Find a unit vector in the direction of the given vector.
v = 9i − 6j

Answers

Answer 1

Given:

The given vector is:

[tex]v=9i-6j[/tex]

To find:

The unit vector in the direction of the given vector.

Solution:

If a vector is [tex]v=ai+bj[/tex], then the unit vector in the direction of the this vector is

[tex]\hat v=\dfrac{v}{|v|}[/tex]

Where, [tex]|v|=\sqrt{a^2+b^2[/tex]

We have,

[tex]v=9i-6j[/tex]

Here, [tex]a=9[/tex] and [tex]b=-6[/tex]. So,

[tex]|v|=\sqrt{9^2+(-6)^2}[/tex]

[tex]|v|=\sqrt{81+36}[/tex]

[tex]|v|=\sqrt{117}[/tex]

[tex]|v|=3\sqrt{13}[/tex]

Now, the unit vector in the direction of the given vector is:

[tex]\hat v=\dfrac{9i-6j}{3\sqrt{13}}[/tex]

[tex]\hat v=\dfrac{9i}{3\sqrt{13}}-\dfrac{6j}{3\sqrt{13}}[/tex]

[tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex]

Therefore, the required unit vector is [tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex].


Related Questions

Find the binomial that completes the factorization.
s^3–1=( ) (s^2+s+1). Help ASAP

Answers

Answer:

(s - 1)(s² + s + 1)

Step-by-step explanation:

s³ - 1 ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

s³ - 1

= s³ - 1³

= (s - 1)(s² + s + 1)

The required factorized form of the given expression is (s - 1)(s² + s + 1).

What is the Factorization?

Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).

We have been given that the expression below as

s³ - 1

We have to determine the factor of the given expression

As per the question, we have

s³ - 1

This is a difference between cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

⇒ s³ - 1 = s³ - 1³

⇒ (s - 1)(s² + s + 1)

Thus, the required factorized form is (s - 1)(s² + s + 1).

Learn more about the Factorization here:

brainly.com/question/4184435

#SPJ2

This pentagonal right pyramid has a base area of 30m^2

What is the volume of the figure?

This Is due soon plz help

Answers

Answer:

50m cubic

Step-by-step explanation:

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!

Answers

Step-by-step explanation:

X = 10 (use pyth)

Y = 11.18(use pyth)

*update* Don't answer, I solved it already.
1) Given the equation y = 35(0.57)^x

a) Does this equation represent growth or decay? ______Decay_________

b) What is the rate of growth or decay? _______43%________ (in percent)
1-0.57=0.43 100x0.43=43%
c) What is the initial value? _____35________

d) Evaluate for x = 3
y=(35)(0.57)^(3)
=(35)(0.185193)
=6.481755

Answers

Answer:

1) Given the equation y = 35(0.57)^x

a) Does this equation represent growth or decay? ______Decay_________

b) What is the rate of growth or decay? _______43%________

1-0.57=0.43 100x0.43=43%

c) What is the initial value? _____35________

d) Evaluate for x = 3

y=(35)(0.57)^(3)

=(35)(0.185193)

=6.481755

I need someone to help me Simplify 7(3n)

Answers

Answer:

21n

Step-by-step explanation:

7(3n)

7×3

21n

I hope this helps

help me pls i give brainliest

Answers

Answer:

Decreased I think because they bumped into the other person

Step-by-step explanation:

Answer:

increased

 i just heard my brother say it because he's in highschool. TwT

The perimeter of a rectangular room is 24 meters.The width of the room is 4 meters. Find the length of the room.

Answers

Answer:

20 metes

Step-by-step explanation:

:)

help! My back door is jammed and my dog is outside! What do I do?

Answers

Answer:

go through the other door and get your dog... and then just wait for a parent to fix the door so you dont rip it of the rims

Step-by-step explanation:

Answer:

Just go out through the backdoor and save your dog and wait for your parents duh

What property is being used: 5 + x = x + 5 *

Answers

Answer:

The answer is The Commutative property

This means the Commutative property states that you can add or multiply regardless of how the numbers are grouped.

Answer:
Commutative property

Why? A+B=B+A (that’s the commutative property

____________of an event is a number that tells how likely it is to happen.

Answers

Answer:

Probability

b-bald Hisoka

Answer:

PROBABILITY

Step-by-step explanation:

Probability of an event is a number that tells how likely it is to happen

Please help will mark brainliest

Answers

I think it’s A. If not, then B.

HELP ⚠⚠⚠ MARKING BRAINLIEST, IF UR CONFUSED, I NEED HELP WITH QUESTION 9 BUT QUESTION 8 IS RELATED TO IT ⚠⚠⚠

Answers

Answer:

John has a sheet of paper that is 8 feet long. He cuts the length of paper into eighths, and then cuts the length of each of these [tex]\frac{1}{8}[/tex] pieces into fourths. How many pieces does he have? How many inches long is each piece?

Step-by-step explanation:

For Quon's first 6 quizzes he had a mean score of 33 points. After his 7th quiz his mean score was 32 points. After the 8th quiz the mean was 34. What was the difference in scores between his 7th and 8th quizzes

Answers

Answer:

Difference in scores between his 7th and 8th quizzes = 22

Step-by-step explanation:

Given: Mean score for first 6 quizzes is 33 points. After his 7th quiz his mean score was 32 points. After the 8th quiz the mean was 34.

To find: difference in scores between his 7th and 8th quizzes

Solution:

Mean scores = Total points scored in quizzes ÷ Number of quizzes

So,

Total points scored in quizzes = Mean scores × Number of quizzes

As mean score for first 6 quizzes is 33 points,

Total points scored in 6 quizzes = 6 × 33 = 198

As mean score for first 7 quizzes is 32 points,

Total points scored in 7 quizzes = 7 × 32 = 224

So,

7th score = Total points scored in 7 quizzes - Total points scored in 6 quizzes

               = 224 - 198

               = 26

As mean score for first 8 quizzes is 34 points,

Total points scored in 8 quizzes = 8 × 34 = 272

So,

8th score = Total points scored in 8 quizzes - Total points scored in 7 quizzes

               = 272 - 224

               = 48

Therefore,

Difference in scores between his 7th and 8th quizzes = 48 - 26

                                                                                          = 22

Help I'll give Brainly Est

Answers

225 I think not sure

Given f(x) = x^4 -3x^3 +10x^2 -9x +1. Is (x-2) a factor? Is x=-3 a zero? Find f(-1) show all work.

Answers

Step-by-step explanation:

(x-2) is not a factor

x = -3 is not a zero

Please mark my answer as the brainliest for further answers :)

a model ship is 0.38 M long how long is the ship in centimeters

Answers

Answer:

Actual length of ship is  150  meters.

Step-by-step explanation:

As model ship is built to a scale of  

1 centimeter  : 5  meters and

length of model ship is  30  centimeters

Actual length of ship is  30 × 5 = 150  meters.

38 centimetres is the answer

please answer fast!!!! The wheels on Jessica's bike are 64 inches in circumference. How many times do the wheels rotate if Jessica rides 300 yards?

Answers

Answer:

169

Step-by-step explanation:

The smelter produces 384 tons of cast iron a day. How much coke is burned per day during smelting if 15 tons of coke is consumed per 16 tons of cast iron?

Answers

Answer:

360 tons

Step-by-step explanation:

Coke burned : cast iron = 15 : 16

The smelter produces 384 tons of cast iron a day

Let x = tons of coke burned

Coke burned : cast iron = x : 384

Equate both ratios

15 : 16 = x : 384

15/16 = x/384

Cross product

15 * 384 = 16 * x

5,760 = 16x

x = 5,760/16

x = 360

x = tons of coke burned = 360 tons

11y^2-19y-10=-4y^2
all real solutions

Answers

Answer:

y=5/3 is the only real solution

Step-by-step explanation:

Solve for y over the real numbers:

11 y^2 - 19 y - 10 = -4 y^2

Add 4 y^2 to both sides:

15 y^2 - 19 y - 10 = 0

The left hand side factors into a product with two terms:

(3 y - 5) (5 y + 2) = 0

Split into two equations:

3 y - 5 = 0 or 5 y + 2 = 0

Add 5 to both sides:

3 y = 5 or 5 y + 2 = 0

Divide both sides by 3:

y = 5/3 or 5 y + 2 = 0

Subtract 2 from both sides:

y = 5/3 or 5 y = -2

Divide both sides by 5:

Answer: |

| y = 5/3 or y = -2/5

A shirt was sold for sh 1054 after a 15% discount . what was the discount given

Answers

Answer: discount was 186

Step-by-step explanation: original price is x.

15 % = 0.15x , and x -0.15x= 1054 and 0.85x = 1054

Then x = 1054/0.85 = 1240. Discount was 1240-1054 = 186

PLZ HELP I NEED TO TURN THIS IN IN 10 mins

Answers

the answer is 2 because if you arrange them 2 in in the middle

Answer:

2 or 4 because it's in the middle I think 2

Step-by-step explanation:

hope this helps have a good rest of your night/day :) ❤

can I please get brainliest if correct only got like 4 pls

Please help you don’t even have to solve it, I just need the equation

Answers

Step-by-step explanation:

Since the 2 side lines are parallel,

[tex]2x + 40 + 5x = 180 \\ 7x + 40 = 180[/tex]

(Note that you can further simplify the equation if you wish to, this is a general equation.)

(Equation formed due to Corresponding angles and Sum of angles on the same straight line)

Find the fourth root of 81 that
graphs on the positive y-axis.

Answers

Answer:

1.732

Step-by-step explanation:

cube root of 81 is

=1.732

Answer: 3(cos(90degrees)+isin(90degrees))

Help and i will give you brainiest

Answers

C: 15,938 + 427 is 4 times as large as (15,938 + 427) /4

i am slow and i need help!!

Answers

Answer:

NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!

Step-by-step explanation:

The answer is a. 4
:)

HELP PLEASE, ITS URGENT

Answers

Answer:

1. 40% 2. 1/10

Step-by-step explanation:

1. 8/20 * 100

800/20=40

2. 1/(3+1+4+2)

1/10

Chirs bought 10.4 gallons of gasoline. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Chirs bought?

Answers

Answer:

39.52

Step-by-step explanation:

just multiply 3.8 by 104 and thats how many liters

Plzzzz guys help me with this i don’t know

Answers

Answer: B

Step-by-step explanation:

if I'm wrong sry lol

Answer:

D

Step-by-step explanation:

- 117° is positioned in the 3rd quadrant where sine < 0

The related acute angle is 180° - 117° = 63°

Then

sin(- 117)°

= - sin63° → D

find the slope-intercept equation of the line that passes through (3,1) and has a slope of 2

Answers

Answer:

y = 2x - 5

Step-by-step explanation:

Hi,

y = 2x + b

1 = 2 (3) + b

1 = 6 + b

-5 = b

y = 2x - 5

I hope this helps :)

3/6 + 7/18. or basically how do I get the answer

Answers

Answer:

8/9

Step-by-step explanation:

3/6 + 7/ 18

Make the denominator common by finding the LCM = 18

Multiply 3 by 3

Therefore sum = 3*3 + 7/ 18

sum = 9+7/18

sum = 16/18

=> 8/9

Please mark my answer as the brainliest for further answers :)

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