Suppose ū= (4,2,-5) and ū= (1,5, 4). Then: 1. The projection of u along v is ______2. The projection of u orthogonal to vis______
Answers
1. The projection of u along v is
\(=(-\frac{100}{27},\frac{100}{27},\frac{40}{27})\)
2. The projection of u orthogonal to v is
\((\frac{35}{27} ,\frac{-19}{27} ,\frac{-40}{27} )\)
Given:
u = (-5, 3, 0) and v = (5, -5, -2)
\(Proj^u_v=\frac{u.v}{|v|^2}v=\frac{(-5,3,0).(5,-5,-2)}{5^2+(-5)^2+(-2)^2}*(5,-5,-2)\\\)
\(=\frac{-25-15}{25+25+4}(5,-5,-2)=\frac{-40}{54}*(5,-5,-2)\\\)
\(=(-\frac{100}{27},\frac{100}{27},\frac{40}{27})\)
Orthogonal to v
\(u-Proj^u_v=(-5,3,0)-\frac{-40}{54}*(5,-5,-2)=(-5,3,0)+\frac{20}{27}*(5,-5,-2)\\\)
\(=(-5+\frac{100}{27},3-\frac{100}{27},0-\frac{40}{27})=(-\frac{35}{27},-\frac{19}{27},-\frac{40}{27})\)
Therefore, the projection of u along v and the projection of u orthogonal to v is \(=(-\frac{100}{27},\frac{100}{27},\frac{40}{27})\) and \((\frac{35}{27} ,\frac{-19}{27} ,\frac{-40}{27} )\).
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Related Questions
Karan and Riya were asked to construct triangles. Before constructing the triangles, they were asked to specify two angles of the triangle they were constructing and give the name of the type of triangle they planned to construct. The submission from Karan and Riya were as below. Karan : ΔXYZ, ∠Y = 85° , ∠Z = 115° , YZ = 5.8 cm, obtuse angled triangle Riya : ΔLMN, ∠L = 60° , ∠M = 90° , MN = 6.2 cm, right angled triangle From the options given below, identify the correct statement.
Answers
Karan plans to construct an obtuse angled triangle ΔXYZ, and Riya plans to construct a right angled triangle ΔLMN.
The given information:
Karan plans to construct an obtuse angled triangle ΔXYZ with ∠Y = 85° and ∠Z = 115°.
Riya plans to construct a right angled triangle ΔLMN with ∠L = 60° and ∠M = 90°.
We can make the following observations:
The sum of angles in a triangle is always 180°.
The measure of the third angle in each triangle as follows:
ΔXYZ:
∠X = 180° - ∠Y - ∠Z
= 180° - 85° - 115°
= 40°
ΔLMN:
∠N = 180° - ∠L - ∠M
= 180° - 60° - 90°
= 30°
In an obtuse angled triangle one angle is greater than 90°.
In ΔXYZ, ∠Z = 115° is greater than 90° so it is indeed an obtuse angled triangle.
In a right angled triangle one angle is exactly 90°.
In ΔLMN, ∠M = 90° is the right angle so it is indeed a right angled triangle.
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. What is the minimum number of rows of bricks
needed to build a wall that is at least 4 feet
a
tall if each brick is 2.25 inches tall?
Answers
Answer: 22 rows
Step-by-step explanation: Divide 48 by 2.25 and round up.
Hope this helps, have a good day
Let f, g : (M, d) → (V, ∥ · ∥) be two functions, where (M, d) is a metric space and (V, ∥ · ∥) is a normed space.
USE THE SEQUENTIAL CRITERION (NOT E-D DEFINITION) to show that if f and g are continuous at x0 ∈ M, so is f + g;
Answers
We have shown that {f+g(xn)} converges to f+g(x0) in V, and f+g is continuous at x0.
To show that f + g is continuous at x0 ∈ M using the sequential criterion, let {xn} be a sequence in M that converges to x0. We need to show that {f+g(xn)} converges to f+g(x0) in V.
Since f and g are continuous at x0, we know that {f(xn)} and {g(xn)} both converge to f(x0) and g(x0), respectively.
Thus, we have two convergent sequences {f(xn)} and {g(xn)}, and we can use the algebraic properties of limits to show that {f(xn) + g(xn)} converges to f(x0) + g(x0).
Specifically, let ε > 0 be given. Since f and g are continuous at x0, there exist δ1, δ2 > 0 such that d(x, x0) < δ1 implies ∥f(x) - f(x0)∥ < ε/2 and d(x, x0) < δ2 implies ∥g(x) - g(x0)∥ < ε/2. Choose δ = min{δ1, δ2}.
Now, let N be such that d(xn, x0) < δ for all n ≥ N. Then we have:
∥(f+g)(xn) - (f+g)(x0)∥ = ∥f(xn) + g(xn) - f(x0) - g(x0)∥
≤ ∥f(xn) - f(x0)∥ + ∥g(xn) - g(x0)∥ (by the triangle inequality for norms)
< ε/2 + ε/2 = ε
Therefore, we have shown that {f+g(xn)} converges to f+g(x0) in V, and hence f+g is continuous at x0.
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in its simplest form, kanban consists of a whiteboard divided into multiple columns. what are they titled?
Answers
The correct option for whiteboard of the Kanban are-
b) Planned; e) Done; f) WIP
Explain the term Kanbanboard?The work that needs to be done, that work that is being done, and the work that has been finished are all displayed on a Kanban Board.
It's a graphic representation of a person's, a team's, or a department's value stream, which has been diagrammed on a board, a wall, or specifically designed Kanban software.The purpose of the Kanban technique applied to knowledge management is the same as it was in manufacturing even though it was developed as a stock management tool in Toyota manufacturing: better visualize work, restrict work progress, optimize flow, and uncover improvement opportunities.Thus, the more visible a Kanban board is, the better; optimum outcomes are likely to be achieved when a team can always see it.
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The complete question is-
In its simplest form, Kanban consists of a whiteboard divided into multiple columns. What are they titled?
a) In Queue
b) Planned
c) Opened Ticket
d) Delayed
e) Done
f) WIP
An airplane flying from los angeles to NYC losess both engines and all steering controols at 10,000 ft of altatude it falls at a constant rate of 500 ft per minute medical staff need to know when this plane will crash
Please hurry if you answer ill mark you brainlest!!!
Answers
Answer:
20 min i hope this answers helps u
Step-by-step explanation:
10000÷500=20
Sierra is downloading songs. In 9 minutes,
she downloads 18 songs. In 18 minutes, she
downloads 36 songs. Is the rate of
downloads per minute constant? If so, what
is the constant of proportionality?
Answers
The rate of downloads per minute is constant because based on the given information, the number of songs is always twice the number of minutes.
Therefore, the constant of proportionality is 2.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the systems of equations with their solution sets. y + 12 = x2 + x x + y = 3 y − 15 = x2 + 4x x − y = 1 y + 5 = x2 − 3x 2x + y = 1 y − 6 = x2 − 3x x + 2y = 2 y − 17 = x2 − 9x -x + y = 1 y − 15 = -x2 + 4x x + y = 1 Solution Set Linear-Quadratic System of Equations {(-2, 3), (7, -6)} arrowRight {(-5, 8), (3, 0)} arrowRight {(-2, 5), (3, -5)} arrowRight {(2, 3), (8, 9)} arrowRight
Answers
Answer:
Step-by-step explanation:
The solution of this systems of equations is the intersection of both graphs
Let's kick start with a:
a)
\(y+12 = x^2+x \\ \\ x+3 = y\)
From the first attached diagram by using graph:
the solution is the set {(-5, 8), (3, 0)}
b)
\(y-15=x^3+4x \\ \\ x-y =1\)
Using the graph tool from the last diagram below;
the solution is the set⇒( there is no solution)
c)
\(y+5 =x^2-3x \\ \\ 2x+y =1\)
From the second attached diagram by using graph:
the solution is the set {(-2, 5), (3, -5)}
d)
\(y-6=x^2-3x \\ \\ x+2y =2\)
the solution is the set ⇒ there is no solution (shown in the last diagram below)
e)
\(y-17=x^2-9x \\ \\ -x+y =1\)
the solution is the set {(2, 3), (8, 9)} as shown in the third diagram
f) Lastly:
\(y-15=-x^2+4x \\ \\ x+y =1\)
Using the graph tool from the fourth diagram below;
the solution is the set {(-2, 3), (7, -6)}
The solution to the system of equations are the truth values of the system of equations
\(\mathbf{(a)\ y + 12 = x^2 + x,\ x + 3 = y}\)
The graphs of the equations intersect at (-5,8) and (3,0).
So, the solution set is {(-5,8), (3,0)}
\(\mathbf{(b)\ y - 15 = x^3 + 4x,\ x - y = 1}\)
The graphs of the equations do not intersect
So, the system has no solution
\(\mathbf{(c)\ y + 5 = x^2 - 3x,\ 2x + y = 1}\)
The graphs of the equations intersect at (-2,5) and (3, -5).
So, the solution set is {(-2, 5), (3, -5)}
\(\mathbf{(d)\ y - 6 = x^2 - 3x,\ x + 2y = 2}\)
The graphs of the equations do not intersect
So, the system has no solution
\(\mathbf{(e)\ y - 17 = x^2 - 9x,\ -x + y = 1}\)
The graphs of the equations intersect at (2,3) and (8,9).
So, the solution set is {(2, 3), (8, 9)}
\(\mathbf{(f)\ y - 15 = -x^2 + 4x,\ x + y = 1}\)
The graphs of the equations intersect at (-2,3) and (7,-6).
So, the solution set is {(-2, 3), (7, -6)}
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a box contains a combination of solid-colored tickets: 1/10 of the tickets are green, 1/2 are red , 1/4 are blue, and the remaining 30 tickets are white. how many blue tickets are in the box?
Answers
There were 50 blue box at total in the box.
What is combination?In mathematics, a cοmbinatiοn is a way οf selecting items frοm a cοllectiοn where the οrder οf selectiοn dοes nοt matter. Suppοse we have a set οf three numbers P, Q and R. Then in hοw many ways we can select twο numbers frοm each set, is defined by cοmbinatiοn.
In smaller cases, it is pοssible tο cοunt the number οf cοmbinatiοns, but fοr the cases which have a large number οf grοup οf elements οr sets, the pοssibility οf a set οf cοmbinatiοn is alsο higher.
The bοx will be represented as (x)
From the question, we form:
White tickets = (1 - 1/10 - 1/2 - 1/4)x = 30
Blue tickets = 3/20 x = 30
Blue tickets = = 30 x 20 / 3 = 200
Blue tickets = 1/4 x 200 = 50
Thus, There were 50 blue box at total in the box
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what would the distance between the ordered pairs (-2,3) and (4,-6) be?
Answers
Answer: 5.099
Step-by-step explanation:
What is the value of n?
1131
nº
160°
A. 290
B. 490
C. 20°
D. 690
Answers
Answer:
c as 131 -180=49° is the answer
In the circle below, if < B = 39 °, what is the measure of arc AB?
Answers
From my analysis, the answer is likely to be D. I don't have a formula to prove it though.
Answer: 78 degrees.
Step-by-step explanation:
The other guy is wrong don't listen to him.
15.
Identify a transformation of the function ƒ(x) = x by observing the equation of the function g(x) = x – a.
A horizontal shift a units to the right.
A vertical shift a units downward.
A horizontal shift a units to the left.
A vertical compression by a factor of 1/a.
Answers
Answer:
A horizontal shift a units to the right.
Step-by-step explanation:
f(x) =x, is a line with the the x-intercept at (0,0)
g(x) = x-a, is a line that has the same slope as line f(x) , yet has a x-intercept at (a,0) the line moved a units to the right
Find f^-1(x) where
f(x) = 3x + 2 / x
Answers
Answer:
denoted interchange solve
Step-by-step explanation:
y= (2-x)/3 Let f(x) be denoted by y, thus y= -3x+2 Now interchange x and y, it becomes x= -3y+2 Solve for y, y= (2-x)/3 This is f^(-1) x
Answer the 4 question in the photo for EASY points ( 20 points )
Answers
The pink ribbon is shortest.
Purple > yellow > silver > pink
Add these fractions, giving your answer
in its simplest form.
6/12 + 2/13 =?
Answers
Answer: 0.6 espero haberte ayuado
Step-by-step explanation:
(I NEED HELP ASAP)Edna has a segment with endpoints F(4, 9) and G(7, 2) that is divided by a point H such that FH and GH form a 1:3 ratio. She knows that the distance between the x-coordinates is 3 units. Which of the following fractions will let her find the x-coordinate for point H? (6 points)
1 over 4
1 over 3
3 over 4
3 over 1
Answers
Answer:
1/4 is your answer.
Step-by-step explanation:
The fraction 1/4 will let Edna find the x-coordinate for point H.
How do we find the coordinates of a point on a line?When the point is (x, y) and the two ends of the segment are (x1, y1) and (x2, y2), the following equation can be used:
x = x1 + [m / (m + n)] × (x2 - x1)
y = y2 + [m / (m + n) ] × (y2 - y1)
m:n is the ratio in which the point divides the line.
The fraction that can be used to find the coordinates of H is:It is given that point H divides the line FG into two at the ratio of 1:3, where F and G are at (4, 9) and (7, 2) respectively.
Therefore, m = 1 and n = 3.
We can now use this to find the fraction. It is known that the formula for finding the fraction is m/m+n. Therefore, the fraction is:
m/m+n = 1/1+3
= 1/4
This is the fraction that can be used to find the coordinates of H. The fraction is 1/4.
Thus, we have found the fraction 1/4 will let Edna find the x-coordinate for point H. The correct answer is option A.
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A plumber charges $25 for a service call plus $50 per hour of survice write an equation in slope-intercept form the cost for,C, after h hours of survice
Answers
The total cost for 8 hours of work is $425.
The total cost for 10 hours of work is $525.
The total amount the plumber earns is made up of a fixed charge and a variable charge. A fixed charge is a charge that remains constant regardless of the number of hours the plumber works. The fixed charge is $25. The variable charge is the charge that increases per hours worked. The variable charge is $50 per hour.
Cost = fixed charge + variable charge
C = $25 + $50h
The total cost for 8 hours
$25 + $50(8)
$25 + $400
= $425.
The total cost for 10 hours
$25 + $50(10)
$25 + $500
$525.
Paul has a 3/4 inch long bolt. he buys a bolt that is longer 1/8 and a bolt that is inch shorter 3/4 - inch than the bolt. what are the lengths of the two bolts he buys?
Answers
Answer:
Step-by-step explanation:
The first bolt he buys has length 3/4 in plus 1/8 in, which comes out to
6/8 + 1/8 inch, or 7/8 inch.
The second bolt length cannot be determined using the information given: "3/4 - inch shorter." Ensure that you have copied down this probjem completely and accurately.
What is the slope of the line represented by the equation y = 4/5x -3?
-3
-4/5
4/5
3
Answers
Therefore m or slope is 4/5
Can someone please help me
Answers
Answer:
A.
Step-by-step explanation:
The Ramirez family and the Stewart family each used their sprinklers last summer. The water output rate for the Ramirez family's sprinkler was 40 L per hour.
The water output rate for the Stewart family's sprinkler was 15 L per hour. The families used their sprinklers for a combined total of 55 hours, resulting in a total
water output of 1575 L. How long was each sprinkler used?
Answers
Answer:
15.5
Step-by-step explanation:
Yes
a rocket rising from the ground has a velocity of v(t) = 2,000 te−t⁄60 ft/s, after t seconds. how far does it rise in the first minute? (round your answer to the nearest foot.)
Answers
The rocket rises to a height of 3604.6 ft in the first minute.
Given that a rocket rising from the ground has a velocity of v(t) = 2,000 te−t/60 ft/s, after t seconds, we need to find how far it rises in the first minute. So, here we can use the following integration rule to calculate the total distance traveled by the rocket in the first minute. s = ∫v(t)dt. Now, integrate v(t) with respect to t to get the expression for s.t = 0, s = 0t = 60, s = ∫₀⁶₀ 2000t * e⁽⁻ᵗ∕₆₀⁾ dt= [ -120000(e⁽⁻ᵗ∕₆₀⁾ ) (t+60)] from 0 to 60≈ 3604.6 ft (rounded to the nearest foot). Therefore, the rocket rises to a height of 3604.6 ft in the first minute.
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My bank account started the day with $550 in it. During the day, I made 2
deposits of $125 each and I wrote 1 check for $60. How much is in my account at
the end of the day?
Answers
Answer:
$740
Step-by-step explanation:
550 + 2(125) -60 =
550 + 250 - 60
800 - 60 = 740
$740
Answer: 740$
Step-by-step explanation:
125x2= 250, 250-60= 190, 550+190= 740
which of the following is the solution of 5e2x - 4 = 11? x = ln 3 x = ln 27 x = ln 3/2 x = 3/ln 3
Answers
Here's the LaTeX representation of the given explanation:
To solve the equation \(\(5e^{2x} - 4 = 11\)\) , we can follow these steps:
Add 4 to both sides of the equation:
\(\[5e^{2x} = 15.\]\)
Divide both sides by 5:
\(\[e^{2x} = 3.\]\)
Take the natural logarithm \((\(\ln\))\) of both sides to eliminate the exponential:
\(\[\ln(e^{2x}) = \ln(3).\]\)
The natural logarithm and exponential functions are inverses of each other, so \(\(\ln(e^a) = a\)\) : \(\[2x = \ln(3).\]\)
Divide both sides by 2 to solve for \(\(x\)\) :
\(\[x = \frac{\ln(3)}{2}.\]\)
Therefore, the solution to the equation is \(\(x = \frac{\ln(3)}{2}\)\) , which corresponds to option c.
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Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 30% of adults will have an IQ score higher than what value?
Answers
Step-by-step explanation:
Use z-score table to find the z-score that corresponds to .7000 ( 70%)
approx .525 s.d. above the mean
.525 * 10 = 5.25 points above 100 = 105.25
The Smith Family is buying a house for $350,000 with a down payment of $70,000 for a 15-year loan, $66 per month insurance, property tax is $230 per month and HOA is $600 per year. Calculate their total monthly payment
Answers
Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.
What is the Monthly Payment?To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.
1. Mortgage Payment:
The loan amount is the house price minus the down payment:
$350,000 - $70,000 = $280,000.
To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).
We can use a mortgage calculator formula to calculate the monthly payment:
M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]
Where:
M = Monthly mortgage payment
P = Loan amount
i = Monthly interest rate
n = Number of months
The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.
i = 4% / 12 = 0.00333 (monthly interest rate)
n = 180 (loan term in months)
Plugging in the values into the formula:
M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]
Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.
2. Insurance:
The monthly insurance payment is given as $66.
3. Property Tax:
The monthly property tax payment is given as $230.
4. HOA Fees:
The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.
Now, let's add up all these expenses:
Mortgage payment: $2,014.99
Insurance: $66
Property tax: $230
HOA fees: $50
Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees
Total monthly payment = $2,014.99 + $66 + $230 + $50
Total monthly payment = $2,360.99
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a square whose side measures 2 centimeters is dilated by a scale factor of 3 . what is the difference between the area of the dilated square and the original square?
Answers
After figuring out the given issue, we discovered that the original square's area and the dilated square's area differ by 32 square centimeters.
What is the area of square formula?Square Area = Side x Side. Hence, Side2 square units are equivalent to the area of the square. and four side units make up a square's perimeter.
The formula for calculating the area of a initial square with sides that are 2 centimeters long is:
A = s²
A = 2²
A = 4 square centimeters
The revised side length of this square after dilation by a scale factor of 3 is:
s' = 3s
s' = 3(2)
s' = 6 centimeters
Calculations for the dilated square's area are as follows:
A' = s'²
A' = 6²
A' = 36 square centimeters
The area of a dilated square differs from the size of the original square by:
A' - A = 36 - 4
A' - A = 32 square centimeters
As a result, the original square's area and the dilated square's area differ by 32 square centimeters.
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A baseball concession stand sells soft pretzels for $4.50 and bags of popcorn for
$3.25.
If the concession stand sold 137 soft pretzels, how many bags of popcorn would they
need to sell to make at least $1,000?
Answers
Answer:
y ≥ 118
Step-by-step explanation:
soft pretzels = $4.50
bags of popcorn = $3.25
Let
x = number of soft pretzels sold
y = number of bags of popcorn
The inequality:
4.50x + 3.25y ≥ 1,000
4.50(137) + 3.25y ≥ 1,000
616.50 + 3.25y ≥ 1,000
3.25y ≥ 1,000 - 616.50
3.25y ≥ 383.50
y ≥ 383.50 / 3.25
y ≥ 118
118 bags of popcorn would
need to be sold to make at least $1,000
What is the slope of the line?
Answers
Answer:
-3
Step-by-step explanation:
ΔX = 0 – -1 = 1
ΔY = -3 – 0 = -3,
y = -3x – 3, so the slope is -3
Sorry if you don't understand, but pls brainliest for level up
Answer:
-2
Step-by-step explanation:
The slope formula is y_2 - y_1 over x_2 - x_1.
We plug in the equation and it's -2 - 0 over 0 +1.
We get by simplifying the expression -2/1.
That is -2 because we ever something is over 1 then you remove the denominator and it becomes a whole number.
During a wheel alignment, the camber on a certain car is measured to be 3°24'. If the maximum acceptable camber for this car is 3.350°, is the camber within this limit?Select the correct choice below and fill in the answer box to complete your choice.A. Yes. The measured value of the camber is? (Type an integer or a decimal.)B. No. The measured value of the camber is? (Type an integer or a decimal.)
Answers
The camber on a certain car is measured to be;
\(3^{\circ}24^{\prime}\)But, the maximum acceptable camber for the car is;
\(3.350^{\circ}\)Thus, the measured camber is within the limit if only it is less or equal to the maximum acceptable camber.
Then, we would convert the measured camber to degree, we have;
\(\begin{gathered} 3^{\circ}24^{\prime}=(3^{}+(\frac{24}{60}))^{\circ} \\ 3^{\circ}24^{\prime}=(3+0.4)^o \\ 3^{\circ}24^{\prime}=3.4^{\circ} \end{gathered}\)CORRECT ANSWER:
B. No, the measured value of the camber is;
\(3.40^{\circ}\)