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].
The perimeter of a rectangular room is 24 meters.The width of the room is 4 meters. Find the length of the room.
Answer:
20 metes
Step-by-step explanation:
:)
A shirt was sold for sh 1054 after a 15% discount . what was the discount given
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
i am slow and i need help!!
Answer:
NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!
Step-by-step explanation:
____________of an event is a number that tells how likely it is to happen.
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 you don’t even have to solve it, I just need the equation
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)
11y^2-19y-10=-4y^2
all real solutions
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
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?
Answer:
169
Step-by-step explanation:
HELP PLEASE, ITS URGENT
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
Find the fourth root of 81 that
graphs on the positive y-axis.
Answer:
1.732
Step-by-step explanation:
cube root of 81 is
=1.732
Answer: 3(cos(90degrees)+isin(90degrees))
I need someone to help me Simplify 7(3n)
Answer:
21n
Step-by-step explanation:
7(3n)
7×3
21n
I hope this helps
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.
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 :)
Plzzzz guys help me with this i don’t know
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
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?
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
Please help will mark brainliest
Help I'll give Brainly Est
Find the binomial that completes the factorization.
s^3–1=( ) (s^2+s+1). Help ASAP
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
help! My back door is jammed and my dog is outside! What do I do?
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
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
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 ⚠⚠⚠ MARKING BRAINLIEST, IF UR CONFUSED, I NEED HELP WITH QUESTION 9 BUT QUESTION 8 IS RELATED TO IT ⚠⚠⚠
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:
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!!!!!
Step-by-step explanation:
X = 10 (use pyth)
Y = 11.18(use pyth)
a model ship is 0.38 M long how long is the ship in centimeters
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.
Help and i will give you brainiest
3/6 + 7/18. or basically how do I get the answer
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 :)
This pentagonal right pyramid has a base area of 30m^2
What is the volume of the figure?
This Is due soon plz help
Answer:
50m cubic
Step-by-step explanation:
*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
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
What property is being used: 5 + x = x + 5 *
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.
PLZ HELP I NEED TO TURN THIS IN IN 10 mins
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
help me pls i give brainliest
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
find the slope-intercept equation of the line that passes through (3,1) and has a slope of 2
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 :)
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?
Answer:
39.52
Step-by-step explanation:
just multiply 3.8 by 104 and thats how many liters