Answer:
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
Step-by-step explanation:
Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:
[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)
Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)
If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:
[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:
[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)
If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:
[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
solve the inequality and graph its solutions on a number line. 5x+3<3(x+2)
Answer:
B
Step-by-step explanation:
Three cats and three dogs, A, B, C, D, E, and F, live on a street in three different-coloured houses. Each house hosts one cat and one dog. One house is red. A is a cat and does not live in the red house. B is a dog and does not live in the same house as C (even though they could). D lives in the blue house. D does not live with A or F (even though it could). E does not live with A and does not live in the yellow house.
Indicate whether each letter correspond to a cat or a dog, and match each cat and each dog with a colored house.
Answer:
1) A is a cat; B is a dog; C is a cat; D is a dog; E is a dog; F is a cat
2) A lives with B in a yellow house; C lives with D in a blue house; E lives with F in a red house.
Step-by-step explanation:
Step 1: First we identify the animals as cats or dogs
A is a cat
B is a Dog
Since B can live with C, C is a cat
Since D can live with A, D is a dog
F is a cat since it can live with D
E is therefore, a dog
Step 2: We then identify the house each two animals live in pairs of a cat and a dog
D lives in a blue house
A lives in a yellow house since it does not live with D or in a red house
C lives with D in a blue house since D does not live with either A or F
E lives in a red house since it does not live with A or in a yellow house
F lives with E in a red house since E does not live with A
Therefore, B lives with A in a yellow house
If 30% of the pupils in a school are boys, what percentage of the pupils are girls?
Answer:
70%
Step-by-step explanation:
4.1 Number Talk: Division
Find each quotient mentally.
645 divided by 100
645 divided by 50
48.6 divided by 30
48.6 divided by x
Answer:
645/100 = 129/20 or 6.45
645/50 = 129/10 or 12.9
48.6/30 = 1.62
48 divided by x = 48.6/x
Step-by-step explanation:
645/100
Factor the number:
= 5*129/100
Factor the number:
= 5*129/5*20
Cancel the common factor:
= 129/20
645/50
Factor the number:
5*129/50
Factor the number:
5*129 / 5*10
Cancel the common factor:
= 129/10
48.6/30
Write the problem in long division format
Multiply the quotient digit (1) by the divisor (30)
Subtract 30 from 48
Add a decimal and bring down the next number
Divide 186 by 30 to get 6
Continue...A few steps later...
Subtract 60 from 60
Solution is 1.62
48.6/x
Re-write division as a fraction:
48.6/x
Greatest common factor of 81
Answer:
81
Step-by-step explanation:
I just looked it up :)
Answer:
27
Step-by-step explanation:
Parker invests $1000 for 5 years at a simple rate of 10%.
A. How much interest will Parker earn after 5 years?
B. What will be the total amount that Parker will have after 5 years?
Answer:
SI=PTR/100
= 1000×5×10/100
=$500
Parker will receive $500 as interest.
Amount=$500+$1000
=$1500
Parker will have $1500 altogether.
Line s has a slope of -7/2 line t is perpendicular to a. What is slope of line t
Answer: 2/7
Step-by-step explanation:The slope of perpendicular lines are opposite reciprocals
What is the product of-3 and-13? Enter your answer as a mixed number, in simplified fom, in the box
Answer:
39
Step-by-step explanation:
-3x(-13) = 39.
If this question was asking for something different I apologize.
HELP ME ASAP!!! I WILL MARK BRAINLIEST!!
A regional office of the Internal Revenue Service randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being too lenient with persons whose returns are being audited. For a simple random sample of 30 of the returns audited by Mr. Jones last year, an average of $340 in extra taxes was collected.
Required:
Assuming a normal population of extra taxes collected with a standard deviation of $90, do the suspicions against Mr. Jones appear to be justified?
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 356[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$340[/tex]
The standard deviation is [tex]\sigma = \$ 90[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 35 6[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne \$ 35 6[/tex]
Let assume the significance level is [tex]\alpha = 0.05[/tex]
Generally the test statistic is mathematically represented as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 340 - 356 }{\frac{90 }{\sqrt{30} } }[/tex]
=> [tex]t =-0.9737 [/tex]
Generally the sample size from the question is small that it is not greater than 30 hence we use t-test
Now the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 30- 1[/tex]
=> [tex]df= 29[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 P (t > -0.9737 )[/tex]
Generally from the t-distribution table , the probability of -0.9737 at a degree of freedom of [tex]df= 29[/tex] for a two -tailed test is
[tex]P (t > -0.9737 ) = 0.33825793[/tex]
Hence p-value is
[tex]p-value = 2*0.33825793[/tex]
[tex]p-value = 0.676 [/tex]
From the value we obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the justification against Mr. Jones appears not to be justified
Multiply 3/5 by 10/21 Express your answer in simplest form
Answer:
2/7
Step-by-step explanation:
Answer:
3/5 * 10/21= 2/7
What does it mean to divide a number by
a fraction (e.g., ¾)?
Answer: You can divide a number by a fraction by flipping over the fraction and multiplying them together.
Step-by-step explanation:
For example:
Lets say we wanted to divide 8 by 3/4
8÷[tex]\frac{3}{4}[/tex]
Change the division symbol into multiplication, and flip over the fraction (a great way to remember doing this is to remember the phrase Copy Dot Flip - Copy the first digit as it is, put a dot for multiplication, and then flip the fraction over)
8 ·[tex]\frac{4}{3}[/tex]
Now, just multiply and reduce/simplify the fraction if needed
Final answer is [tex]\frac{32}{3}[/tex], no need to simplify or reduce
Hope that helps!!
A 40-foot powerboat is for sale by the owner. How long is the boat to
the nearest yard?
a bottle of hand lotion is on sale for $2.25. if this price represents a 50% discount from the original price, what is the original price to the nearest cent?
Answer:
4.50
Step-by-step explanation:
2.25 plus 2.25 aka half
Please help! Number 7 and 8 don't forget to put the graph points thank you!
Answer:
Step-by-step explanation:
7- is (0,1)(1,3)
8- is(-3,0)(-3,0)
most ants can lift 50 times their own weight. If an ant weighs 5 milligrams, how many ants would it take to lift a 500 gram bag of sugar?
Answer:
2000
Step-by-step explanation:
5*50=250 mg
250*4=1000 mg
1000*500=500 m
4*500=2000
It would take 2,000 ants to hoist a 500-gram bag of sugar.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, most ants can lift 50 times their own weight.
also given every ant has 5 mg weight.
So, 1 ant can lift = 5mg * 50 = 250mg
Since 1 gram has 1000 mg
Ant can lift = 1/4 grams
thus,
1/4 gram of sugar can be lifted by = 1 ant
1 gram of sugar can be lifted by = 4 ant
500 grams of sugar can be lifted by = 4 * 500 ant = 2000 ants
Therefore, 2000 ants would it take to lift a 500-gram bag of sugar.
Learn more about proportionalities here:
https://brainly.com/question/3254974
#SPJ2
Find the product of (18k+ 2m)(m + k)
Answer:
18k^2+2m^2+20km
Step-by-step explanation:
3/4x-4=5/6
Rewrite so it doesn’t have any fraction
dai is comparing how many trading cards he has with friends Maura
Answer:
ok
Step-by-step explanation:
An ordered pair that satisfies all the equations in a linear system of equations is called a(n) __________ of the linear system.
Answer:solution
Step-by-step explanation:
An ordered pair that satisfies all the equations in a linear system of equations is called a: solution of the linear system.
A linear function is a function that has a positive relationship between its variables.
Hence, an increase in one variable (input variable) causes an increase in the other variable (output variable) because the variables are directly proportional.
Mathematically, the graph of a linear function is a straight-line and its slope is always constant.
On a related note, a linear system of equation is an algebraic equation of the first order with two variables and each of its term having an exponent of one.
Generally, a system of linear equations in two variables must have at least two solution.
In conclusion, a solution of the linear system is an ordered pair that satisfies all the equations in a linear system of equations.
Read more: https://brainly.com/question/24085666
Vickie bought 54 tickets for a ride at an amusement park.each ride cost 3 tickets and Vickie has been on x rides so far.which expression to the number of tickets that Vickie has left?
Answer: 18
Steps: 54/3=18
1 8
3/54
-3
24
-24
0
PLZ HURRY IT'S URGENT!!
What is the slope of the line?
x=−8
options:
undefined
-8
1
0
Answer:
im pretty sure it's -8
Answer:
undefined
Step-by-step explanation:
the line goes straight down
Add:
3 + 6 =
6 + (-4) =
Answer:
3 + 6 = 9
6 + (-4) = 2
Step-by-step explanation:
Answer:
9 and 2
Step-by-step explanation:
3 + 6 =
9
6 + (-4) =
6-4=
2
Help ASAP!!!.
Simplify the expression:
2x + 1 + 7x
If A and B are independent events, which equation must be true?
Α.
P(B/A) = P(A)
B.
P(B/A) = P(B)
C.
P(B/A) = P(A) P(B)
D.
P(B/A) = P(A) + P(B)
Answer:
B. P(B/A)=P(B)
The system shown below is
.
3x – 4y = 12
6x – 8y = 21
Answer:
inconsistent
Step-by-step explanation:
Answer:
inconsent
Step-by-step explanation:
PLEASE MIDDLE SCHOOL MATH NEED HELP!!!! THIS IS URGENT 13 POINTS TO FULL ANSWER!!!
I bought 7 1/3 pounds of apples from Store A and 9 2/6 pounds of apples from Store B. I made apple sauce using 2 1/2 pounds of apples, how many pounds do I have left?
Answer:
14 1/6
Step-by-step explanation:
7(1/3)+ 9(2/6)= 16(2/3)
16(2/3)
16(2/3)-2(1/2)= 14(1/6)
Answer:
14 1/6
Step-by-step explanation:
7 + 9 =16
convert 2/6 = 1/3
1/3 +1/3=2/3+16=
16 2/3 -2 1/2=
what is the population of A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.
Answer:
lovely peachlings
Step-by-step explanation:
what are the slopes of the two different lines? are they undefined?
Answer:
m = (y2 -- y1) / (x2 -- x1)
Step-by-step explanation:
The average of 4,-8,6,14,-3 is
Answer: The average is 2.6
Step-by-step explanation:
The average is the same as the mean so to find the mean of the numbers add them up and divide it by the number of values.
(4) + (-8) + (6) + ( 14) + (-3) = 13
13/5 = 2.6