(a) Write down the angle between the vector i + j and the vector i- j.
(6) Calculate the angle between the vector 2i + 5j and the vector 4i.
(2)
(c) Two forces, A = (14i +2j) N and B = (2i - 6j) N, act on a ball.
Show that the magnitude of A is Root k times larger than the magnitude of B, where k is
an integer
(3)

(a) Write Down The Angle Between The Vector I + J And The Vector I- J.(6) Calculate The Angle Between

Answers

Answer 1
(a) Let θ be the angle between i + j and i - j. Then
(i + j) • (i - j) = ||i + j|| ||i -j|| cos(θ)
We also recall that for any vector x,
||x||² = x • x
We have
(i + j) • (i - j) = (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= (i • i) + (j • i) + (i • (-j)) + (j • (-j))
= ||i||² + (i • j) - (i • j) - ||j||²
= 1 + 0 - 1
= 0
and
||i + j|| = √(1² + 1²) = √2
||i - j|| = √(1² + (-1)²) = √2
So,
0 = 2 cos(θ)
cos(θ) = 0
θ = arccos(0) = 180°

(b) By the same process, we find
(2i + 5j) • 4i = 8
||2i + 5j|| = √(2² + 5²) = √29
||4i|| = 4
Then if θ is the angle between 2i + 5j and 4i, we have
8 = 4√29 cos(θ)
cos(θ) = 2/√29
θ = arccos(2/√29) ≈ 68.1986°

(c) Compute the magnitudes:
||A|| = √(14² + 2²) = √200 = 10√2
||B|| = √(2² + (-6)²) = √40 = 2√10
Now we can write
||B|| = 2√10 = 2 √(5 × 2) = 2√5 × √2 = 1/√5 × 10 √2 = 1/√5 ||A||
or
||A|| = √5 ||B||
so that k = 5.

Related Questions

Evaluate lim x²-1 x/x^2+3x-4​

Answers

Nandyan na po

Step-by-step explanation:

I hope I help

Which of these inequalities means that
18 is greater than three times a number?

Answers

hello!

Let's write this verbal phrase as an inequality.

First of all, let the number be n.

"three times n" can be written like so:-

[tex]\pmb{3n}[/tex]

Now, 18 is greater than 3n:-

[tex]\pmb{18 > 3n}[/tex]

Which means 3n is less than 18:-

[tex]\bigstar{\boxed{\pmb{3n < 18}}}[/tex]

note:-

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)

Help pls!!!!!!!!!! :<<<<

Answers

The answer to this question is D 2/4

The amount of work to move a chair to the living room is equal to 10 joules. How much work would it be to move the same chair using a simple machine?

Answers

The work done by the machine is the product of force and distance

The amount of work done by the machine is 10 joules

How to determine the amount of work?

The amount of work done is calculated using:

W = Fd

Where:

F represents the forced represents the distance

The distance moved to the living room is the same when you move the chair or a machine does is the same.

Also, if the force applied in moving the chair remains unchanged, the amount of work done would be the same.

Hence, the amount of work done by the machine is 10 joules

Read more about work done at:

https://brainly.com/question/18762601

Write the following in words in international system with comas:
34407615​

Answers

Answer:

34,407,615

Explanation : 34 millions 407 thousands 615

The entire graph of the function f is shown in the figure below.

Write the domain and range of f using interval notation.

Answers

Answer:

no idea

is the answer

if you like my answer please like comment and mark me as brilliant

integrate the following by parts |x^2 e^2x dx​

Answers

Answer:

The answer is shown in the picture. you basically have to do integration by parts 2 times to get final answer.

Jacob can swim the 400-meter distance in 6.4 minutes now.How many more meters per minutes will Jacob need to swim to reach is goal?Explain how you found your answer.

Answers

Answer:

62.5 meters per minutes

Step-by-step explanation:

Landry is going to wrap a birthday present for his mom. He needs to know how much wrapping paper he needs to wrap the present with no overlap.

volume
or
surface area​

Answers

Answer:

  surface area

Step-by-step explanation:

Wrapping paper covers the surface of an object.

To know how much paper he needs, Landry will need to determine the surface area of the present.

These diagrams show the dimensions of two different windows. Which of the following statements are true? Choose all that apply.
Window A
3 ft
8 ft
Window
B
4 ft
6 ft
O A. The windows have the same area.
B. The perimeter of Window A is less than the perimeter of Window B.
C. The perimeter of Window B is 20 feet.
OD. The area of Window A is 22 square feet.

Answers

A, and C is the answer

What did is the total volume,in cubic feet of the shape below

Answers

Answer:

64ft^3 (The ^3 is meant to be cubed) 64 feet cubed.

Step-by-step explanation:

The picture has already split the two shapes.

*Remember Volume Formula: LWH or Length times Width times Height.*

The first shape is 4ft x 2ft x 2ft

The second shape is a little bit of a fuss but it's alright.

*Talking about the length of Shape no.2*

Since the second shape is longer than the first one (by length). You need to double it meaning: 4x2 or 4+4 = 8ft

The second shape is 8ft x 2ft x 3ft

First shape should have a volume of 16ft

Second shape should have a volume of 48ft

Now, you need to add the two volumes:

48ft + 16ft = 64ft cubed

A rectangle has a length of 10 cm and a width of 7 cm. What is its perimeter?
44 cm
70 cm
34 cm
17 cm

Answers

Answer:

34 cm

Step-by-step explanation:

Keep in mind that the perimeter of a rectangle is the sum of the measures of its sides. This means that the sum of the longer sides and the shorter sides is the perimeter of the rectangle.

Let "L" represent the longer side (length) of the rectangle and "S" represent the shorter side (width) of the rectangle.

⇒ Perimeter of rectangle = L + S + L + S

⇒ Perimeter of rectangle = 2(L) + 2(S)

⇒ Perimeter of rectangle = 2(L + S)

Now, let's substitute the length and the width in the perimeter and simplify.

⇒ Perimeter of rectangle = 2(10 + 7)                                                [L = 10; S = 7]

⇒ Perimeter of rectangle = 2(17)

Perimeter of rectangle = 34 cm

Answer: 70 cm

Step-by-step explanation: 10 x 7 = 70

hope this helps

Enter the output values (Y) with the given function and input values (X).

Answers

Answer:

y = 3x - 2

X Y

6 16 3(6)-2 -> 18-2 = 16

5 13 3(5)-2 -> 15-2= 13

4 10 3(4)-2 -> 12-2= 10

7 19 3(7)-2 -> 21-2= 19

The circumference of circles

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the circumference of given circle ~

Circumference :

[tex]\qquad \tt  \dashrightarrow \: \pi{d}^{}[/tex]

where, d = diameter

Now, let's calculate it ~

[tex]\qquad \tt  \dashrightarrow \: c = 4×\pi{}^{}[/tex]

[tex]\qquad \tt  \dashrightarrow \: c = 4\pi\: \: in[/tex]

That's the answer I terms of π, but we can also plug in the approximate value of pi as 3.14

[tex]\qquad \tt  \dashrightarrow \: c = 4 \times 3.14{}^{}  \\\qquad \tt  \dashrightarrow \: c = 12.56\: \: in\\\qquad\tt \dashrightarrow \: c \approx 12.6\: \: in[/tex]

a
Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes between
$250 and $300.
Answer using the 68 - 95 - 99.7 rule.
[ ? ]%

Answers

Answer:

2 Answers By Expert Tutors

Since 400 is the mean and the standard deviation is 50, $400-$450 is +1 standard deviation. One standard deviation is 34.1% probability that the worker's wages would fall in this range.

What is the equation for the graph shown?

Answers

Answer:

[tex]y = \frac{2}{3}x + 4[/tex]

Step-by-step explanation:

The rule for graphs is:

[tex]y = mx + c[/tex]

Where [tex]m[/tex] is the gradient and [tex]c[/tex] is the y-intercept (where the line crosses the y-axis)

We can work out c by looking at our graph.

Our line crosses the y-axis at (0, 4). So... [tex]c=4[/tex]

To work out our gradient of a straight line (which is what we have)

We use the formula:

[tex]m = \frac{\triangle y}{\triangle x}[/tex]

The triangle [tex]\triangle[/tex] just means the "change in" the coordinates between any two points.

To calculate the change in y, we can pick any two points on our line!

Let's go for (0, 4) and (-6, 0)

To work out the gradient:

[tex]m = \frac{\triangle y}{\triangle x} = \frac{0 - 4}{-6 - 0} = \frac{-4}{-6} = \frac{4}{6} = \frac{2}{3}[/tex]

Using our formula

[tex]y = mx + c[/tex]
[tex]y = \frac{2}{3}x + 4[/tex]

Find the surface area of the pyramid.

Answers

Answer:

i think the answer is 87.

Step-by-step explanation:

i think its 87.

equivalent (x+ 4)(2r - 1)

Answers

Answer:

Step-by-step explanation:

r (2 x + 8) - x - 4

(2 r - 1) x + 8 r - 4

Is 5/2 to the right of number 1 on number line?

Answers

Answer:

Yes;

Step-by-step explanation:

5/2 = 2 1/2

2 1/2 > 1

Yes, 5/2 is to the right of 1 on a number line.

Yes it would be to the right of number one


Explanation:the fraction 5/2 represents 2 and a half thus since numbers greater than one are to the right of the number line 5/2 is to the right

Sadie is saving for a new car. Below is the total amount of money in her savings account on the last day of each month. show all steps to find the mean amount of money Sadie saves each month. Round your answers to the nearest cent.

Are physical activities becoming safer or more dangerous

Answers

The mean amount of money Sadie saves each month is $10,724.29.

What is the mean amount of money saved each month?

Mean is a measure of central tendency that is used to determine the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(10150 + 102211 + 10424 + 10769 + 11155 + 11477) / 7 =  $10,724.29.

To learn more about mean, please check: https://brainly.com/question/25842202

Mandy paints four square walls that are ten feet on each side. Which expression represents the total square footage that Mandy painted?

4 × 102
42 × 10
4 × 10 × 2
102 + 4

Answers

Answer:

C. 4 × 10 × 2

Step-by-step explanation:

There are four walls that are ten feet on each side.

You would take 4 (number of walls) × 10 (number of feet in length), and because there are 2 sides of the walls, you would take that × 2.

Therefore, your answer is 4 × 10 ×2

Enter a recursive rule for the geometric sequence.
3, - 12, 48, - 192, ..

Answers

Start at 3 and multiply by -4 each time.

GIVING BRAINLIEST!

2pi8^2 + 2pi8*8=?

the answer should be 150, show the steps

Answers

Answer:

256π

Step-by-step explanation:

2π(8²) + 2π(8)(8) <== exponents first

2π(64) + 2π(64) <== multiply

128π + 128π <== add

256π <== final answer

Note: 8 * 8 can also be written as 8²

Hope this helps!

Answer:

256π

Step-by-step explanation:

4π(8²) =   4π(64)=  804.2477193

804.2477193/π = 256π

) A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ. Calculate a 95% confidence interval for μ for the following situation:

n=20, x¯¯¯=63.8, s=2.84
≤μ≤

Answers

Answer:

ask MisterBrainly for help

show work. A 2​-ft wide circular track for a camera dolly is set up for a movie scene. The two rails of the track form concentric circles. The radius of the inner circle is 59 ft. How much farther does a wheel on the outer rail travel than a wheel on the inner rail of the track in one​ turn?

Answers

Step-by-step explanation:

oh that is again something you can nicely envision :

the inner circle has a radius of 59 ft.

so, because of the 2 ft wide track the outer circle has a radius of 59+2 = 61 ft.

the circumference of a circle is

2×pi×r

the answer to the question is simply the difference bergen the 2 circumference values.

inner circle :

2×pi×59 = 118pi

outer circle :

2×pi×61 = 122pi

the difference is

122pi - 118pi = 4pi = 12.56637061... ft ≈ 12.6 ft

the wheel on the outer track travels about 12.6 ft farther than a wheel on the inner track in one full turn.

Help picture below problem 9

Answers

Answer:

sometimes...

Step-by-step explanation:

mark me brainliest

A parallelogram is sometimes a rectangle.

A) sometimes

Explanation:

because the vertices join the adjacent sides at 90° angles and it has two sets of parallel sides and two pairs of opposite sides that are congruent. (a rectangle has all of the properties of a parallelogram.)

Given m n, find the value of x.
(7X-10)9
(6x-5)°

Answers

Answer:

x = 15

Step-by-step explanation:

Since m and n are parallel to the line t.

Then (7x - 10) + (6x - 5) = 180° supplementary angles for a linear pair.

(7x - 10) + (6x - 5) = 180°

13x -15 = 180°

13x = 195°

x = 15

Plug x into the angles to solve for angle.

(7x - 10)

(7*15 - 10) = 105 - 10 = 95°

(6x - 5) =

(6*15 - 5) = 90 - 5 = 85°

what is the distance of 53 yards square

Answers

Answer:

477 square foot

Step-by-step explanation:

cause yea

Question - I need more ----- inside of my life

Answers

Answer:

Hi, this is not really a question it is a statement but if you really need help with math then you can provide an actual question.

Step-by-step explanation:

Answer:

Then you must improve to get more things in your life

The clients who get haircuts at Cameron's salon have a variety of hair colors.
brown 7
black 7
blond 4
4
What is the experimental probability that the next client to get a haircut Cameron's salon will
have blond hair?
Write your answer as a fraction or whole number.
P(blond)

Answers

Using it's concept, it is found that there is a [tex]\frac{2}{9}[/tex] experimental probability that the next client to get a haircut Cameron's salon will have blond hair.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these number of outcomes are taken from previous trials.

In this problem, 4 out of 18 clients had blond hair, hence the probability is given by:

P(blond) = 4/18 = 2/9

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

Other Questions
The cost to rent a condominium at the beach is $1,500 per week. If two people share the cost, they each have to pay $750. Explain why the relationship between the cost per person varies inversely with the number of persons sharing the cost. Then write an inverse variation function that can be used to calculate the cost per person, c, of p persons sharing the rental fee. HELP ASAP will get brainly user !!! Across the sdlc phases which among these activities see a substantial amount of automation Write an equation for a line that contains the point (0,4) that is parallel to the equation below.y= -7x+1 If you are NOT beinggreat78, DO NOT ANSWER THIS. Beinggreat still answer this fast though bc ppl are mean When the islanders started fighting amongst themselves _____ the monkeys took control. 2. The islanders were weary of fighting _____ consequently, the monkeys faced little resistance. 3. As soon as the monkeys were in charge of Fire Island _____ things began to change. 4. David was afraid of Tiny, the leader of the monkeys _____ because David had heard things. 5. Tiny demanded all kinds of crazy things from the islanders _____ this troubled them greatly. 6. One warm summer morning _____ Tiny marched to the village square and pronounced a new law. 7. This law shocked and appalled the islanders _____ they could not accept such ridiculous leadership. 8. After much hemming and hawing _____ the elders decided to accept the law afterall. 9. The islanders had lost their spirit for fighting _____ furthermore, no one wanted to provoke Tiny's ire. 10. David _____ however, had had enough. 2) Who benefitted from it and how did they benefit? write an equation of the line in slope-intercept form where slope equals 1/4 and y-intercept equals 0, - 5 Please solve this for me Taking a test, please help!!Which sentence from the passage states a connection between the idea of a national official language and a violation of human rights?(6) The right to benefit from their government should not be limited by language barriers. Language communication via radio, television, and written material is essential for a basic understanding of an already intimidating political process for many non-native English speakers.(7) Under S.356, in my role as a government official, my hands would be tied when dealing with my own constituents, for many of whom English is a second language. To suggest that I cannot represent those constituents to the best of my ability and will be forced to essentially exclude them from the political process through English-only written communication is preposterous and insulting. The Constitution of the United States guarantees freedom of speech. Nowhere does it say that it has to be in English. If we enact this bill it will be a limitation of our free society. What historical event resulted in many lost jobs for musicians, as aristocrats could no longer afford to maintain private opera houses, orchestras, an Jill usually rides her bike at a speed of 10 miles per hour. Let x represent the hours and y represent miles. Write an equation that shows the relationship between x and y. One recurring problem in many game development projects is scope creep, where teams keep wanting to add more and more features to a game as they come up with great ideas during development. However, each new feature costs more and more time and sometimes makes the game more complicated than it needs to be. Describe at least one tool or concept you learned about in this course that could help minimize scope creep. determine the elements of the relation A A if -A = { 1 , 2 , 3 }thankyou ~ What is the area, in square feet, of the rectangle shown below 2. What is needed for water to change from liquid from a gas? In a parking lot there are only white cars, green cars, and red cars. If one car is selected at random from the lot, the probability that the selected car would be a green car is 1/6, and the probability that it would be a red car is 1/8. What is the probability that it would be a white car? How do I graph h(x) = 4|x+4| +3 walking in Hollywood ( please tell me what you think ) written by meI was walking in hollywood I had to turn around But my car was towed To the other side of townI walked 3 miles Without a smile I Asked for a rideI wanted to cryeveryone so no so i sat down and cryed A video game allows players to design their own character using the following options.Video Game Character What is the probability of designing a female character with long, red hair?A. 1/24B. 1/12C. 1/9D. 1/4