 + 2/7 - 2/9)du = (4/3 - 24/5 + 2/7 - 2/9)
Therefore, the integral is:
∬s(x y z)ds = (4/3 - 24/5 + 2/7 - 2/9) = -6/45
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please i seriously need step-by-step on this tyty
Answers
Answer: G=4
Step-by-step explanation:
