in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Answers

Answer 1

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].


Related Questions

Choose the best explanation that describes in words what the numerical value of the slope tells you.

a. Every increase in coral growth of one centimeter will result in an average of 5.25 fewer degrees Celsius of sea surface temperature per year.
b. Every increase in coral growth of one centimeter will result in an average of 5.25 more degrees Celsius of sea surface temperature per year.
c. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 more centimeters of coral growth per year.
d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Answers

Data for the question :

Sea surface temperature 26.7 26.6 26.6 26.5 26.3 26.1

Growth 0.85 0.85 0.79 0.86 0.89 0.92

Answer:

d. Every increase in sea surface temperature of one degree Celsius will result in an average of 0.1578 fewer centimeters of coral growth per year.

Step-by-step explanation:

Given the data :

Surface Temperature (X) : 26.7 26.6 26.6 26.5 26.3 26.1

Growth (Y) : 0.85 0.85 0.79 0.86 0.89 0.92

Using a regression calculator, we can find the model equation and extract the slope :

The regression equation obtained is :

y=5.039-0.1578x

From y = mx + c

Where m = gradient or slope

c = intercept

x and y are predictor and predicted variables respectively.

Hence, the gradient or slope (m) of the model = - 0.157. We have a negative slope, hence, increase in x will result una decrease in y.

The slope thus means: for every 1 degree increase in sea surface temperature (x), there is an average decline of about 0.1578 cm in growth per year.

A giant garter snake is at least 64 inches long. If 1 inch is equal to
2.5 cm, how long is the Giant garter snake in cm?

Answers

Answer:

The snake would equal 160cm.

Step-by-step explanation:

Correct me if im wrong plz

At 7:00 one Summer morning Harry and Hermione hopped into their speedy more motorboat and left Hogwarts dock. They arrived at Dumbledore Wharf 35 minutes later. During the busy summer months a car ferry departs from Dumbledore wharf every five minutes. Tourists crowd onto the ferry for the 55 minute ride to Hogswarts dock. If Harry and Hermione followed the route that the car ferries take, how many car ferries did they see on their trip?

Answers

9514 1404 393

Answer:

  19

Step-by-step explanation:

If we assume that the car ferries start at or before 6:05, and each 5 minutes thereafter, and if we count the ferries at the dock on either end, the total number seen is the number of ferries encountered in ...

  55 +35 = 90 . . . minutes

That is, it is the number already in transit when they leave, plus the number that start while they are traveling.

That's 90/5 +1* = 19 ferries.

_____

The attached diagram can give an idea. Each up-sloping line represents a ferry in-transit. The left side is Dumbledore Wharf; the right side is Hogwarts dock. Each horizontal unit represents the distance traveled by a ferry in 5 minutes. Each vertical unit represents a 5-minute interval.

The down-sloping line represents the motorboat travel. The dots at either end of the latter line represent car ferries that are at the dock, just arriving or just-departing. Altogether, there are 17 places where the lines cross, in addition to the boats at the docks.

__

* the +1 is because the number of points defining intervals is 1 more than the number of intervals.

Can someone plz plz help me with the last 2 problems #5 and #6

Answers

i believe your answers would be

1/2c+7 and 2H-9

the missing number in the series?
4, 18, ?, 100, 180, 294, 448
A) 48
B) 50
C) 58
D) 60

Answers

A)48

Explanation:

2^3 - 2^2 = 8 - 4 = 4
3^3 - 3^2 = 27 - 9 = 18
4^3 - 4^2 = 64 - 16 = 48
5^3 - 5^2 = 125 - 25 = 100
6^3 - 6^2 = 216 - 36 = 180
7^3 - 7^2 = 343 - 49 = 294
8^3 - 8^2 = 512 - 64 = 448

1
6 + 10 ÷ 2 − 32 = ?

A.
2
B.
1
C.
0
D.
−1
E.
−2

Answers

Answer:

b

Step-by-step explanation:

its b

f(x) = -x^2+10x-6
Find f(-5)

Answers

9514 1404 393

Answer:

  f(-5) = -81

Step-by-step explanation:

Put -5 where x is and do the arithmetic.

  f(-5) = -(-5)^2 +10(-5) -6

  f(-5) = -25 -50 -6

  f(-5) = -81

Answer:

-81

Step-by-step explanation:

a package of 4 pairs of isulated gloves costs $33.96. what is the unit price of gloves​

Answers

Answer:

8.49 per pair/pack of gloves

Step-by-step explanation:

i got this by taking 33.96 divided by 4 so i could find out how much for one pair

The sum of three numbers is 97. The third number is 2 times the second. The second number is 9 less than the first. What are the numbers?

Answers

Answer:

The numbers are 26.5, 53 and 17.5.

Step-by-step explanation:

97=x+(x-9)+2x

97+9=4x

106/4=4x/4

x= 26.5

x-9 = 17.5

2x= 53

What is the answer to thus ...?

Answers

(10/7)/(3/7) can be KCF method into (10/7)•(7/3)= 3.33 or 10/3

Find the value of x and measure of ∠3
∠3=2x+7
∠6=6x+21

Answers

Answer:

the answer is four

Step-by-step explanation:

The average cost of a compact car at a certain dealership over the last 10 years has ranged from $15,000 to $24,500. Suppose you were going to plot these points on a coordinate grid. (a) What is a good scale [range] would be good to use for the y-axis to make a nicely sized graph? Explain your reasoning. (b) What is a good interval [step size] would be good to use for the y-axis to make a nicely sized graph? Explain your reasoning. (c) What is a good scale [range] would be good to use for the x-axis to make a nicely sized graph? Explain your reasoning. (d) What is a good interval [step size] would be good to use for the x-axis to make a nicely sized graph? Explain your reasoning. Note: The step size the distance between the marks on the graph, and the range is the maximum and minimum values (ex: -10 to 10).

Answers

Answer:

this is what i did i apologize if i’m late and u no longer need the answer or if i’m wrong

Step-by-step explanation:

How many proportional relationships are shown in the coordinate plane below? Please answer quick i will give 35 points

Answers

Answer:

its not zero i check and got in incorrect the correct answer is 1

Step-by-step explanation:

Answer:

The answer is B) There is one proportional relationship

Step-by-step explanation:

The green line (the one at the top) does not go through the origin. This is not a proportional relationship.

Problem: It does not go through 0,0

----------------------------------------------------------------------------------------------------------------

The blue line (the one in the middle) is a straight line through the origin. This is a proportional relationship.

Reason: It goes through 0,0

----------------------------------------------------------------------------------------------------------------

The purple line (the one at the bottom) does not go through the origin. This is not a proportional relationship.

Problem: It does not go through 0,0

----------------------------------------------------------------------------------------------------------------

Conclusion: Since the green and purple lines are not proportional but the blue line is, this means only 1 line is proportional.

Note:

I know my answer is very late but I wanted to help anyone who needs it for future reference.

Valerie runs track and field. At meets, Valerie lkes to buy protein bars, bananas and sports drinks Protein bars are $1. bananas are S0.50, and sports drinks are S2. Valerie has S10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars. Let represent the number of protein bars. represent the number of bananas. and represent the number of sports drinks that Valerie buys. Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p

Answers

Complete Question

Valerie runs track and field. At meets, Valerie likes to buy protein bars, bananas, and sports drinks. Protein bars are $1, bananas are $0.50, and sports drinks are $2. Valerie has $10 to spend. She will spend no more than twice as much on sports drinks as bananas and at least three times as much on bananas as protein bars.

Let p represent the number of protein bars, b represent the number of bananas, and d represent the number of sports drinks that Valerie buys.

Which statements are true regarding Valerie's situation? Select all that apply A: p + 0.5b + 2d < 10 B: 0.5d + b + 3p < 10. C: d < 2b. D: b > 3p. E: 2d < b. F: 3b > p

Answer:

The statements that are true regarding Valerie's situation:

A: p + 0.5b + 2d < 10

C: d < 2b

D: b > 3p

Step-by-step explanation:

Lets represent

The number of protein bars as p.

The number of bananas as b.

The number of sports drinks that Valerie buys as d.

From the question:

We are told

Protein bars are $1

Bananas are $0.50

Sports drinks are $2.

She will spend no more than twice as much on sports drinks as bananas

d ≤ 2b = d < 2b

At least three times as much on bananas as protein bars.

b ≥ 3p = b > 3p

We are also told that:

Valerie has $10 to spend.

Hence:

$1 × p + $0.50 × b + $2 × d < $10

= p + 0.5b + 2d < 10

Therefore, the statements that are true regarding Valerie's situation:

A: p + 0.5b + 2d < 10

C: d < 2b

D: b > 3p

2. How far does light travel in water in 5.0 X
102 seconds, if the speed of light in water is 3
108 m/s?

Answers

It travels 3637474848362.626 miles a second.

AsKevin Selma madelyn Louis

Answers

very cool yes yes yes

I mark as brainliest ​

Answers

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

:)

The regular admission price for an amusement park is $72. For a group of 15, or more, the admission price is reduce by $25 per person. How many people need to be in a group to save $500?

Answers

Answer:  20 people

=========================================

Explanation:

x = number of people

Without the discount, each person pays $72, so the total cost is 72x dollars if x people go through the gate individually.

Now applying the group discount, those x people pay 72-25 = 47 dollars each. Meaning the total cost is now 47x. Keep in mind that [tex]x \ge 15[/tex] in order for the discount to kick in.

Subtracting the two amounts leads to 72x-47x = 25x. It is not a coincidence that we get a coefficient of 25 here.

Set this equal to 500 and solve for x

25x = 500

x = 500/25

x = 20

------------

If x = 20 people attend individually, then they pay 72*x = 72*20 = 1440 dollars.

If 20 people go as one group, they pay 47x = 47*20 = 940 dollars

We have a savings of 1440-940 = 500 dollars. This confirms the answer.

All 20 people must go as one group if they want to save $500.

Question 1 Part A: How many beads did Jiao send out? *
Wooden Beads
Oak
4,525
Maple
6,950
Ash
3,720
Ebony
2,475
Bayong
1,250

Answers

Answer:

Jiao sent out 18,920 beads.

Step-by-step explanation:

All I did was add.

</3 hope this helps.

The US emerged as a world power because of its success in
A. the Korean War
B. World War I
C. World War II
D. the Cold War

Answers

Answer:

its c

Step-by-step explanation:

trust and dont vote me out! its not me i sware its cyan he sus!

Answer:

It's C

Step-by-step explanation:

55 points and Brainliest!

Answers

I believe it's a 45 degree angle

Answer:

Um

Step-by-step explanation:

The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area will be 299 square meters. Find the length and width of the original rectangle.
HELP HELP HELP HELP

Answers

Answer:

L = 20

W = 10

Step-by-step explanation:

L = (w + 10)

NL = (w + 13)

Divide 299 by 13:

299 ÷ 13 = 23

So, 23 x 13 = 299

L = 23

W = 13

Subtract 3 from both to get the original length and width

Review the graph.

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point z 1 is (4, negative 3) and point z 2 is (negative 3, 2).

Suppose z3 = z1 – z2.Which quadrant contains z3?

quadrant I
quadrant II
quadrant III
quadrant IV

Answers

The position of z3 is (d) quadrant IV

The given parameters are:

[tex]\mathbf{z_1 = (4,-3)}[/tex]

[tex]\mathbf{z_2 = (-3,2)}[/tex]

The expression for z3 is given as:

[tex]\mathbf{z_3 = z_1 -z_2}[/tex]

So, we have:

[tex]\mathbf{z_3 = (4,-3) - (-3,2)}[/tex]

This gives

[tex]\mathbf{z_3 = (4 + 3,-3 - 2)}[/tex]

[tex]\mathbf{z_3 = (7,-5)}[/tex]

When the x-coordinate is positive, and the y-coordinate is negative, the point is in the fourth quadrant.

Hence, the position of z3 is (d) quadrant IV

Read more about quadrants at:

https://brainly.com/question/20226319

A stack of books is 62 inches high. How high is it in feet and inches?

Answers

Answer:

5 feet and .16667 inches

Step-by-step explanation:

if you where to simplify the inches it would be 2 inches because the 6 next to the 1 is greater then five making the 1 a 2

HELP!!!!!!!! I LOVE YOU AND ILL EVEN GIVE BRAIN

Answers

Answer It’s the last choice

Consider a 25 factorial design. (a) How many factors and levels are considered in this factorial experiment

Answers

Answer:

Step-by-step explanation:

From the information given;

We are to take a look at a 2⁵ factorial design.

The factorial design consists of carrying out the design of equipment by testing it by modifying not the parameters one by one but by modifying several simultaneous parameters.

An experiment is termed to be a 2⁵ factorial experiment if in the experiment 5 factors are studied consecutively with each at two-level.

Thus, there are five factors and 2 levels in the experiment.

Find the measure of an angle such that the sum of its supplement and four times its
complement is 13° less than twice the angle.
Show work

Answers

Answer:

Angle=79°

Step-by-step explanation:

Hope it helps!

Jill runs 3/4 of a mile, and
Amy runs 2/3 of a mile.
How far did Jill and Amy
run combined?

Answers

Answer:

1 1/5 mile

Step-by-step explanation:

3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 1/5

What is 5 8/100
as a decimal?
O
A. 5.008
0
B. 5.08
O
C. 5.8
0 D. 58

Answers

Answer:

5.08

Step-by-step explanation:

5   8/100

Since there are 2 zero's in 100, we need two numbers in the top

Replace 8 with 08 which is the same number

5  08/100

Now write as a decimal

5.08

Answer:

B. 5.08

Step-by-step explanation:

[tex]5\frac{8}{100} = \frac{508}{100}[/tex]  508 ÷ 100 = 5.08

I hope this helps!

identify the first term of the algebraic expression. Indicate whether the term is a variable or a constant term.
5y + 8b

Answers

Answer:

Someone text me on sc queenalyssa_05

Step-by-step explanation:

Answer:5

Step-by-step explanation:

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