Find the measure of the angle between the vectors 〈6, –3, 1〉 and 〈8, 9, –11〉

A:90°
B:30°
C:84.8°
D:102.6°​

Answers

Answer 1

Answer:

Option C.

Step-by-step explanation:

We know that for two vectors:

A = 〈a₁, a₂, a₃ 〉and  B =〈b₁, b₂, b₃〉.

The dot product between A and B is:

A.B = IAI*IBI*cos(θ)

Where θ is the angle between the vectors.

And the dot product can be also written as:

A.B = a₁*b₁ + a₂*b₂ + a₃*b₃

With that, we can find the angle between our vectors.

In this case, the vectors are:

A = 〈6, –3, 1〉 and B = 〈8, 9, –11〉

The modules are:

IAI = √( 6^2 + (-3)^2 + 1^2) = 6.78

IBI = √( 8^2 + 9^2 + (-11)^2) = 16.31

And the dot product between A and B is:

A.B = 6*8 + (-3)*9 + 1*(-11) = 10

Then we have that:

10 = IAI*IBI*cos(θ) = ( 6.78)*(16.31)*cos(θ)

10/(6.78*16.31) = cos(θ)

Now remember the inverse cosine function, Acos(x), this function has the property:

Acos(cos(x)) = x

If we apply this to both sides, we get:

Acos(10/(6.78*16.31)) = Acos(cos(θ)) = θ = 84.8°

The correct option is C.


Related Questions

Directions: Select all the correct answers.
Yvette needs 5/8 of a teaspoon of salt, 2/3 of a tablespoon of baking soda, and 3/4 of a cup of sugar to bake a cake.

The order of the measurements from least to greatest are 5/8 < 3/4 < 2/3.
The order of the measurements from least to greatest are 5/8 < 2/3 < 3/4.
The numbers 5/8 and 3/4 are terminating decimals while 2/3 is a non-terminating decimal.
The numbers 5/8 and 2/3 are terminating decimals.
The number 5/8 is a terminating decimal while 3/4 and 2/3 are non-terminating decimals.
The number expands to 0.75 while expands to 0.6.
The number 5/8 expands to 0.625 while 3/4 expands to 0.75.
The order of the measurements from least to greatest are 2/3 < 5/8 < 3/4

Answers

Answer:

The order of the measurements from least to greatest are 5/8 < 3/4 < 2/3.

Step-by-step explanation:

Answer:

The numbers 5/8 and 2/3 are terminating decimals.

The order of the measurements from least to greatest are .

2/3<,5/8,<3/4

Step-by-step explanation:

study island

can someone please help me with this question??

Answers

Answer:

90

Step-by-step explanation:

radius = 6/2 = 3

(3x3x3x10)/3 = 270/3 = 90

It takes Lauren 13 minutes to walk 1 mile. How many miles can
Lauren walk in 52 minutes?

Answers

Answer:

4

Step-by-step explanation:

if it takes her 13 mins to walk 1 mile and we need to know how many miles she can walk in 52 mins than the equation for this word problem would be: 52÷13=4

3.
If the researchers add food in the simple maze such that the probability of each mouse turning left is now 0.7, what
is the probability that only one of the two mice will turn left?

Answers

Answer:

0.49

Step-by-step explanation:

Pls mark brainliest if correct!

Is 4.53 a real number?
yes or no

Answers

Answer:

yur

Step-by-step explanation:

Answer:

yeah it's a decimal so yes

what is the next step in solving this equation

a. -5x-8=9
b. -13x=9
c. 11x-24=9
d. -21x-24=9

Answers

A. -5x-8=9
Hope this helps

Factorise using the sum and product method with all the steps!
British curriculum

No links or websites please !

Answers

Answer:

(2x+3)(x-5)

Step-by-step explanation:

Given the expression 2x²-7x-15

Factorize

2x²-10x+3x-15 =0

2x(x-5)+3(x-5)

(2x+3)(x-5)

Hence the factored form of the expression is (2x+3)(x-5)

HI thts way tooo much to answer but ye

Mike wants to pull as much juice as possible in his cup.His cup is 10.2 inches tall and has a 2.6 inch radius. How much juice can mike pour in his cup

Answers

Answer: [tex]V=216.64\ in.^3[/tex]

Step-by-step explanation:

Given

Height of cup [tex]h=10.2\ inch.[/tex]

radius of cup [tex]r=2.6\ inch.[/tex]

assume the cup is in the shape of a cylinder

The volume of the cylinder is [tex]\pi r^2h[/tex]

Put the values

[tex]\Rightarrow V=\pi \times 2.6^2\times 10.2\\\Rightarrow V=216.64\ in.^3[/tex]

I've got 5 questions and I'm very stuck so I yall can pls HELP and answer them for me pls, thank you

Answers

Answer:

1. 11cm

2. 31.2cm

3. 20m

4. 11cm

5. 314feet

Step-by-step explanation:

1. 5.5 × 2 = 11cm

2. 15.6 × 2 = 31.2cm

3. 40m ÷ 2 = 20m

4. From the centre of a circle to the edge is the radius of a circle.

5. Circumference = πD

D = 2r = 2 × 50 = 100

π × 100 = 314feet

If the degree of a term is negative, the term is still a monomial.


A. True
B. False

Answers

Answer:

a

Step-by-step explanation:

Answer:

B) false

Step-by-step explanation:

degree cant be negative because if it was then the trioxians of the neutrino would implode to a sub zero quantum ordinate and the multiverse would incenerate itself and turn into a meca black hole...and that is why we dont want monomials to have a negative degree

Two decimals numbers, to the thousandths, that have a sum of about 5 and a difference of about 3. Then do the math to prove it works.

Answers

Answer:

The numbers are approximately: 4.000 and 1.000

Step-by-step explanation:

The given parameters can be expressed as:

[tex]\frac{x}{1000} + \frac{y}{1000} \approx 5[/tex]

[tex]\frac{x}{1000} - \frac{y}{1000} \approx 3[/tex]

Required

Determine the numbers

In each of the equations, multiply by 1000

[tex]1000 * [\frac{x}{1000} + \frac{y}{1000} \approx 5][/tex]

[tex]x + y \approx 5000[/tex]

[tex]1000 * [\frac{x}{1000} - \frac{y}{1000} \approx 3][/tex]

[tex]x-y \approx 3000[/tex]

So, we have:

[tex]x + y \approx 5000[/tex]

[tex]x-y \approx 3000[/tex]

Add the two equations

[tex]x + x + y - y \approx 5000 + 3000[/tex]

[tex]2x \approx 8000[/tex]

Solve for x

[tex]x \approx 8000/2[/tex]

[tex]x \approx 4000[/tex]

Substitute [tex]x \approx 4000[/tex] in [tex]x + y \approx 5000[/tex]

[tex]4000 + y \approx 5000[/tex]

[tex]y \approx 5000 - 4000[/tex]

[tex]y \approx 1000[/tex]

Using:

[tex]\frac{x}{1000} + \frac{y}{1000} \approx 5[/tex]

We have:

[tex]\frac{4000}{1000} + \frac{1000}{1000} \approx 5[/tex]

[tex]4.000 + 1.000 \approx5[/tex]

This implies that, the numbers approximates to 4.000 and 1.000, respectively.

please help it's the last question

Answers

Answer:

1 is the answer

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

option 1!

Step-by-step explanation:

it started at 15 and ended at 23. also when u look at the sequence, 19 is in the middle. which shows in the graph that 19 is matching the line. but u might be confused since option 2 also has 19 matching the line... but look carefully. the square started at 17, but the sequence does not have 17 in it.

i hope this helped :D

5 tons of fertilizer cost $14,100.00. What is the price per pound?

Answers

Answer:

$2,820

Step-by-step explanation:

$14,100.00 / 5= $2,820

Please answer correctly

Answers

Answer: 125

Explanation: Angle H + Angle L = 180
L +55 = 180
Angle L = 125

KLJ= 125º

Hope this helps!!

Answer this please i am stuck

Answers

Answer:

no one knows i think

Step-by-step explanation:

Answer:

junkijunki

Step-by-step explanation:

The first play in a football game starts at the
50-yard line and results in a gain of 25 yards for
Team A. On the next play, Team B has a gain of
25 yards in the opposite direction. Where is the
ball after the second play?

Answers

It’s back in the 50 yard line

If you place a 40-foot ladder against the top of a building and the bottom of the ladder is 17 feet from the bottom of the building, how tall is the building? Round to the nearest tenth of a foot.

Answers

Answer:

no se ingles pero, alguien me puede ayudar?

Answer:

The building is 36.2 ft tall.

Step-by-step explanation:

i got it right on the deltamath

Find the are of the triangle below in square units

(The triangle is in the picture, please help! :,))

Answers

Answer:

252

Step-by-step explanation:

14 x 6 x 12 = 1008/2 = 504/2 = 252

Use the law of sines to find the value of a.
B
95°
D
40°
a
4.7 cm
С
sin(A)
a
sin(B)
Law of sines:
sin(C)
C

Answers

Answer:

Step-by-step explanation:

''he Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles . Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.''

The best approximation value of a by using sine rule is 3.0cm. so option C is correct.

What is sine rule?

The sides and angles of non-right triangles are related according to the Law of Sines.

The relationship between the angles and lengths of the sides:

a/sinA = b/sinB = c/sinC

We know according to law of sines:

a/sinA = b/sinB = c/sinC

by putting the values we can write,

a/sin40° = 4.7/sin95°

a = (4.7 ×sin40°)/sin95°

  =  3.032

by putting the value of Sin40° and Sin95°.

we get a = 3.03cm.

Approximation value of a is 3.0cm.

To know more about sine rule check:

https://brainly.com/question/26952873

#SPJ7

The complete question:

what is the best approximation of the value of a?

2.4 cm

2.7 cm

3.0 cm

3.3 cm

Given triangle ABC with ∠BAC=40°, ∠ABC=95°,AC = 4.7cm, BC = a cm.

Suppose a sample of 256 was taken from a population with a standard deviation of 64 centimeters. What is the margin of error for a 68% confidence interval?
A. 6
B. 8
C. 10
D. 4

Answers

The correct margin of error for a 68% confidence interval is option D 4 centimeters.

Let's calculate the margin of error correctly for a 68% confidence interval.

To calculate the margin of error, we need to determine the critical value associated with a 68% confidence interval. For a normal distribution, the critical value is approximately ±1 standard deviation.

Given that the standard deviation is 64 centimeters, the margin of error can be calculated as:

Margin of Error = 1 * (Standard Deviation / √Sample Size)

= 1 * (64 / √256)

= 1 * (64 / 16)

= 1 * 4

= 4

Therefore, the correct margin of error for a 68% confidence interval, based on the given information, is 4 centimeters. The correct answer is option D.

Know more about   interval  here:

https://brainly.com/question/30460486

#SPJ8

Answer:

D

Step-by-step explanation:

Just took the test

**NO LINKS** Only need part D

Answers

Answer:

Step-by-step explanation:

Use SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

well you know it's a 90°   so do you know what  Sin(90) is?   you should :D

I think this is kinda a trick question too b/c Opp here is also Hyp  

so it would like like    sin(90) = Opp / Hyp  but  that's  427/427 for this question.   seems kinda confusing  why ask it  that way.. huh  :/

sin(90) = 1

From the set {7, 15, 18), which of the values can be substituted for c to make the
equation true.

90 - 2c = 60

A. 7
B. 18
C. none of these
D. 15

Answers

Answer:

7-2=5

18-2=16

15-2=13

90-20=70

Which are possible employers in the Financial career cluster? Check ALL that apply.
-private company
-government
-nonprofit organization
-bank
-stock market

Answers

Answer:

pretty sure its

government

nonprofit organization

bank

Step-by-step explanation:

doing exam thingy

Answer:

hes right

Step-by-step explanation:


TIME REMAINING
43:34
A department store is hiring for the positions of manager, associate manager, and assistant manager. If 15 people have applied for all the positions and are equally qualified for each position, in how many ways can the positions be filled?

Answers

Answer:

The positions can be filled in 2730 ways

Step-by-step explanation:

The number of all posible ways is equal to the number of possibilities of who can become the manager, times the number of possibilities of who can become the associate manager, times the number of possibilities of who can become the assistant manager.

Now...

The number of possibilities of who can become the associate manager = 15

The number of possibilities of who can become the associate manager = 14

(it decrease by one because one person already got the position of manager)

The number of possibilities of who can become the assistant manager = 13

(based on the same logic as for the number of who can become the associate manager)

So now we know the number of ways equals...

15 x 14 x 13 = 2730  

2730 is the answer!!!!!! The

In circle J with mZHLK = 21°, find the angle measure of minor arc HK .
K
H
L
Answer: m HK
Submit Answer
attempt 2 out of 2
PLZ HELP

Answers

Answer:

HK=42°

Step-by-step explanation:

because the arc of HK is two time bigger than HLK measurement

HLK=1/2HK

21°=1/2HK cross production

HK=2×21°

HK=42°

At a car wash fundraiser, $168 was raised for washing 24 cars. The next day, $280 was raised for washing 40 cars. Are the rates equivalent? Explain your reasoning.

Answers

Step-by-step explanation:

168/24 = 7 dollars per car

280/40 = 7 dollars per car

the rates are equivalent.

for brainiest:):):):):):):):):):):):)

Answers

Answer:

P: 15  Area: 8

Step-by-step explanation:

Use the line to split the shape. For P add all the numbers and add a 4 and a 1 too. For the area, you have to multiply 2 by 2 because of the cube, then mulitply 4 by 1 because 2+2=4 and the other number is one. REMEMBER TO SHOW YOUR WORK AND DOUBLE-CHECK!

Algebra 2 functions. Will mark Brainliest!

Answers

Answer:

f-1(x) is just the opposite of f(x) therefore -x(x-2) =f-1(x)

Step-by-step explanation:

Select the correct answer. Which is the minimum or maximum value of the given function?
A. The function has a maximum value of -3.
B. The function has a minimum value of -3.
C. The function has a maximum value of -4.
D. The function has a minimum value of -4.​

Answers

Answer:

The answer is D I believe

Step-by-step explanation:

If you look at the lowest point it lands on -4

Pythagorean theorem level 2 delta math

Answers

The third side is [tex]\sqrt{42}[/tex]

So Pythagorean's theorem is the following

[tex]Short^2 + Long^2 = Hypotenuse^2[/tex]

From here we can input the following information that we know

[tex]Short^2 + 4\sqrt{3}^2 = 8^2\\Short^2 + 12 = 64\\Short^2 = 64 - 12\\Short^2 = 42\\Short = \sqrt{42}\\[/tex]

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