Problem 6. 2 3 (12 points) Let y = -2 and u = 2 2 1 (a) Find the orthogonal projection of y onto u. proj.y = (b) Compute the distance d from y to the line through u and the origin. d= Note: You can earn partial credit on this problem.

Answers

Answer 1

To solve problem 6, we first need to find the orthogonal projection of y onto u. To do this, we use the formula for the projection of a vector y onto a vector u: proj_y = (y·u)/(u·u) * u. . Plugging in y = -2 and u = [2, 1],

Calculate the dot products: y·u = (-2)(2) + 0(1) = -4 and u·u = (2)(2) + (1)(1) = 5.


Next, we need to compute the distance d from y to the line through u and the origin. To do this, we first find the vector v that connects the point y to the line through u and the origin. We do this by subtracting the projection of y onto u from y: use the formula: d = ||y - proj_y||.

y - proj_y = [-2 - (-8/5), 0 - (-4/5)] = [2/5, 4/5].


Finally, we find the length of v, which is equal to the distance d: d = √[(2/5)^2 + (4/5)^2] = √(20/25) = √(4/5) = 2/√5.


In conclusion, the orthogonal projection of y onto u is [-8/5, -4/5], and the distance from y to the line through u and the origin is 2/√5.

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Related Questions

Two supplementary angles are in the ratio of 5 to 7. Find positive difference of the measure of the two angles. Do the same problem, only do it for complementary angles instead of supplementary angles.​

Answers

Answer:

30° is the difference if they are supplement

15° is the difference if they are complementary

Step-by-step explanation:

Let 5x = the measure of the smaller angle

and 7x =  the measure of the larger angle

If they are supplementary, then 5x + 7x = 180

                                                        12x = 180

                                                            x = 15

5x = 5(15) = 75 = the measure of the smaller angle

7x = 7(15) = 105 = the measure of the larger angle

105 - 75 = 30 = difference of the measures

Now, if they are complementary, then 5x + 7x = 90

                                                                   12x = 90

                                                                       x = 7.5

5x = 7(7.5) = 37.5 = the measure of the smaller angle

7x = 7(7.5) = 52.5 = the measure of the larger angle

52.5 - 37.5 = 15 = difference of the measures

What is the slope of the line that connects the points (0.5, 4.5) and (1.5, 2.5)?​

Answers

Answer:

Slope is -2

Step-by-step explanation:

Slope is: -2 yghuysyaywu


Choose the correct description of the graph of the compound
inequality (1 point)
x -3 <-11 or x + 5 2 14,
• A number line with a closed circle on 8, shading to the left, and
an open circle on 9, shading to the right

A number line with an open circle on
8, a closed circle on 9, and
shading in between
O A number line with an open circle on -8, shading to the left, and
a closed circle on 9, shading to the right
A number line with a closed circle on -8, an open circle on 9, and
shading in between

Answers

Answer:

A number line with a closed circle on -8, an open circle on 9, and shading in between

On average, A person spends $240 every 3 months on their cell phone bill... What would the price be for 1 month be?... How much would this person pay over the course of one year?
Pls help me asap!!

Answers

Answer:

$81 for 1 month

$972 for 1 year

Step-by-step explanation:

Answer:

$80 for one month and $960 over the course of one year

Step-by-step explanation:

240 / 3 = 80

12 x 80 = 960

I need help with math

Answers

Answer:

0,-2        0,-5

2,-3          1,-4

Step-by-step explanation:

CALCULUS: Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = cos(t) - sin(t) and v(0) = 3.

A. v(t) = sin(t) + cos(t) + 3
B. v(t) = sin(t) + cos(t) + 2
C. v(t) = sin(t) - cos(t) + 3
D. v(t) = sin(t) - cos(t) + 4

I picked A., which was marked wrong, although I truly believe that is the answer because I got sin(t) - (-cos(t)) + 3. Please tell me whether you believe this is right or am I doing something wrong. I really want to learn/master this concept. Thanks is advance.

Answers

Answer:

B. v(t) = sin(t) + cos(t) + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Function Notation

Calculus

Antiderivatives - Integrals

Integration Constant C

Solving Integration Equations

Integration Property [Addition/Subtraction]:                                                         [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Step-by-step explanation:

*Note: Remember that the velocity function is the integral of the acceleration function/acceleration is the derivative of velocity.

[tex]\displaystyle v'(t) = a(t)\\v(t) = \int {a(t)} \, dt[/tex]

Step 1: Define

a(t) = cos(t) - sin(t)

v(0) = 3

Step 2: Integrate

Set up integral:                                                                                               [tex]\displaystyle v(t) = \int {cos(t) - sin(t)} \, dt[/tex][integral] Rewrite [Integration Property - Subtraction]:                                 [tex]\displaystyle v(t) = \int {cos(t)} \, dt - \int {sin(t)} \, dt[/tex][Integral] Trig integration:                                                                              [tex]\displaystyle v(t) = sin(t) - [-cos(t)] + C[/tex][Velocity Integration] Simplify:                                                                          [tex]\displaystyle v(t) = sin(t) + cos(t) + C[/tex]

Step 3: Find Function

We need to solve for the entire function, meaning we need to find constant C.

Substitute in given point [Velocity Integration]:                                           [tex]\displaystyle v(0) = sin(0) + cos(0) + C[/tex][Velocity Integration] Substitute:                                                                   [tex]\displaystyle 3 = sin(0) + cos(0) + C[/tex][Velocity Integration] Evaluate trig:                                                               [tex]\displaystyle 3 = 0 + 1 + C[/tex][Velocity Integration] Add:                                                                             [tex]\displaystyle 3 = 1 + C[/tex][Velocity Integration] Isolate C [Subtraction Property of Equality]:              [tex]\displaystyle 2 = C[/tex][Velocity Integration] Rewrite:                                                                       [tex]\displaystyle C = 2[/tex][Velocity Function] Substitute in C [Velocity Integration]:                           [tex]\displaystyle v(t) = sin(t) + cos(t) + 2[/tex]

Topic: Calculus

Unit: Basic Integration

Book: College Calculus 10e

Mary ate x pounds of cherries. Leslie ate LaTeX: \frac{6}{9}6 9 more. Write an expression to represent how many pounds of cherries Leslie ate.

Answers

Answer:

The expression to represent number of cherries Leslie ate = ( x + [tex]\frac{6}{9}[/tex] ) pound.

Step-by-step explanation:

As given,

Mary ate cherries = x pound

And

Leslie ate [tex]\frac{6}{9}[/tex] more.

⇒Leslie ate cherries = ( x + [tex]\frac{6}{9}[/tex]  ) pound.

Like seriously I gat no idea what the the answer is

Answers

The answer 25 bro good luck

Here is the assignment : You are "selling" the polynomial. You must convince the buyer you have the Best polynomial on the market by describing as many of its specific characteristics.
(Have fun and be creative, but most importantly, be accurate to avoid bad reviews)

Here is your Polynomial: f(x)=x^3-10x^2+28x-24

Answers

Step-by-step explanation:

A polynomial is an expression that can be built from constants and symbols called variables or indeterminates by means of addition, multiplication and exponentiation to a non-negative integer power. Two such expressions that may be transformed, one to the other, by applying the usual properties of commutativity, associativity and distributivity of addition and multiplication, are considered as defining the same polynomial.

A polynomial in a single indeterminate x can always be written (or rewritten) in the form

{\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},}a_{n}x^{n}+a_{n-1}x^{n-1}+\dotsb +a_{2}x^{2}+a_{1}x+a_{0},

where {\displaystyle a_{0},\ldots ,a_{n}}a_{0},\ldots ,a_{n} are constants and {\displaystyle x}x is the indeterminate.[2][3] The word "indeterminate" means that {\displaystyle x}x represents no particular value, although any value may be substituted for it. The mapping that associates the result of this substitution to the substituted value is a function, called a polynomial function.

This can be expressed more concisely by using summation notation:

{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}{\displaystyle \sum _{k=0}^{n}a_{k}x^{k}}

That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms. Each term consists of the product of a number – called the coefficient of the term[a] – and a finite number of indeterminates, raised to nonnegative integer

In AHIJ, h = 38 inches, i = 45 inches and j=61 inches. Find the measure of ZH to the nearest degree.

Answers

Answer:

38°

Step-by-step explanation:

Delta math

if the ratio of the length to perimeter is 5:16 what is the area of the rectangle

Answers

The area is 15
Multiply the length by 2
5(2)
Subtract the length from the perimeter
16-10
Divide the remainder by 2 to find the width
6/2
The width is 3
Length times width equals area
3(5)=15

A Train crosses a bridge 100 m in 45 sec at a speed of 60 km/h find a time taken by the train to cross a clock tower​

Answers

Ans is 351/8.

hope it is helpful

The church's goal for the fundraiser was $18,000. They exceeded their goal by 8%. How much money did they raise?

Answers

Answer:

Step-by-step explanation:

18000(1+8/100)

18000(108)/100

19440

cuánto es 30+30 me lo dices ​

Answers

Answer:

60

Step-by-step explanation:

3+3 es 6, después ponele el 0 al final

Rectangle A has a length of 6 and width of 4. Rectangle A prime has a length of 9 and width of 6. Find the scale factor of the dilation shown. 1/2 3/2 2 2/3

Answers

Answer: The scale factor of the dilation [tex]=\dfrac32[/tex]

Step-by-step explanation:

[tex]\text{Scale factor}=\dfrac{\text{Side in image}}{\text{Corresponding side in preimage}}[/tex]

Given: Rectangle A has a length of 6 and width of 4.

Rectangle A prime has a length of 9 and width of 6.

Scale factor = [tex]\dfrac{9}{6}\ \ \ or \ \ \dfrac{6}{4}[/tex]

[tex]=\dfrac32[/tex]

Hence, the scale factor of the dilation [tex]=\dfrac32[/tex]

Answer:

3/2

Step-by-step explanation:

Question: 2 out of 10
~!¡! Volume !¡!~
(Pleaaase go try to answer the first one- )

Answers

Answer:

B) 2,340

Step-by-step explanation:


Kevin received 1105 marbles. Kevin would like to give each of his friends some marbles. If Kevin has 12 friends, how many marbles would each person, including Kevin, receive?

Answers

Answer:

85 for each person including kevin

Graph the image of rectangle STUV after a reflection over the line y= –x

Answers

Answer:

U (7,1)

T (10,1)

V (7,9)

S (10,9)

Step-by-step explanation:

The image of the rectangle STUV after a reflection over the line y= –x is attached below.

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The coordinates of the points in the graph are S(-9,-10) , T(-1,-110) , U(-1,-7) , V(-9,-7)

We have to graph the image of the rectangle STUV after a reflection over the line y= –x

The points obtained after graphing ate,

U (7,1)

T (10,1)

V (7,9)

S (10,9)

Thus, the image of the rectangle STUV after a reflection over the line y= –x is attached below.

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what number makes this equation true?
7 x ? = 8 3/4

Answers

Answer:

1 1/4   or  1.25

Step-by-step explanation:

7 x ? = 8 3/4

(8 3/4) / 7 = 1 1/4

a. a triangle with one right angle and two congruent sides​

Answers

Answer:

is an isosceles right triangle, angles 45, 45, & 90 degrees

Step-by-step explanation:

For every pound a company spends on advertising, it spends £0.45 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.

Answers

equals 1 dollar usdddddf 877

The sail of a boat is in the shape of a right triangle. Which expression shows the height, in meters, of the sail?

The sail of a boat is a right triangle with an acute angle equal to 35 degrees and the side of the sail which is the hypotenuse to the right triangle is 8 meters long.

cosine 35 degrees over 8
8(tan 35°)
tangent 35 degrees over 8
8(cos 35°)

Answers

Answer:

8(cos35)

Step-by-step explanation:

Your welcome.

The expression that models the height is  8 cos35

SOH CAH TOA identity

From the given information, we have the following

Hypotenuse = 8metersHeight  = adjacent

Using the SOH CAH TOA identity

cos theta = adj/hyp

cos 35 = adj/hyp

cos 35 = adj/8

Hyp  = 8 cos35

Hence the expression that models the height is  8 cos35

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Peter and Myra are on their school's activity planning committee. They are polling each
homeroom class to find how many students are in after-school clubs. In Peter's class, 9 out of
the 20 students are in clubs. In Myra's class, 12 out of the 24 students are in clubs. Do the
two classes have the same ratio of students in clubs to total students?
yes
No

Answers

Answer: No

Step-by-step explanation: because 12 out of 24 is 1/2 while 9/20 is a bit off of one half therefore no

No cause if you simplify 12/24 it’s 1/2 and 9/20 can’t be simplified (not the same ratio)

SO HARDDD
What is the square root of 267.8?

lol

“Stay close to anything that makes you glad you are alive.” – Hafez.

C h a t here Bradyn and Lis, plz. I keep getting logged out when I use the other one :p

Answers

Answer:

16.3645959315

Step-by-step explanation:

What's the negative reciprocal of –7

Answers

Answer:

0.14285714285

Step-by-step explanation:

This is what I got from the calculator.

Answer:

1/7 (1 over 7)

Step-by-step explanation:

The negative reciprocal of –7 is 1/7 (1 over 7)

Math problem please help

Answers

Answer:

The second one and the last one

Step-by-step explanation:

The third quadrant is of all negitive. The reason it is, is because it is on the left side of the x axis which makes it go lower like subtracting and dividing, then it is on the bottom half of the y axis which again is the same reason

i hope i helped and have a great day!

Answer:

B and D

Step-by-step explanation:

because in the 3rd quadrant both the x and y will be negative

1st quadrant all x and y are positive

2nd quadrant y are positive but x are negative

and in 4th quadrant x are positive and y are negative.

if brainiest is earned its greatly appreciated

can someone please help me and if you could explain your answer so I can try to do the others on my own that be awesome :)

Answers

Answer:

Step-by-step explanation:

its 6

Ms. Potts washed 1/4 of her laundry. Her son washed 3/7 of it. Who washed most of the laundry? How much of the laundry still needs to be washed?

Answers

Answer:

Son washed moreRemaining 9/28 of the laundry

Step-by-step explanation:

Make denominators common to see the difference in fractions:

1/4 = 7/283/7 = 12/28

Son washed more laundry as 12/28 > 7/28

Together they washed:

7/28 + 12/28 = 19/28 of the laundry

Remaining part is:

1 - 19/28 = 28/28 - 19/28 =9/28 of the laundry

Step-by-step explanation:

9/28 is your answer......

An empty rectangular tank measures 60 cm by 50 cm by 56 cm. It is being filled with water flowing from a tap at a rate of 8 liters per minute. How long will it take to fill up the tank? (1 liter = 1000 cm3)

Answers

Answer:

21 min

Step-by-step explanation:

V = lwh

V = 60(50)(56) = 168000 cu. cm

8 liters = 8000 cu cm

168000/8000 = 21 min.

A group of friends were working on a student film that had a budget of $900. They used 33% of their budget on equipment. How much money did they spend on equipment?​

Answers

They used 33/100 of their money on equipment which means if they have a budget of 900 dollars they used...

900*33/100=9*33=297 dollars on equipment.

The amount used on equipment is $297.

What is a percentage?

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Budget = $900

Percentage of the budget used.

= 33%

Now,

The amount of budget used.

= 33% of 900

= 33/100 x 900

= $297

Thus,

The amount used on equipment is $297.

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