To find the eigenvalues and eigenvectors of a matrix, we need to solve the equation Ax = λx, where A is the matrix, λ is the eigenvalue, and x is the eigenvector. In this case, we have a 3x3 matrix, so we expect to find three eigenvalues and three eigenvectors.
Without performing the calculations, it is difficult to determine the exact eigenvalues and eigenvectors of matrix D. However, based on the structure of the matrix, we can make some observations. We notice that the matrix has a repeating pattern of the number 5, which suggests that 5 is a dominant eigenvalue. Additionally, the matrix is symmetric, so we know that the eigenvectors will be orthogonal.
One possible approach to finding the eigenvectors is to use the Gram-Schmidt process, which is a method for orthogonalizing a set of vectors. We can start with a vector that is parallel to one of the columns of the matrix, and then subtract the projection of that vector onto the next column to obtain a vector that is orthogonal to the first. We can continue this process for each column to obtain a set of orthogonal vectors, which will be our eigenvectors.
Based on these observations, we can hypothesize that 5 is an eigenvalue of D and that we can find two linearly independent eigenvectors by using the Gram-Schmidt process on the columns of the matrix. However, we would need to perform the calculations to confirm this hypothesis and determine the exact values of the eigenvectors.
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Order the given steps for the perpendicular bisector construction of the segment below.
The steps for the perpendicular bisector construction when ordered are :
Label the endpoints of the segment A and B.Draw circle A: center A, radius AB, and circle B: center B, radius BA.Label the points of intersections as C and D.Draw line CD, which is the perpendicular bisector of segment AB.How to bisect the segment ?Identify the two endpoints of the given segment AB and labeling them as A and B. This is important for the subsequent steps of the construction. Then draw two circles: one centered at A with a radius equal to the length of AB, and the other centered at B with a radius equal to the length of BA (which is the same as AB).
The two circles drawn in Step 2 intersect at two points. These points are labeled as C and D. Note that these points are equidistant from A and B, since they lie on the circles with radii AB and BA.
Finally, we draw a line through points C and D. This line is the perpendicular bisector of the segment AB, meaning it intersects AB at its midpoint and is perpendicular to AB.
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use the equation that you wrote in excerise 21 to find the number of vertices of a cube, which has 12 edges and 6 faces
The cube has 8 vertices. Exercise 21 states that for a polyhedron with V vertices, E edges, and F faces, the following equation holds:
V - E + F = 2
To use this equation to find the number of vertices of a cube with 12 edges and 6 faces, we first need to identify the values of E and F.
A cube has 12 edges, as given in the problem statement, and it has 6 faces since a cube has 6 square faces.
Substituting these values into the equation, we get:
V - 12 + 6 = 2
Simplifying this equation, we have:
V - 6 = 2
Adding 6 to both sides, we get:
V = 8
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The sum of three numbers is 70 . The third number is 2 times the first. The first number is 6 less than the second. What are the numbers?
Answer:
16, 22, and 32.
Step-by-step explanation:
Set up a system of equations to represent the situation with 3 unknown.
x + y + z = 70
z = 2x
x = y - 6 → y = x + 6
The second two equations are the y and z in terms of x, so substitute both into the first equation.
x + (x + 6) + 2x = 70
4x + 6 = 70
4x = 64
x = 16
Use this number to calculate the value of the other unknowns.
y = x + 6
y = 16 + 6
y = 22
Calculate z.
z = 2x
z = 2(16)
z = 32
So, the three numbers are 16, 22, and 32.
HELP ME!!!! DUE TODAY IF I GET IT RIGHT YOUR BRAINLIEST!
Answer:
see step by step.
Step-by-step explanation:
The THEORETICALLY probability is 0.5000 (this is, 50% each one) since each one have equal chance of being in list A or List B, but this is still a random probability, so this is not the same that if you have 60 students, 30 of them are going to be in the list A and the other 30 in B.
The experimental result show:
[tex]P (ListA) = \frac{27}{60} =0.45[/tex]
[tex]P (ListB) = \frac{33}{60} =0.55[/tex]
This is 45% of being in list A and 55% of being in list B, notice these values are close the the experimental value (50%) but still are lightly higher or lower. Additionally notice if you add both of them you still have 100% (0.45+0.55=1.00)
multiple linear regression with coefficient standard deviation and mean to get new multiple regression
Multiple linear regression is a statistical technique used to model the relationship between a dependent variable and multiple independent variables.
In multiple linear regression,
The dependent variable is modeled as a linear function of several independent variables.
Regression coefficient that quantifies the strength and direction of the relationship between independent and dependent variable.
Coefficient standard deviation refers to the standard deviation of the estimated regression coefficients in multiple linear regression.
Provides a measure of the variability of the estimated coefficients and can be used to assess the precision of the estimates.
New multiple regression model,
Collect data on the dependent variable and multiple independent variables of interest.
Perform a multiple linear regression analysis, which involves fitting a linear equation to the data using the method of least squares.
Estimates the regression coefficients and their standard deviations.
Used to assess the significance of each independent variable and the overall fit of the model.
Therefore, multiple regression model consider adding or removing independent variables, transforming the data, or machine learning algorithms.
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The above question is incomplete , the complete question is:
What is multiple linear regression with coefficient standard deviation and mean to get new multiple regression ?
In a small town 50% of 2 story homes own computers and 35% of one story homes own computers. In dawn's neighborhood 75% of homes are 2 story. What is the probability that a two story home in dawn's neighborhood owns a computer
To solve this problem, we can use Bayes' theorem. Let's define:
- A: two story home
- B: owning a computer
We want to find the probability of B given A, which we can write as P(B|A). Using Bayes' theorem, we have:
P(B|A) = P(A|B) * P(B) / P(A)
We know that 50% of two story homes own computers, so P(B) = 0.5. We also know that 75% of homes in Dawn's neighborhood are two story, so P(A) = 0.75.
To find P(A|B), we need to use the conditional probability formula:
P(A|B) = P(A and B) / P(B)
We don't have the probabilities for A and B happening together, but we know that:
P(A and B) = P(B|A) * P(A)
Substituting this into the conditional probability formula gives:
P(A|B) = (P(B|A) * P(A)) / P(B)
Putting all the values together, we get:
P(B|A) = (P(A|B) * P(B)) / P(A)
= ((P(B|A) * P(A)) / P(B)) * P(B) / P(A)
= (P(B and A) / P(B)) * P(B) / P(A)
= P(A and B) / P(B)
Substituting the values gives:
P(B|A) = (0.5 * 0.75) / 0.5
= 0.75
Therefore, the probability that a two story home in Dawn's neighborhood owns a computer is 0.75.
What is the period of f(x)=secx?
Enter your answer in the box.
period of f(x)=secx:
Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.
What is function?The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.
Here,
=> F(x) = sec(x) has a 2 phase.
Because the secant function is periodic, its values recur after a predetermined amount of time.
This interval's length is equal to the secant function's duration.
The formula for the secant function is
=> sec(x) = 1/cos.(x).
The cosine function repeats its values every 2 units of x, which is known as its period.
Consequently, the secant function has a period of 2 as well.
Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.
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For Activities 7 through 12, Match each given situation to a possible graph of its density function. Explain.
A random number generator is used to choose a real number between 0 and 100. The random variable x is the number chosen.
The probability that the computer generates a number between 1 and 4 is 4/11.
Since X has a uniform distribution, the probability of generating any number between 0 and 10 is equally likely. Therefore, the probability of generating a number between 1 and 4 is the same as the probability of generating a number between 0 and 4 minus the probability of generating 0
P(1 ≤ X ≤ 4) = P(X ≤ 4) - P(X = 0)
Since X has a uniform distribution, the probability of generating any specific number is 1/11. Therefore
P(X ≤ 4) = (4 + 1)/11 = 5/11
and
P(X = 0) = 1/11
So,
P(1 ≤ X ≤ 4) = (5/11) - (1/11) = 4/11
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I have solved the question in general, as the given question is incomplete,
The complete question is:
A random number generator generates numbers between 0 and 10. Let random variable X be the number generated. Suppose X has a uniform distribution. What is the probability that the computer generates a number between 1 and 4?
find the following answer
According to the Venn diagram the value of [tex]n(A ^ C \cap B ^ C) = {3}[/tex] so the number of elements in that set is 1.
What is Venn diagram ?
A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets. It is usually represented as a rectangle or a circle for each set and the overlapping areas between them, showing the common elements that belong to more than one set. Venn diagrams are widely used in mathematics, logic, statistics, and computer science to visualize the relationships between different sets and help solve problems related to set theory.
According to the question:
To solve this problem, we first need to understand the notation used.
n(A) denotes the set A and the numbers within the braces {} indicate the elements in set A. For example, n(A)={7,4,3,9} means that the set A contains 7, 4, 3, and 9.
n(AnB) denotes the intersection of sets A and B, i.e., the elements that are common to both A and B. For example, n(AnB)={4,3} means that the sets A and B have 4 and 3 in common.
^ denotes intersection of sets
cap denotes the intersection of sets
Now, we need to find the elements that are common to sets A and C, and sets B and C. We can do this by taking the intersection of A and C, and the intersection of B and C, and then taking the intersection of the two resulting sets.
[tex]n(A ^ C) = n(A \cap C) = {3,9}[/tex]
[tex]n(B ^ C) = n(B\cap C) = {3,5}[/tex]
Now, we take the intersection of [tex]n(A ^ C)[/tex] and [tex]n(B ^ C)[/tex]:
[tex]n(A ^ C \cap B ^ C) = {3}[/tex]
Therefore, the answer is 1.
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h(r) = 11r² - 6
g(r) = r² + 8r+ 9
Find h(-2) + g(-2)
According to the solving the function the value of h(-2) + g(-2) is 45.
What exactly is function?function is a mathematical phrase, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are used frequently in mathematics and are crucial for constructing physical links in the sciences.
According to the given information:To find h(-2) + g(-2), we need to evaluate h(r) and g(r) when r = -2, and then add the results:
h(-2) = 11(-2)² - 6 = 44
g(-2) = (-2)² + 8(-2) + 9 = 1
So, h(-2) + g(-2) = 44 + 1 = 45.
Therefore, h(-2) + g(-2) = 45.
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50 pts to anyone that answers
An animator uses green tiles to design a pattern that grows each second, as shown in this diagram. Use the drop-down menus to build functions that describe how the pattern is changing.
The function of tiles with no empty spaces is n(t) = t² + 2t, the function of tiles removed to create empty spaces is r(t) = t.
The function of tiles with no empty spacesWe have a sequence of tiles represented by the numbers 3, 8, and 15.
This sequence can be described as a quadratic sequence, which can be expressed using the formula
n(t) = at² + bt + c.
By substituting the values of the first three terms into this formula, we can find the values of a, b, and c.
a + b + c = 3
4a + 2b + c = 8
9a + 3b + c = 15
These values can also be determined by graphing the sequence. In this case, a = 1, b = 2, and c = 0.
Therefore, the quadratic sequence can be written as n(t) = t² + 2t.
The function of tiles removed to create empty spacesThe given sequence of tiles can be represented as a linear sequence in which the current term is equal to the number of spaces.
Therefore, the function r(t) can be defined as r(t) = t.
The function of tiles usedThe given equation is expressed as:
A(t) = n(t) + r(t)
Therefore, substituting t² + 2t + t for A(t), we get:
A(t) = t² + 2t + t
Consequently, the function can be represented as
A(t) = t² + 3t
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CAN SOMEONE PLEASE HELP thank you so so much please!!!
Step-by-step explanation:
try this option, all the details are in the attachment.
Find the area of a semicircle whose diameter is 28cm
Answer:
The area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.
Step-by-step explanation:
A semicircle is a two-dimensional shape that is exactly half of a circle.
The area of a circle is given by the formula:
[tex]\sf A=\pi r^2[/tex]
where A is the area of the circle, and r is the radius of the circle.
The diameter of a circle is twice its radius.
Given the diameter of the semicircle is 28 cm, the radius is:
[tex]\sf r = \dfrac{28}{2} = 14 \; cm[/tex]
Substituting this into the formula for the area of a circle, we get:
[tex]\sf A = \pi(14)^2[/tex]
[tex]\sf A = 196 \pi[/tex]
Finally, divide this by two to get the area of the semicircle:
[tex]\sf Area\;of\;semicircle = \dfrac{1}{2} \cdot 196 \pi[/tex]
[tex]\sf Area\;of\;semicircle = 98 \pi\; cm^2[/tex]
So the area of a semicircle with diameter 28 cm is 98π cm², or 307.88 cm² to the nearest tenth.
PLEASE HELP ASAP! This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for n. Round to the nearest hundredth. Show your work.
The area of this composite figure made from placing a sector of a circle on a triangle is 95.55 square cm
Calculating the area of the composite figureThe sector area
The area of the sector is calculated as
Area = x/360 * πr²
Where
r² = 8² + 6²
So, we have
r² = 100
This means that
Area = 82/360 * π * 100
Evaluate
Area = 71.55
The triangle area
This is calculated as
Area = 0.5bh
So, we have
Area = 0.5 * 8 * 6
Evaluate
Area = 24
So, the area of the figure is
Figure = 24 + 71.55
Figure = 95.55
Hence, the area is 95.55
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Line AB contains point A(1, 2) and point B (−2, −1). Find the coordinates of A′ and B′ after a dilation with a scale factor of 5 with a center point of dilation at the origin
The coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.
How to find dilated coordinate of A and B?To find the coordinates of the points A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin, we can use the following formula:
[tex]$$(x', y') = (5(x - 0), 5(y - 0)) = (5x, 5y)$$[/tex]
where (x, y) are the original coordinates of the point, and (x', y') are the new coordinates after the dilation.
For point A(1, 2), the new coordinates A' are:
[tex]$$(x_A', y_A') = (5(1), 5(2)) = (5, 10)$$[/tex]
Therefore, the coordinates of point A' are (5, 10).
For point B(-2, -1), the new coordinates B' are:
[tex]$$(x_B', y_B') = (5(-2), 5(-1)) = (-10, -5)$$[/tex]
Therefore, the coordinates of point B' are (-10, -5).
Therefore, the coordinates of A' and B' after a dilation with a scale factor of 5 and a center point of dilation at the origin are A'(5, 10) and B'(-10, -5), respectively.
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if the sum of a number and eight is doubled, the result is seven less than the number. Find the number.
Answer:
Step-by-step explanation:
Let's call the number we're looking for "x".
The problem tells us that "if the sum of a number and eight is doubled, the result is seven less than the number", which can be translated into an equation:
2(x+8) = x-7
Now let's solve for x:
2x + 16 = x - 7
2x - x = -7 - 16
x = -23
Therefore, the number we're looking for is -23.
A lender requires a minimum down payment of 16% of the value of the home. You have $39,000
cash available to use as a down payment toward a home. Determine the maximum home value
that you can finance.
There is a $243,570 cap on the amount you may finance.
Which type of arithmetic is used in finance?MentaI arithmetic, aIso known as "quick math," aIgebra, trigonometry, statistics, and probabiIity are some of the key mathematicaI concepts and abiIities needed in the financiaI sector. A fundamentaI knowIedge of these abiIities shouId be sufficient to quaIify you for the majority of finance occupations.
The highest home vaIue that may be financed is x.
$39,000 in avaiIabIe cash for a down payment
16% is the needed down payment percentage.
16% of the home's worth can be expressed as,
x × 16/100=$39,000
x=39,000/0.16
x=$243,570
We can then infer that the highest vaIue you couId finance is $243,570.
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Point E represents the center of this circle. Angle DEF
has a measure of 80%.
Drag and drop a number into the box to correctly
complete the statement.
An angle measure of 80° is the size of an angle
that turns through
20
50
one-degree turns.
80
100
K
The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.
What are angles?Two lines intersect at a location, creating an angle.
An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.
Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.
In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.
An angle has two primary components: the arms and the vertex. T
he two rays' shared vertex serves as their common terminal.
Hence, The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.
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Which of the following describes the transformation from Figure 1 to Figure 2?
On a coordinate plane, figure 1 has points (negative 2, 5), (negative 2, 4), (negative 3, 4), (negative 3, 2), (negative 5, 2), (negative 5, 5). Figure 2 has points (2, negative 5), (2, negative 4), (3, negative 4), (3, negative 2), (5, negative 2), (5, negative 5).
Initially, while maintaining the very same [tex]x-[/tex]coordinates, the negative reflect across the [tex]x-axis[/tex] modifies the signs of all locations' [tex]y-[/tex]coordinates.
Negative: Does it signify plus or minus?A negative value is one that always has a value lower than zero and is denoted by the minus (-) symbol. In a number line, negative values are displayed just left of zero.
What is the significance of both positive and negative values in math?If a number is higher than zero, it is considered positive. Or less zero numbers are referred to as negative numbers. If a number is bigger than that or equal to zero, it is not negative. If a number falls below or equal to zero, it is non-positive.
This transforms Figure [tex]1[/tex] into a new figure with points [tex](-2, -5), (-2, -4), (-3, -4), (-3, -2), (-5, -2), (-5, -5)[/tex].
Next, the [tex]180^{0}[/tex] rotation about the origin swaps the signs of both [tex]x[/tex] and [tex]y[/tex] coordinates of each point. This results in the final figure with points [tex](2, -5), (2, -4), (3, -4), (3, -2), (5, -2), (5, -5)[/tex].
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Please help!!!!!!!!!!!!!!
Step-by-step explanation:
try this option (see the attachment), answers are marked with red colour.
Please help fast!! Find the slope of a line parallel to the line whose equation is 3x+18y=−486.
Fully simplify your answer.
Answer: -1/6
Step-by-step explanation:
Put the equation into y = mx + b (slope) form.
3x + 18y = -486
18y = -3x - 486
y = -1/6x - 27
If the line is parallel to this line, the slope must be the same.
Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch. (1 point)
help me pls D;
The length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.
How to find the dimensions of rectangle?Since the area of the soap carvings is 300 square inches, we want the top of the bookcase to have the same area. Let's assume the length of the top of the bookcase is "l" and the width is "b". Then we have:
Area of top of bookcase = lb
We want this area to be equal to 300 square inches. Therefore, we can write:
lb = 300
We are solving for "b", so we can rearrange this equation to solve for "b":
b = 300/l
Since we don't know the value of "l", we can't solve for "b" exactly. However, we can approximate it by assuming a value for "l". Let's say we assume that "l" is 20 inches. Then we can calculate "b" as follows:
b = 300/20 = 15
So if the length of the top of the bookcase is 20 inches, the width should be 15 inches to have the correct area.
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Suppose that the volume, V,
of a right circular cylinder is
1280 cubic centimeters and
the radius of its base is
8 centimeters. What is the
height of the cylinder?
0
The height οf the cylinder is apprοximately 6.38 centimetres.
What is the name fοr a cylinder's height?The cylinder's altitude is a perpendicular segment frοm the plane οf οne base tο the plane οf the οther, and the cylinder's height is the length οf the altitude. A cylinder's axis is the segment cοntaining the centres οf the twο bases.
The vοlume οf a right circular cylinder is calculated as fοllοws:
[tex]V = \pi r^2h[/tex]
where V is the vοlume, r is the radius οf the base, and h is the cylinder's height.
Substituting the fοllοwing values:
[tex]1280 = \pi(8^2)h[/tex]
Simplifying:
[tex]1280 = 64\pi h[/tex]
By dividing bοth sides by 64, we get:
[tex]h = 1280/(64\pi)[/tex]
Simplifying and rοunding tο the nearest twο decimal places:
h ≈ 6.38
As a result, the cylinder's height is apprοximately 6.38 centimetres.
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20. Took the quiz, and received a 100 percent.
What is the limit of (n!)^(1/n) as n approaches infinity?
Note: n! means n factorial, which is the product of all positive integers up to n.
Answer:
Step-by-step explanation:
To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:
n! ≈ (n/e)^n √(2πn)
where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.
Using this approximation, we can rewrite (n!)^(1/n) as:
(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)
Taking the limit as n approaches infinity, we have:
lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)
Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:
lim [√(2πn)]^(1/n) = 1
For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:
lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1
Therefore, combining the two terms, we have:
lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1
Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.
Answer:1
Step-by-step explanation:
Subtract 1/9 - 1/14 and give answer as improper fraction if necessary.
Answer:
To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.
So, we will convert both fractions to have a denominator of 126:
1/9 = 14/126
1/14 = 9/126
Now we can subtract them:
1/9 - 1/14 = 14/126 - 9/126
Simplifying the right-hand side by subtracting the numerators, we get:
5/126
Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.
Answer:
1/9-1/14
=14-9/9*14
=5/126
= 25 1/5
Complete the recursive formula of the arithmetic s -17,-8, 1, 10, .... a(1) = -17 a(n) = a(n − 1)+
Answer:
The common difference between consecutive terms in the sequence is 8 (since -17 + 8 = -9, -9 + 8 = -1, -1 + 8 = 7, and so on). Therefore, the recursive formula for this arithmetic sequence is:
a(1) = -17
a(n) = a(n-1) + 8 for n >= 2
This formula says that the first term in the sequence is -17, and each subsequent term is found by adding 8 to the previous term.
(please mark my answer as brainliest)
find a linear homogeneous constant-coefficient differential equation with the general solution that has the form
The linear homogeneous constant-coefficient equation is y'' - 4y' + 2y = 0
A linear homogeneous constant-coefficient equation is of the form:
ay'' + by' + cy = 0
where a, b, and c are constants, and y is a function of x. The general solution of this equation can be written as:
[tex]y(x) = c_1e^{(r_1x)} + c_2e^{(r_2x)}[/tex]
where r₁ and r₂ are the roots of the characteristic equation:
ar² + br + c = 0
In our case, the general solution is given as:
y(x) = [tex]Ae^{2x}[/tex] + Bcos(2x) + Csin(2x)
To find the linear homogeneous constant-coefficient equation that has this general solution, we need to first write the general solution in the form:
[tex]y(x) = c_1e^{(r_1x)} + c_2e^{(r_2x)}[/tex]
where r₁ and r₂ are the roots of the characteristic equation. Comparing this form with the given general solution, we see that r₁ = 2, r₂ = 2i, and r3 = -2i.
Therefore, the characteristic equation is:
a(r-2)(r-2i)(r+2i) = 0
Expanding this equation, we get:
a(r³ - 2r²i - 2ri² + 4r² + 8i²r - 8i) = 0
Simplifying and grouping the real and imaginary terms, we get:
a(r³ - 4r) + 2a(r² + 4) = 0
Dividing by a, we get:
r³ - 4r + 2(r² + 4) = y'' - 4y' + 2y = 0
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Complete Question:
Find a linear homogeneous constant-coefficient equation with the given general solution
y(x)=Ae²ˣ+Bcos(2x)+Csin(2x)
Calculate the area of the shaded segments in the following diagrams. (a) 12 cm 40° (b) 58° 16 cm
(a) 12 cm 40° : Area of shaded segments = 301.44 sq. cm.
(b) 58° 16 cm : Area of shaded segments = 777.04 sq. cm.
Explain about the sector of circle?Two radii that meet at the center to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle calculation and radius measurement are both crucial for solving circle-related difficulties.
Area of sector of circle = Ф/360 * πr²
π = 3.14
r is the radius
Ф is the angle subtended.
(a) 12 cm 40°
Area of shaded segments = 40/60 * 3.14* 12²
Area of shaded segments = 40/60 * 452.16
Area of shaded segments = 301.44 sq. cm.
(b) 58° 16 cm
Area of shaded segments = 58/60 * 3.14* 16²
Area of shaded segments = 58/60 * 803.84
Area of shaded segments = 777.04 sq. cm.
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The diagram for the question is attached.
Find the zeros of the function.
y = (x + 1)(x-2)(x - 5)
The zero(s) of the function are
(Use a comma to separate answers as needed.)
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) an = e−8/√n lim n→[infinity] an =
The sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex], is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).
The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, [tex]a_n =e ^{\frac{{-8}}{\sqrt{n}}}[/tex]. We have to check whether the sequence converges or diverges. Using limits, [tex]lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} [/tex]
n approaches infinity, so square root of n approaches infinity,
= e⁻⁰
= 1/e⁰ = 1 ( finite )
Therefore, it is a convergent sequence.
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