When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.
What is matrix?
A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.
The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.
When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.
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Write as a single fraction in its simplest form.
[tex] \frac{ {x}^{2} - 3x}{ {x}^{2} - 9 } [/tex]
Answer:
[tex]\frac{x}{x+3}[/tex]
Step-by-step explanation:
[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]
[tex]\frac{x}{x+3}[/tex]
1. Given CR bisects ∠A C D , find x.
Answer:
x = 4
Hope it helps.
if you apply demorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))), you get:
Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).
DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).
Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).
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You install 538 feet of fencing along the perimeter of a rectangular yard. The width of the yard is 127 feet. What is the length of the yard?
Solve the following system of equations graphically on the set of axes below.
y=- 5/2 x-6
x - y= -1
Plot two lines by clicking the graph.
Click a line to delete it.
We have drawn the graph, and point (-2, -1) satisfies both equations and lies on the graph of the system.
What is the system of equations?
A system of equations is a set of two or more equations that are solved simultaneously. In other words, a system of equations is a group of equations that are related to each other and must be considered together in order to find a solution.
The given equations are
y = -5/2x -6
x - y = 1
To find the points of these equations on the graph, we need to solve the system of equations formed by the two given equations.
After solving these equations, we get the point (-2, -1).
Hence, we have drawn the graph, and point (-2, -1) satisfies both equations and lies on the graph of the system.
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Let U = {−8, −7, −6, −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8}, A = {−7, −4, −2, −1, 1, 4, 8}, B = {−7, −6, −3, −2, −1, 3}, and C = {−4, 0, 2, 4, 7}. Use the roster method to write the set. Enter EMPTY or ∅ for the empty set.) (a) Find B' (b) Find A' ∪ (B ∩ C).
After solving the following sets in roster form we get B' = {-8,-5,-4,0,1,2,4,5,6,7,8} and
A' U (B ^ C) = {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }
What are sets and roster form?
Either elements or members of a set are terms used to describe the objects that make up a set. A set's components are denoted by curly brackets enclosing them and commas separating them. The sign "" is used to indicate that an element is part of a set. 2 A in the previous illustration. The symbol "" is used to designate an element that is not a part of a set. Here, 3 ∉ A.
The roster notation, in which the components of the sets are contained in curly brackets and separated by commas, is the most popular way to express sets. Set B, for instance, which is made up of the first five even integers, is equal to 2, 4, 6, 8, and 10. The order of the set's components in a roster form is irrelevant; for instance, the first five even integers can equally be described as 2, 6, 8, 10, 4. Additionally, if a set has an infinite number of items, the endless list is defined by adding a string of dots to the end of the final element. For instance, the representation of infinite sets is X = 1, 2, 3, 4, 5,..., where X is the set of natural numbers.
Please see the examples below for a summary of the roster form's notation.
Set A = 1, 2, 3, 4, and 5 in the finite roster notation of sets (The first five natural numbers)
Sets in Infinite Roster Notation: Set B = {5, 10, 15, 20 ....} (The multiples of 5) (The multiples of 5)
a) B' = U - B = {-8,-5,-4,0,1,2,4,5,6,7,8}
b) A' U (B ^ C)
A' = U - A = {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }
B intersection C = ∅
A' U (B ^ C) = A' = {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }
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Find the angle round to the nearest degree. please help.
63 degrees is the angle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angle triangle.
The opposite side length is 85 and the adjacent side is 38.
Opposite side=85
Adjacent side=38.
Calculate Opposite/Adjacent
= 85/38= 2.236
Which is tanθ=2.236
Now tan inverse on both the sides
θ=tan⁻¹2.236
θ=tan⁻¹2
θ=63 degrees.
Hence, the angle is 63 degrees.
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The medians of ATUV are TX, UY, and VW. They meet at a single point Z.
(In other words, Z is the centroid of ATUV.)
Suppose UY=27, TZ=24, and ZW = 10.
Find the following lengths.
Note that the figure is not drawn
to scale..
7
U
X
VW =
UZ = 0
ZX = 0
The lengths of the segments are VW = 10, UZ = 37, and ZX = 34.
What is a centroid of a triangle?
The centroid is the center point of the object. The point in which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians.
Point Z is the centroid of ΔTUV.
Since Z is the centroid of ATUV, the medians of the triangle split each other into segments that are in the ratio 2:1. Therefore, segment ZW is twice as long as segment WZ. Since segment ZW has length 10, segment WZ has length 10 / 2 = 5.
Since Z is the centroid of the triangle, the lengths of the medians of the triangle are also proportional to the lengths of the corresponding sides of the triangle. Therefore, the length of VW is twice the length of WZ, which is 5. Therefore, VW has length 2 * 5 = 10.
To find the length of UZ, you can add the lengths of UY and ZW: UZ = UY + ZW = 27 + 10 = 37.
To find the length of ZX, you can add the lengths of TZ and ZW: ZX = TZ + ZW = 24 + 10 = 34.
Therefore, the lengths of the segments are VW = 10, UZ = 37, and ZX = 34.
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Can anyone help me ASAP?
What is the value of p ?
By using the fact that the sum of the internal angles of a triangle is 180°, we will see that p = 80°
What is the value of p?Notice that on the top vertex of the triangle we have a plane angle, then we can write:
p + 49° + A = 180°
So we can solve that really simple linear equation we can find the value of A, the top internal angle of the triangle:
A = 180° - 49° - p
A = 131° - p
Now remember that the sum of the 3 internal angles of a triangle is equal to 180°, so now we can write the equation:
131° - p + p - 16° + p- 15° = 180°
p = 180° - 131° + 16° + 15°
p = 80°
The value of p is 80°.
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The area of a rectangle is given by the function A(x) = 2x3 + 6x2 + 5x + 15. If the length is defined by x + 3, what is the width of the rectangle?
Answer:
2x² +5
Step-by-step explanation:
You want the width of a rectangle with a length of x+3 and an area of A(x) = 2x³ +6x² +5x +15.
AreaThe area is the product of length and width, so the width will be ...
A = LW
W = A/L = (2x³ +6x² +5x +15)/(x +3)
The cubic expression can be factored by grouping, so we have ...
Area = (2x³ +6x²) +(5x +15)
= 2x²(x +3) +5(x +3)
= (2x² +5)(x +3)
Then the width is ...
[tex]\text{width}=\dfrac{(x+3)(2x^2+5)}{x+3}=\boxed{2x^2+5}[/tex]
The width of the rectangle is 2x² +5.
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8w-16 how do i answer this
The factor of the expression 8w - 16 will be 8 and (w - 2).
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.
The expression is given below.
⇒ 8w - 16
The factor of each term in the expression, then we have
8w = 8 x w
16 = 8 x 2
Then the expression is written as,
⇒ 8w - 16
⇒ 8 × w - 8 × 2
⇒ 8 × (w - 2)
⇒ 8(w - 2)
The component of the articulation 8w - 16 will be 8 and (w - 2).
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a number has the same digit in its hundreds place and in its hundreds place. how many times greater is the value of the digit in the hundreds place than the value of the digit in the hundreds place
A number has the same digit in its hundreds place and in its hundreds place. 10,000
What is the value of the digit?Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.
Let's say that the digit is a 1.
Therefore, the value of the hundreds position in a number is equal to 100.
The value of the hundredth position in a number is equal to 0.01%.
The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:
As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.
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CQ
A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?
A. 100,00
B. 100
C. 1,000
D. 10,000
Can someone please explain step by step on how I solve this equation?
-1 - (-0.25) = ?
Answer: -1 - (-0.25) = -0.75
Step-by-step explanation:
The way you would do that is by first pretending as the negative sign (-), isn't present.
Then do "1 - 0.25".
1.00 - 0.25 = 0.75
After you solved the equation, then we can add the negative sign (-), back into the equation = -1 - (-0.25) = -0.75 ✅
consider all postive interges that are multiples of 20 and that are less than or equal to 300. what fraction of those interges are multple of 15
Answer:
1/3
Step-by-step explanation:
Every third multiple of 20 is a multiple of 15.
LAST QUESTION PLEASE HELP ASAP I HAVE 5 MINS!!!
Answer:
Step-by-step explanation:
When any value of x, other than 0, is multiplied by itself the result will ALWAYS be a POSITIVE value. Therefore, equations in the form x square =p, where p is GREATER THAN 0, will have 2 SOLUTIONS.
I need help with this please help me
The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).
What does a math translation mean?Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.
What does math formula translation mean?Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.
Briefing:The image of the translation is (9,-2).
The point is given as: P = (-6, -4)
The image of the point is: P' = (-2, 3)
The translation rule is calculated as:
T = x - 2 - (-6), y+3-(-4)
so, T = x + 4, y + 7
So, the image of (5, -1) is:
the Image of the translation = 5 + 4, -1 + 7
Hence, the image of the translation is (9, 6).
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In what ways did WWII-era policies deliver prosperity to white veterans and their families while preventing the same for Americans and veterans of color?
The WW2 era helped tp deliver several prosperity to the whites in the forms of college education funding, It gave them unemployment insurances in the nation and also helped them with housing benefits.
How did WW2 help the US?This bill, commonly known as the G.I. Bill, was passed by President Franklin D. Roosevelt on June 22, 1944, and it gave World War II veterans money for housing, unemployment insurance, and college tuition. Millions of WWII and post-World War II military veterans now have access to higher education.
It made it possible for hundreds of thousands of men and women to pursue higher education, many of whom would not have been able to do so without its assistance. Although it left many minority veterans behind, the bill also contributed to the growth of the middle class in America.
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When an observed difference between two groups on the dependent variable is attributed to the effect of the dependent variable through statistical hypothesis testing then we know that
it is unlikely that the difference would occur by chance alone
It is true that when difference on dependent variable is attributed to effect of that variable through statistical hypothesis testing then it is unlikely that the difference would occur by chance alone
A formal assertion about the nature of a phenomenon made within the constraints of a statistical model is known as a statistical hypothesis.
Statistical hypothesis is a description of the makeup of a population. A population parameter is frequently used to express it.
There are two statistical hypotheses used in hypothesis testing. The above-described null hypothesis (H0) is the first.
If it turns out that the null hypothesis is statistically invalid, an alternative hypothesis (Ha) for each H0 will be given preference. Depending on the research hypothesis, the Ha may be directed or nondirectional.
About the statement in the question,
It is improbable that an observed difference between two groups on the dependent variable would occur by chance alone when the difference is explained by the effect of the dependent variable through statistical hypothesis testing.
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A phone company surveys a sample of current customers to determine if they use their phones most often to text or use the Internet. They sort the data by payment plans, as shown below. Plan A: 27 text, 21 Internet Plan B: 13 text, 10 Internet Answer the questions to determine a conditional probability. What is the probability that a randomly selected customer who is on plan B uses the phone most often to text? Give the answer in fraction form.
The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23
How to solve fraction word problems?We are given that;
The data by payment plans are;
Plan A: 27 texts, 21 Internet
Plan B: 13 texts, 10 Internet
Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.
The total number of observations for plan B is; 13 +10 = 23
The number of customers that are on payment plan B = 23 customers are on payment plan B.
The number of customers that are on plan B text is; 13
Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;
Probability = 13/23
The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.
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- At a bake sale, the Math Club raised $225 by selling 300 baked goods. If the amount
raised varies directly with the baked goods sold, how much money will be raised for
selling 450 baked goods?
Record your answer on the answer document.
5x3
The amount of money for selling 450 baked goods will be
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Now,
Let the amount of money for selling 450 baked goods = x
Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.
And, The amount raised varies directly with the baked goods sold.
Hence, By definition of proportion we get;
⇒ $225/300 = x / 450
⇒ x = 225 × 450 / 300
⇒ x = $337.5
Thus, The amount of money for selling 450 baked goods = $337.5
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What are the domain and range of the function F(x) = 3/4 x + 5?
Domain (-infinite, infinite)
Range (-infinite, infinite)
Domain (3/4, infinite)
Range (-infinite, 5)
Domain (-infinite, 3/4)
Range (5, infinite)
Domain (3/4, infinite)
Range (5, infinite
The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.
What is function?A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
What is domain and range?The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).
Here,
f(x)=3/4x+5
Domain=(-infinite, 3/4)
Range=(5, infinite)
The domain for given function is (-infinite, 3/4) and range is (5, infinite).
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which are prime polynomials
-12f+21
f-36
-3f-23
5f+10
Answer:
f - 36
-3f - 23
are your prime polynomials.
In the short run, if average variable cost equals $50, average total cost equals $75, and output equals 100, the total fixed cost must be
A. $25
B. $2,500
C. $5,000
D. $7,500
The total fixed cost must be B . $2,500 .
Given :
Average variable cost ( AVC ) = $50
Average total cost ( ATC ) = $75
Output ( Q ) = 100
Since Average fixed cost is the difference between the average total cost and the average Variable cost. This will be:
Average fixed cost = average total cost - average Variable cost
Average fixed cost = $75 - $50
Average fixed cost = $25
We know that :
AFC = TFC / Q
TFC = AFC × Q
TFC = $25 × 100
TFC = $2500
Therefore, total fixed cost is $2500
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A scientist began measuring the temperature of a solution when it was 100 °F. The temperature of the solution
decreased at a constant rate of 1.5 °F per hour.
Which function can be used to find y, the temperature of the solution in degrees Fahrenheit after x hours?
Ay 1.5x - 100
By 1.5x + 100
y 100x1.5
Oy - 100x + 1.5
Conditional problems are problems that involve one or more conditions that must be met in order for a certain action to be taken or a certain result to be obtained. The temperature of the solution in degrees Fahrenheit after x hours, is y = 1.5x - 100.
The required details for Conditional problems in given paragraph
This function models the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. The initial temperature of the solution is 100 °F, and the temperature decreases by 1.5 °F for each hour that passes. Therefore, the temperature of the solution after x hours can be found by subtracting 1.5x degrees from the initial temperature of 100 degrees.
For example, if we plug in x = 2 into the function, we get y = 1.5 * 2 - 100 = 3 - 100 = -97, which means that the temperature of the solution after 2 hours is -97 °F.
The other options listed are not correct because they do not correctly model the temperature of the solution as it decreases at a constant rate of 1.5 °F per hour. Option A is incorrect because it adds 1.5x degrees to the initial temperature, rather than subtracting it. Option B is incorrect because it adds 100 degrees to the temperature, rather than subtracting it. Option C is incorrect because it multiplies the initial temperature by 1.5x, rather than subtracting 1.5x degrees from it. Option D is incorrect because it adds 1.5 to the temperature, rather than subtracting 1.5x degrees from it.
what are conditional problems?
Conditional problems are often expressed using words like "if," "then," or "when." For example, a conditional problem might involve finding the value of a variable x if it satisfies a certain condition, such as "If x is greater than 5, then x is even." In this case, the problem specifies that x must be greater than 5 in order for it to be even.
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Which number is a solution of the inequality?
x(7-x) > 8
x(7 - x) > 8
Steps for calculationFirst solve x(7 - x) = 8
x^2 - 7x + 8 = 0
x = 5.56, 1.44
If we plug in these values into the original equation we can see that solution is
1.44 < x < 5.56
Meaning and definition of systems of inequality:The value of the variable(s) that transforms the inequality into a true statement is the solution. Think about the example (x+3>5). If we provide any real value bigger than (2) for this inequality, it will be true (x). (therefore) This inequality's answer is (x>2)A collection of two or more inequalities in one or more variables is referred to as a system of inequalities. Systems of inequalities are utilized when a scenario calls for several solutions but also places multiple restrictions on those answers.The best answer is often found by solving a set of linear inequalities. This response could be as simple as calculating the number of products that need be produced in order to maximize profit or as complex as selecting the ideal medication regimen for a patient. The different kinds of inequalities and how to solve them will be covered in this article.To learn more about Systems of inequalities refer https://brainly.com/question/26119697
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Hey what is 0.18 x 0.02
Answer:
0.0036
Step-by-step explanation:
Answer: 0.0036
Step by step explin
You are making several purchases from the I.B. Electric electronics store. You can buy from this store online or in a physical store. You have a coupon for 10% off that can only be used in the physical store and a $5.00 off coupon that can only be used online. The sales tax of 5% only applies to the physical store. Shipping for the online store is a flat rate of $6.99. Using this information and the information below, which way would you save the most money?
15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.
Which way would you save the most money?$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.
Let's say the entire amount spent was $100.
In a physical store, 100 times 15% equals 15 off.
100 - 15 = 85 is the item's reduced cost.
85 x 6% is 5.1 sales tax.
85 + 5.1 = 90.10 as a whole price
Internet shop:
Discounted cost of item: 100 - 5 = 95
95 plus 8.99 is 103.99 in total.
15% discount; 6% sales tax in-store.
Online retailer: $5 discount; $8.99 for delivery.
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Consider the vector function given below. r(t) = (9t, 4 cos(t), 4 sin(t)) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) N(t) = (b) Use this formula to find the curvature. k(t) = Consider the following vector function. r(t) = (2V2t, ezt, e-2t) (a) Find the unit tangent and unit normal vectors T(t) and N(t).
From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
(a) To find the unit tangent and unit normal vectors, we use the following formula:
T(t) = (1/|r'(t)|) * r'(t)
N(t) = (1/|r'(t)|) * (r'(t) x r"(t))
where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.
For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).
Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))
To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).
Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))
and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).
(b) To find the curvature, we use the following formula:
k(t) = |r'(t) x r"(t)| / |r'(t)|3
For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).
Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3
= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)
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Please help me with this question
Answer:
Point of intersection is (13.72, 660)
Step-by-step explanation:
You have to use your graphing tool to answer questions 2 and 3.
Then click on the point of intersection and note the coordinates.
That's it.
This can also be solved mathematically but since the question does not ask I have not given that solution process.
Graph attached
