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

A junior basketball player has a goal of scoring at least 1,000 points in his high-school career. His team plays twenty games per year, and after two years he has 320 points

Answers

He would need to score 340 points a year for the last 2 years to reach his

Explanation: 1,000-320=680
680 divided by 2 = 340

Frank plans to spend no more than $85 on plants for his front garden. He purchases a salvia and three azaleas. The azaleas cost $22 each. Let c be the cost for a salvia. Which inequality below could be used to show how much money Frank spent on salvia?

Answers

Answer:  3×22+c≤85

Step-by-step explanation: i think the answer is 3×22+c≤85 because 3x 22 represent the total cost of azaleas + c the cost of salvia is less than or equal to 85 because the buget is 85 and it cannot be greater

Hope this helped

The inequality for the given situation is 66+c ≤ 85.

Given that, Frank plans to spend no more than $85 on plants for his front garden. He purchases a salvia and 3 azaleas. The azaleas cost $22 each.

What is inequality?

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Let c be the cost for a salvia.

Three azaleas + A salvia ≤ 85

3×22+c ≤ 85

⇒ 66+c ≤ 85

Therefore, the inequality for the given situation is 66+c ≤ 85.

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Arachnophobia is the fear of spiders. People with arachnophobia suffer to different degrees, but they tend to react intensely to visible signs of the presence of spiders, such as webs. The director of a clinic decides to investigate different treatment types for arachnophobia. She gathers three groups of clients: One group receives in vivo flooding, which involves prolonged or repeated exposure to the actual anxiety-producing stimuli. The second group receives imaginal flooding, which involves the same techniques as in vivo flooding, except the exposure occurs in the client’s imagination. The third group receives no treatment. The results come in, and a statistician conducts an analysis of variance.


The ___________ is that there is no difference between the population means (in other words, there is no treatment effect).
The ___________is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).

Answers

Answer:

1. The null hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).

2. The alternative hypothesis is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).

Step-by-step explanation:

In a statistical analysis, the statistician shares his participants into several groups and administers treatments to them. After administering the treatment, he might want to compare the values obtained to see if there is a difference. If he accepts the null hypothesis as true, that means that there was no difference between the population means. This can also be taken to mean that the result had no difference among the groups.

But if the alternative hypothesis was true, that means that the population means were not all equal and so, there was an effect from the treatment administered.  

Answer:

1. The null hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).

2. The alternative hypothesis is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).

Write 257% as decimal

Answers

Answer:

please mark brainliest!

Step-by-step explanation:

2.57

Answer:

2.57

Hope this helps! Mark me brainliest

god bless!

Sammie bought just enough fencing to border either a rectangular plot or a square plot,

shown. The perimeters of the plots are the same. How many feet of fencing did she buy?


(3x + 6) feet.

———————

| |

| | (x - 1) feet

|__________|


(x + 6) feet

___________

| |

| |

| | (x + 6) feet

| |

|__________ |


Sammie bought____feet of fencing.

Answers

Answer:

3.5 feet

Step-by-step explanation:

The question isn't formatted properly.

We have:

(x + 6) feet on each side of the square

(3x + 6) feet horizontally on the rectangle

(x - 1) feet vertically on the rectangular

First, we need to determine the perimeter of the square:

[tex]Perimeter = 4 * Length[/tex]

[tex]Perimeter = 4 * (x + 6)[/tex]

[tex]Perimeter = 4x + 24[/tex]

Next, we determine the perimeter of the rectangle

[tex]Perimeter = 2(Length + Width)[/tex]

[tex]Perimeter = 2(3x + 6 + x - 1)[/tex]

[tex]Perimeter = 2(3x + x+ 6 - 1)[/tex]

[tex]Perimeter = 2(4x+ 5)[/tex]

[tex]Perimeter = 8x+ 10[/tex]

Equate both perimeters:

[tex]8x + 10 = 4x + 24[/tex]

Collect Like Terms

[tex]8x - 4x = 24 - 10[/tex]

[tex]4x = 14[/tex]

Solve for x

[tex]x = 14/4[/tex]

[tex]x = 3.5[/tex]

what is the solution to -3/4x + 2

Answers

Answer: 1/4x(3x+8)

Step-by-step explanation:

hope this helps

let me know if its correct!!



Rewrite it as a function and isolate Y. ​

Answers

Answer: y= -2x + 12

or f (y ) = 6 - [tex]\frac{y}{2}[/tex]

Step-by-step explanation:

just subtract the 2x to get the y alone

Find the 15th term of the arithmetic sequence if the first term is -3 and the common difference is 2. Write the equation first, then substitute to find the answer

Answers

Answer:

25.

Step-by-step explanation:

f(x)=-3+2(x-1)

f(15)=-3+2(15-1)

f(15)=-3+2(14)

f(15)=-3+28

f(15)=25

find the equation of the graphed function.
f(x)= _________​

Answers

Answer:

y =(x+3) ^2

Step-by-step explanation:

The zero is -3 and it  is the vertex  (-3,0)

Using the vertex form of a parabola  where  ( h,k) is the vertex

y = a( x-h)^2 +k

y =a(x- -3) ^2+0

y =a(x+3) ^2

We also know another point is ( -1,4)

Substituting that point into the equation

4 = a( -1+3) ^2

4 = a( 2)^2

4 = a*4

Divide each side by 4

1 =a

The equation is

y =(x+3) ^2

CAN YOU PLS ANSWER THIS QUICK!!! WHAT IS THE ANSWER TO THIS MATH EQUATION??? GEOMETRY/COLLEGE!!!

Answers

The answer is undefined

3.2654376... Rational or Irrational *
O Rational
O Irrational

Answers

Answer:

its irrational if the number goes on forever my g

Yes it’s irrational because you can’t predict what the next number is.

#16 What is the product of
3.4 and 15.56?

Answers

Answer:

53.04

Step-by-step explanation:

Answer:

52.904

Step-by-step explanation:

s x = –4 a valid solution this linear equation? 2x + 9(x – 1) = 8(2x + 2) – 5 No. When –4 is substituted for the variable, the result is a true statement. No. When –4 is substituted for the variable, the result is a false statement. Yes. When –4 is substituted for the variable, the result is a true statement. Yes. When –4 is substituted for the variable, the result is a false statement.

Answers

Answer:your answer is C!

Step-by-step explanation: I got it right

Answer:

c) Yes. When –4 is substituted for the variable, the result is a true statement.

Step-by-step explanation:

i verified with my teacher may i plz get brainliest

The price of a sweater was reduced from $20 to $12, By what percentage was the price of the sweater reduced?

Answers

Answer:

40%

Step-by-step explanation:

12 ÷ 20 = .6

You can convert the .6 to a percentage by multiplying it:

.6 x 100 = 60%

If 12 is 60% of 20, then that means 40% was taken away.

 Price of the sweater was reduced by 40%.

   Given in the question,

Original Price of a sweater is $20.Price of the sweater was reduced from $20 to $12.

Percentage reduction in the price from $20 to $12 can be calculated from the expression,

Percentage reduction = [tex]\frac{\text{Change in price}}{\text{Original price}}\times 100[/tex]

                                     = [tex](\frac{20-12}{12})\times 100[/tex]

                                     = [tex]\frac{8}{12}\times 100[/tex]

                                     = 40%

     Therefore, price of the sweater was reduced by 40%.

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3
Describe and correct the error a student made when graphing the linear equation y = -3/4x -6

Answers

Answer:

In step 1 the y-intercept should be plotted at (0,-6)

Step-by-step explanation:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Since the formula is y = -3/4x -6

We just insert a 0 insted of the "x"

y = -3/4(0) -6

y=0-6

y=6

So the y-intercept sould be placed in (0,-6)

That's what he did wrong when graphing the equation.

Answer:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Step-by-step explanation:

Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.

Since the formula is y = -3/4x -6

We just insert a 0 insted of the "x"

y = -3/4(0) -6

y=0-6

y=6

So the y-intercept sould be placed in (0,-6)

That's what he did wrong when graphing the equation.

what is the answer for this -6+x=-11

Answers

Answer:

x = -5

Step-by-step explanation:

-6 + x = -11

x = -11 + 6

x = -5

Answer:

x=17

Step-by-step explanation:

17+ -6= 11

pls mark brainlest for real ('>')

what’s 3/4 of 2/5 ?

** I WILL MAKE UP BRAIN LIST OR SOMETHING

Answers

Answer:

[tex] \frac{3}{10} [/tex]

Step-by-step explanation:

[tex] = \frac{3}{4} \times \frac{2}{5} [/tex]

[tex] = \frac{3 \times 2}{4 \times 5} [/tex]

[tex] = \frac{6}{20} [/tex]

[tex] = \frac{6 \div 2}{20 \div 2} [/tex]

[tex] = \frac{3}{10} [/tex]

Answer:

[tex] \frac{3}{10} [/tex]

Step-by-step explanation:

This is a shorter explanation. It's better to use this if you are good at maths or in a higher level.

[tex] \frac{3}{4} \times \frac{2}{5} [/tex]

[tex] = \frac{6}{20} [/tex]

[tex] = \frac{3}{10} [/tex]

That's it.

The life span of a graphing calculator manufactured by Texas Instruments has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company guarantees that any calculator that starts malfunctioning within 36 months of the purchase will be replaced by a new one. You apply the normal model and discover that this is approximately 1.22% of their graphing calculators. Texas Instruments has sold 75 million graphing calculators world- wide. How many of these would you expect to malfunction within 3 months (and thus need to be replaced)? Explain.

Answers

Answer:

The expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

Step-by-step explanation:

Let X represents the number of graphing calculator that starts malfunctioning within 36 months of the purchase and needs to be replaced by a new one.

It is provided that X follows a normal distribution with a mean of 54 months and a standard deviation of 8 months.

Also, using the normal model it was determined that 1.22% of graphing calculator manufactured by Texas Instruments malfunctions and needs replacement.

That is,

P (X) = 0.0122

Texas Instruments has sold 75 million graphing calculators world- wide.

Compute the expected number of graphing calculators that malfunctions within 3 months and need to be replaced as follows:

E (X) = n × P (X)

        = 75 × 10⁶ × 0.0122

        = 915000

Thus, the expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

A composition of transformations maps pre-image EFGH to final image E"F"G"H".

Trapezoid E F G H is shifted down and to the left to trapezoid E prime F prime G prime H prime. Trapezoid E prime F prime G prime H prime is reflected across the line of reflection c to form trapezoid E double-prime F double-prime G double-prime H double-prime.

The first transformation for this composition is [________], and the second transformation is a reflection across line c.

a 180° rotation about point G
a 180° rotation about point H
a translation down and to the left
a translation up and to the right

Answers

Answer:

c. a translation down and to the left

Step-by-step explanation:

As per translation of a graph, the first transformation for this composition is translation down and to the left.

What is the translation of a graph?

"A translation of a graph is its rigid movement, vertically or horizontally."

Here, A composition of transformations maps pre-image EFGH to final image E"F"G"H".

Trapezoid E F G H is shifted down and to the left to trapezoid E prime F prime G prime H prime.

Therefore, this transformation for this composition is translation down and to the left, and the second transformation is a reflection across line c.

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Help!!!
Lines b and c are parallel.
What is the measure of 26?

Answers

Answer:

m∠6 = 54°

Step-by-step explanation:

∠6 is equal to (5x + 9) because they are vertical angles. But, to be able to find the measure of ∠6, you will need to find the value of (5x + 9). So, since ∠5 is equal to (13x + 9) because they are Corresponding Angles, (5x + 9) and (13x + 9) are supplementary because they are a linear pair.

So:

m6 = 5x + 9 and

5x + 9 + 13x + 9 = 180°

18x + 18 = 180

18x = 162

x = 9

To find m∠6, plug in values:

m6 = 5x + 9

         = 5(9) + 9

         = 45 + 9

         = 54°

If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 2, subtract 3 and multiply the result by 4.​

Answers

Answer:

4(2x-3)

Step-by-step explanation:

Answer:

4 x (2x-3)

I hope it helps

Pls mark as Brainliest

At a middle school, 3 out of 4 students ride a bus to school. There are 600 studenta at the school. How many students ride a bus to school

Answers

Answer:

450 students ride a bus to school.

Step-by-step explanation:

If 3 out of 4 middle school students attend class by bus, it could be stated that 75% of the students use this means of transport to get to class (3/4 = 0.75).

Therefore, if this school has a total of 600 students, and 75% of them use the bus, it could be stated that 450 students attend school using this means of transport (600 x 75/100 = 450).

Answer:

450 students

Step-by-step explanation:

1/4 = 0.25

3/4 = 0.75

600 x 0.75 = 450 students

Hope this helps!

From the table below, determine whether the data shows an exponential function. Explain why or why not.
х
3 1 -1 -3
у
1 2 3 4
a. No; the domain values are at regular intervals and the range values have a common sum 1.
b. No; the domain values are not at regular intervals.
C. Yes; the domain values are at regular intervals and the range values have a common factor 2.
d. Yes; the domain values are at regular intervals and the range values have a common sum 1.

Answers

Answer:

B because the domains repeat themselves so it can not be a function

No; the domain values are not at regular intervals.

The correct option is b.

What is an exponential function?

Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.

In an exponential function, the domain values are usually at regular intervals, and the range values have a common factor or a common sum.

In the given data, the domain values are not at regular intervals.

The difference between 3 and 1 is 2, and the difference between 1 and -1 is 2, but the difference between -1 and -3 is -2.

This indicates that the domain values are not at regular intervals, which means that the data cannot be modeled by an exponential function.

Additionally, the range values also do not have a common factor or a common sum. The difference between consecutive y-values is 1, which is not a constant factor or sum.

Therefore, the data cannot be modeled by an exponential function.

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free brainlyest if answer 9+10 the right way

Answers

Answer:

19

Step-by-step explanation:

literally if this is wrong i swear

Answer:

19

Step-by-step explanation:

A map has a scale of 2 in: 6 mi. If Clayton
and Centerville are 10 in apart on the map
then how far apart are the real cities?

Answers

Both cities are 30 miles apart in real

Write a linear equation that passes through the points (1,-6) and (-3, 10) *


HAHAHA HELP PLS

Answers

y=-4x-2

Step-by-step explanation:

Answer:

y= -4x-2

Step-by-step explanation:

10- -6/-3-1

10+6/-3-1

16/-4

-4

what is the best estimate of 45 percent of 76

Answers

9514 1404 393

Answer:

In order of improvement:

383434.2 (actual value)

Step-by-step explanation:

In my engineering experience, a method of estimating should satisfy two requirements:

it should be relatively easy to accomplish mentallyit should provide a means of estimating the error in the estimate

__

Multiplication and division by 2 are generally easy to perform mentally.

We note that 45% is about 50%.

  50% of 76 is 76/2 = 38 . . . a good starting estimate

45% is down 5% from 50%, so the actual value will be 5/50 = 10% lower than this first estimate

A good second estimate is 38 -0.10(40) = 34.

A better estimate is 38 -3.8 = 34.2, which is the actual value of the expression.

_____

Alternate approach

You could also transform the problem to 76% of 45, which is about 3/4 of 44, or about 33. Figuring the error adjustment on this approach is somewhat more difficult, as it is factors of 1/75 and 1/44 too low. 1 part in 44 is not too difficult to figure, as it is 33/44 = 3/4, so a better estimate is 33.75. It takes a calculator to figure 1 part in 75 of this, which is 0.45. Adding that amount gets you to the actual value of 34.2.

What do you think the important skills necessary in solving problems in differential calculus?

Answers

Answer:

idk if this helps but here:

Cutoff points are a crucial piece of calculus and are among the main things that understudies find out about in a calculus class. So, finding the constraint of a capacity implies figuring out what esteem the capacity approaches as it draws nearer and more like a specific point.

Step-by-step explanation:

What sample size is needed to give a margin of error within in estimating a population mean with 99% confidence, assuming a previous sample had .

Answers

This question is Incomplete

Complete Question

What sample size is needed to give a margin of error within ± 13 in estimating a population mean with 99% confidence, assuming a previous sample had s=116

Answer:

The sample size n = 530 samples

Step-by-step explanation:

Margin of Error formula = z × standard deviation/√n

Margin of Error = ± 13

Standard deviation = 116

z = z score of 99% = 2.58

±13 = 2.58 × 116/√n

Cross Multiply

±13 × √n = 2.58× 116

±13 × √n = 299.28

√n = 299.28/±13

√n = ± 23.0215384615

Square both sides

(√n)² = (±23.0215384615)²

n = 529.991233134

Approximately , n = 530 samples

20 points & Brainliest

Why are rotations a rigid motion?

Answers

Answer:

RC,\α is a rigid motion.

Here C, is the rotacenter which is the fixed point and around C all other points move in a fixed distance by the definition of rotation.

the motion follows in a circularmanner with C as the center.

consider a point Q which changes to Q1 after rotation by an angle\alpha

Step-by-step explanation:

When considering rotational motion and subsequently rotational mechanics every point on the body must have same angular velocity and angular acceleration. If the body is not rigid different points on the body will have different angular velocity and angular acceleration.

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