find u, v , u , v , and d(u, v) for the given inner product defined on rn. u = (−12, 5), v = (−8, 15), u, v = u · v (a) u, v (b) u (c) v (d) d(u, v)
Answers
The values of u, v, u, v, and d(u, v) are given below:(a) u, v = 171(b) ||u|| = 13(c) ||v|| = 17(d) u/||u|| = (-12/13, 5/13), v/||v|| = (-8/17, 15/17)(e) d(u, v) = 2√29
Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v. The values of u, v, u, v, and d(u, v) are to be calculated.
Solution: Given inner product defined on Rn, u = (−12, 5), v = (−8, 15) and u, v = u · v.
The dot product of u and v is given by u . v= (-12 * -8) + (5 * 15)u . v= 96 + 75u . v= 171
Now, we have to calculate the norm of u and v, which can be calculated as follows: ||u|| = √u1² + u2²||u|| = √(-12)² + 5²||u|| = √144 + 25||u|| = √169||u|| = 13
Similarly,||v|| = √v1² + v2²||v|| = √(-8)² + 15²||v|| = √64 + 225||v|| = √289||v|| = 17
Now, we have to calculate the unit vector of u and v. T
he unit vector of u and v is given by: u/||u|| = (-12/13, 5/13)v/||v|| = (-8/17, 15/17)Now, we have to calculate d(u, v). The formula to calculate d(u, v) is given by: d(u, v) = ||u - v||d(u, v) = √(u1 - v1)² + (u2 - v2)²d(u, v) = √(-12 - (-8))² + (5 - 15)²d(u, v) = √(-4)² + (-10)²d(u, v) = √16 + 100d(u, v) = √116d(u, v) = 2√29
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Related Questions
2. Ebony and her sister want to open a store where children can buy a doll that they can personalize themselves. They plan to name the store “Make a Friend!” Children purchasing a doll at the store can choose the doll’s hair color, as well as an outfit that consists of a top and a bottom. The possible choices are: Hair color: brown, black, or blonde Top: pink ruffle blouse, blue tank top, black T-shirt Bottom: Pink skirt, blue jeans, black pants, brown shorts (a) How many different unique dolls are possible? Show your work. (b) What are all the possible combinations of hair color, tops, and bottoms? Use a tree diagram or an organized list. (c) Ebony wants to advertise that there are at least 100 different types of dolls available. If she adds another category to make this advertisement true, what is the minimum number of options she will need in this new category? Explain your reasoning. (d) Ebony’s sister says she wants to keep costs down by making sure they add the fewest number of options needed to make the above advertisement true. She believes it would be better to just increase the number of options in each of the current categories. Is Ebony’s sister right? Explain your reasoning. (e) Ebony comes up with a fun promotion called “Mismatch Day,” using the current options. The promotion gives customers a 10% discount if they choose an outfit in which the colors of the top and the bottom do not match. How many fewer choices of dolls do customers have if they take advantage of this promotion? Show your work.
Answers
Answer:
Did you ever get the answer?
Step-by-step explanation:
Solve the systems of equations.
\(y = \frac{2}{3} x +5\\-2x + 3y = 15\)
Answers
The solution for the given system of equations as required to be determined is such that; it has infinitely many solutions.
What is the solution for the given system of equations?It follows from the task content that;
y = (2/3)x + 5 and -2x + 3y = 15.
Also, by substitution, we have that;
-2x + 3 ( (2/3)x + 5 ) = 15
-2x + 2x + 15 = 15
15 = 15.
Consequently; it follows that the system of equations given has infinitely many solutions as the equations are coinciding equations and form coinciding lines when graphed.
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Find f(g(x)] if f(x) = x^2+ 1 and g(x) = x^5
O (x^5+ 1)²
O (x² + 1)^5
O x^10 + 1
None of these
Answers
What is 85 divided by 4973?
Answers
Step Move the decimal point three places to the left in the dividend (85): 0.085
Step 2: Divide 0.085 by 4973: 0.01712
To solve 85/4973, how many times does 4973 go into 85? 0 so subtract 85 by 0, which is 0 and put a 0 with a decimal point on top of the division bar. Carry down a zero that make 85 transform to 850. How many times does 4973 go into 850? 0 so put a above the division bar and do 850 - 0 = 850. Carry a zero down making 850 into 8500. How many times does 4973 go into 8500? 1 so put it above the division bar and subtract 4973 from 8500 = 3527. Carry down a zero to make 3527 into 35270. How many times does 4973 go into 35279? 7 so write it above the division bar. Above the division bar, you should have 0.017. Round it to the nearest hundredth, which is 0.02 since 7 rounds up a number.
(b) The man is going to exit the stairwell at the 4th floor, which is at a height of 42 feet above
ground level. Let t be equal to the number of second it takes for him to get to the 4th floor.
Set up and solve an equation to find the value of t. Round your answer to the nearest tenth
of a second.
Answers
The time taken to get to the 4th can be obtained by dividing the distance given by the speed of the lift.
Distance, height from ground to 4th floor = 42 feets
Time taken to get to the 4th floor = t
Recall :
Time = Distance / speed
We aren't given the speed of the lift ;Assume speed of lift is 7 ft/secThe time taken to get to the 4th floor will be :
\(t = \frac{42}{7} = 6 \: seconds\)Therefore, to obtain the time taken, divide the distance or height of the 4th floor by the speed of the lift.
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steps to solve 6-3y=-6
Answers
Answer:
y = -4
Step-by-step explanation:
6 - 3y = 6
now were going to get the variable and the numbers on different sides
6 - 3y - 6 = - 3y
6 + 6 = 12
now divide each side by -3
-3y / -3 = y
12 / -3 = -4
y = -4
Which of the following statements is false?
• A. A square is a regular quadrilateral.
B. A rectangle is an equiangular quadrilateral.
C. Adjacent angles in a parallelogram are complementary.
•D. Opposite sides of a parallelogram are congruent.
Answers
The statement that is false of quadrilaterals is C. Adjacent angles in a parallelogram are complementary.
What are the type of angles in a parallelogram ?In the tapestry of geometrical relationships, adjacent angles within a parallelogram are not bestowed with the nature of complementarity. Rather, they exhibit a distinct quality known as supplementary.
Unlike the enchanting dance of complementary angles, which combine to form a sum of 90 degrees, adjacent angles in a parallelogram intertwine their measures to yield a sum of 180 degrees. The allure of the parallelogram resides in the congruence of its opposite angles, not the complementarity of its adjacent angles.
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A library bookshelf has 6 shelves. Nine books can fit on each shelf. How many books can the bookshelf hold?
Answers
multiply 6 by 9
please rank brainliest!!!:)
Answer:
54
Step-by-step explanation:
each shelf has 9 books so the equation would be 9x6=54 because there are 6 shelves in total<3
is the quotient of two integers positive negative or zero
Answers
The quotient of two integers can be positive, negative, or zero depending on the signs of the dividend and divisor.
When dividing two integers, the quotient can be positive, negative, or zero. The sign of the quotient depends on the signs of the dividend and the divisor. If both the dividend and divisor have the same sign (both positive or both negative), the quotient will be positive.
If they have opposite signs, the quotient will be negative. If the dividend is zero, the quotient is zero regardless of the divisor.
For example, when we divide 12 by 4, we get a quotient of 3, which is positive because both 12 and 4 are positive integers. However, when we divide -12 by 4, we get a quotient of -3, which is negative because the dividend (-12) is negative and the divisor (4) is positive.
Finally, if we divide 0 by any integer, the quotient is always 0.
Therefore, the quotient of two integers can be positive, negative, or zero depending on the signs of the dividend and divisor.
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help please I will upvote
Let Y₁ and Y₁ be independent continuous random variables each with density function f(y) = Be-By for y> 0 and ß>0 Let X₁ = ₁ + 2Y₂ and X₂ = 2Y₁ + Y₂. What is the joint density of X1 a
Answers
The joint density of X1 and X2 is f(x₁, x₂) = (1/3)B²e-(B(x₁+x₂)/3), where B = ß, X₁ = Y₁ + 2Y₂, and X₂ = 2Y₁ + Y₂.
The joint density function of X₁ and X₂ can be found using the following method;
First, let's write the given random variables in terms of Y1 and Y2:X₁ = Y₁ + 2Y₂X₂ = 2Y₁ + Y₂
The Jacobian matrix of the transformation from (Y₁, Y₂) to (X₁, X₂) is given by:J = [∂(X₁, X₂)/∂(Y₁, Y₂)] = [1 2; 2 1]
The determinant of J is:|J| = -3
The inverse of J is:J^(-1) = (1/|J|) * [-1 2; 2 -1]
The joint density function of X₁ and X₂ is given by:f(x₁, x₂) = f(y₁, y₂) * |J^(-1)|where f(y₁, y₂) is the joint density function of Y₁ and Y₂.
Substituting f(y) = Be-By in f(y₁, y₂) gives:f(y₁, y₂) = Be-By1 * Be-By2= B²e-(B(y₁+y₂))where B = ßSince Y₁ and Y₂ are independent, the joint density function of X₁ and X₂ can be written as:f(x₁, x₂) = B²e-(B(x₁+x₂)/3) * (1/3) * |-3|f(x₁, x₂) = (1/3)B²e-(B(x₁+x₂)/3)
Therefore, the joint density of X1 and X2 is f(x₁, x₂) = (1/3)B²e-(B(x₁+x₂)/3), where B = ß, X₁ = Y₁ + 2Y₂, and X₂ = 2Y₁ + Y₂.
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hello hope all is well with you can you help me with number 2 3 or 4 please
Answers
Given the equation,
\(\chi+2\chi+8=x\)Using hands-on equation kit,
\(\begin{gathered} \text{Where,} \\ \chi=-2 \\ x=2 \end{gathered}\)Substitute your values for the variables in the equation,
\(\begin{gathered} -2+2(-2)+8=2 \\ -2+(-4)+8=2 \\ -2-4+8=2 \\ -6+8=2 \\ 2=2 \end{gathered}\)Hence,
\(\begin{gathered} \chi=-2\text{ and} \\ x=2\text{ } \\ \text{Check is 2=2} \end{gathered}\)The answers have been deduced above.
Explain how you could transform a function to reflect it over the line x = y.
Answers
we will interchange the x coordinates and the y coordinates.
Explanation:
To transform a function to reflect over the line y = x, the x axis and y axis switch places.
For example, if we reflect the point (2, 3) over the line y = x
the x-coordinate and y-coordinate change places:
It becomes: (3, 2)
Since transforming a function to reflect over the line y = x is the same as transforming a function to reflect it over the line x = y.
So, (x, y) becomes (y, x)
We can conclude that, to transform a function to reflect it over the line x = y, we will interchange the x coordinates and the y coordinates.
please answer this asap please
Answers
Answer:
x=3
y=4
Step-by-step explanation:
y=3x-9
5x+4y=32
You substitute what y is into the equation:
5x + 4(3x - 9) = 32
5x + 12x - 36 = 32
17x - 36 = 32
17x = 68
x = 4
Now you substitute x into y:
y = 3x - 9
12 - 9 = 3
y = 3
models that are based on mathematic formula are called _____ models.
Answers
Symbolic models are those that are based on mathematical formulas.
By symbolic model, what do you mean?The goal of symbolic modelling is to help clients become more aware of their own "symbolic domain of experience," allowing them to create their own "metaphor landscape" and explore internal metaphors, which are believed by conceptual metaphor theory to influence behaviour.
What benefits do symbolic models offer?
One of the most significant and defining technologies of next-generation modelling methodologies is swiftly emerging as symbolic computation. It allows the freedom to easily create model equations, manage models more effectively, and reach the best outcomes more quickly.
Describe domain through an example.
the domain name example.com might be connected to the address 198.102. 434.8.
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give a big-o estimate of the product of the first n odd positive integers.
Answers
The product of the first n odd positive integers can be represented as n!! (pronounced "n double factorial"). To estimate its time complexity using big-O notation, we need to analyze the number of operations required to calculate this product.
When calculating n!!, we need to multiply all the odd positive integers from 1 to n. Since there are n/2 odd numbers from 1 to n, the number of operations required is proportional to n/2. Therefore, the time complexity can be approximated as O(n/2).
However, in big-O notation, we simplify this approximation by dropping the constant factor. Therefore, the big-O estimate of the product of the first n odd positive integers is O(n).
In summary, the big-O estimate of the product of the first n odd positive integers is O(n), indicating that the time complexity grows linearly with the size of n.
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How do you find the x value of an angle
Answers
Answer:
Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle. If you are working with equilateral triangles, divide 180 by three to find the value of X.
Step-by-step explanation:
I hope this helps you.
t and w are inversely proportional.
The equation of proportionality is t = 4/w
How will the value of t change if the value
of w is multiplied by 6?
Answers
Step-by-step explanation:
If t and w are inversely proportional, it means that as one variable increases, the other variable will decrease by the same factor. In this case, we have the equation t = 4/w, which means that if we multiply w by a certain factor, t will be divided by the same factor.
If we multiply w by 6, the new value of w will be 6 times the original value:
w' = 6w
To find the new value of t, we can substitute w' into the equation:
t' = 4/w'
t' = 4/(6w)
t' = 2/3w
So we see that t has been divided by 6/1 = 6. Therefore, the value of t will decrease by a factor of 6 if the value of w is multiplied by 6.
After substituting that coordinate, what is the flux dΦ through the patch in terms of dA?
Answers
After substituting the given coordinate in the flux equation, the resulting flux dΦ through the patch can be expressed in terms of dA as dΦ = E⋅dA⋅cosθ
Here, E represents the electric field intensity, dA is the area of the patch, and cosθ is the angle between the normal vector of the patch and the electric field lines passing through it.The term dA represents the differential area of the patch and is used to calculate the total flux through the entire surface by integrating over the entire area. This integration process adds up the contributions of all the small patches of the surface.
Therefore, the flux through any small patch of the surface can be calculated using the above equation by substituting the appropriate values of E, dA, and cosθ. This formula is particularly useful in calculating the flux through curved surfaces or irregularly shaped patches.In summary, after substituting the given coordinate, the flux dΦ through the patch can be expressed in terms of dA using the formula dΦ = E⋅dA⋅cosθ, which helps in determining the total flux through the entire surface.
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The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Marco is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years:
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
Answers
The percentage given shows that the amount is decreasing by 8%.
How to illustrate the information?From the information given, the function is f(x) = 9,628(0.92)x. This illustrates that the amount is decreasing by 8% she compared to the previous year. This was computed as:
= 1 - 0.92
= 0.08
= 8%
For part B, the percentage change will be:
= (8,972 - 8,074.80)/8972 × 10
= 10%
Therefore, the account recorded a greater percentage change in amount of money over the previous year is account B as 20% is lore than 8%.
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Which of the following is an acceptable way to express the useful life of a depreciable asset?a.Expected number of units to be produced by the depreciable asset b.Expected number of hours the depreciable asset will remain productive .c .Expected number of miles a depreciable vehicle will be driven d.Expected life in years of the depreciable asset
Answers
d. Expected life in years of the depreciable asset. The acceptable way to express the useful life of a depreciable asset is in terms of the expected life in years.
The useful life refers to the period of time over which the asset is expected to contribute to the revenue-generating activities of a business.
While options a, b, and c may be relevant factors for certain specific assets (such as units produced, hours of productivity, or miles driven), they do not encompass the overall concept of useful life. Useful life is a broader measure that takes into account the anticipated duration of productive use, regardless of specific output or activity metrics.
Expressing the useful life in years provides a common standard for comparison and allows for consistency in depreciation calculations and financial reporting. It is a practical and widely accepted approach to estimating the lifespan of a depreciable asset.
It is worth noting that the estimated useful life in years may vary depending on the nature of the asset and industry practices. It is typically determined based on factors such as technological advancements, physical wear and tear, economic obsolescence, and the intended purpose of the asset.
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can someone help please
Answers
Answer:
1.6
Step-by-step explanation:
define the type of sequence 7, 14, 28, 56, 112
Answers
Answer:
This is a geometric sequence.
Identify the property that justifies the statement. OP ≅ RS, so RS ≅ OP
Please Hurry!!!!
Answers
Answer: Sym. Prop. of ≅
Step-by-step explanation:
no explanation
Please help me I’ll make u brainliest I swear please
Answers
Since the provided equation is inconsistent, it cannot intersect.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Here,
we can see that the second set of equation,
4x+2y=12
20x+10y=30
4/20=2/10≠12/30
1/5=1/5≠2/5
The given equation is inconsistent so it does not intersect.
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Find the measure of angle A.
1+ 38
x + 68
A) 30°
C) 26°
B) 35°
D) 60°
Answers
Answer:
b
Step-by-step explanation:
b
Please please help I’m failing quadrilateral EFGH has vertices at e (10,4) f (16,4) g (16,10) and h (10,10).
Based on the properties of the diagonals is quadrilateral EFGH a rectangle rhombus or square use the distance and slope formulas to prove your conclusion show your work.
Answers
Answer:
It's a square; vertice f is 6 units to the right of vertice e and g is 6 units above f, and h is 6 units to the left of g. This means there are four sides of equal length, with equal angles.
do you need more than that?
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answers
So subtract both values given from 180
180 - 111 = 69, 69 - 41 = 28
X = 28
An online furniture store sells chairs for $200 each and tables for $700 each. Every
day, the store can ship no more than 18 pieces of furniture and must sell at least
$7600 worth of chairs and tables. If 6 chairs were sold, determine all possible values
for the number of tables that the store must sell in order to meet the requirements.
Your answer should be a comma separated list of values. If there are no possible
solutions, submit an empty answer.
Answers
The possible values for the number of tables that the store must sell in order to meet the requirements are 9 and 10.
Let's solve the problem step by step:
The price of each chair is $200, and if 6 chairs were sold, the total value of chairs sold is 6 \(\times\) $200 = $1200.
The store must sell at least $7600 worth of chairs and tables combined. Since we have already sold $1200 worth of chairs, the remaining amount to be sold is $7600 - $1200 = $6400.
The price of each table is $700. To find the possible values for the number of tables, we divide the remaining amount by the price of each table: $6400 / $700 ≈ 9.1428.
Since the number of tables must be a whole number, the possible values for the number of tables are 9 and 10.
Therefore, the possible values for the number of tables that the store must sell in order to meet the requirements are 9 and 10.
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-75x/4>14/2 I don't get this can someone help me with this?
Answers
Is this the equation ur supposed to solve because the question was a little bit messy
\( \frac{ - 75x}{4} > \frac{14}{2} \)
Answer
Answer two questions about Systems A and B:
System A System B
x-7y=-3 4x+y=7
4x+y=7 x−7y=−3
1) How can we get System B from System A?
Choose 1 answer:
A. Swap only the left-hand sides of both equations
B. Swap the order of the equations
C. Replace one equation with itself where a quantity is added to only one side
D. Replace one equation with itself where the same quantity is added to both sides
2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? A. Yes B. No
Answers
Answer:
B.) swap the order of the equations