Mathematics College

The magnitude and direction of two vectors are shown in the diagram. What is the magnitude of their sum? ​

The Magnitude And Direction Of Two Vectors Are Shown In The Diagram. What Is The Magnitude Of Their Sum?

Answers

Answer 1

Separate the vectors into their x- and y-components. Let u be the vector on the right and v the vector on the left, so that

u = 4 cos(45°) x + 4 sin(45°) y

v = 2 cos(135°) x + 2 sin(135°) y

where x and y denote the unit vectors in the x and y directions.

Then the sum is

u + v = (4 cos(45°) + 2 cos(135°)) x + (4 sin(45°) + 2 sin(135°)) y

and its magnitude is

||u + v|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)

… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))

… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))

… = √(16 + 16 cos(135° - 45°) + 4)

… = √(20 + 16 cos(90°))

… = √20 = 2√5

Answer 2

Answer: 2√5

Step-by-step explanation:

Use the Sine Law of triangles: In triangle with sides of length 1,2,3 that are opposite to angles 1,2,3 we have

1/sin1=2/sin2=3/sin3.

Related Questions

i don’t understand, what’s the answer to this pleaseeee

Answers

Answer:

I don't know the answer but I suggest u get help from a tutor

they help a LOT

x= 8.4852
Because that is the right triangle so you can use the Pythagorean theorem to find for x

Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions
that a randomly chosen student answered correctly. Here is the probability distribution of X along with
summary statistics:
0
1
2
2.
3
X = # correct
P(X)
0.05
0.20
0.50
0.25
Mean: Hex = 1.95
Standard deviation: Ox 0.8
Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give
every student 5 additional bonus points. Let Y represent a random student's score.
What are the mean and standard deviation of Y?
Hy =
points
Oy
points

Answers

Answer:

24.5 points

8 points

Step-by-step explanation:

khan academy

The mean is 1.95 and the standard deviation is 2.41 for the given distribution.

What is the standard deviation?

A standard deviation (σ) is a measure of the distribution of the data in reference to the mean.

The given data as :

Correct question (x)  Probability                

        0                           0.05  

        1                            0.20

        2                           0.50

        3                           0.25  

In this scenario, we must calculate the mean, which is the product of the correct question and the probability. The mean will then be subtracted from the correct question. multiply the difference between the correct question and the mean by probability. This indicates the pay variance. off's The standard deviation of the distribution is given by taking the square root of the variance of the correct question.

Mean = 0 × 0.05  + 1 × 0.20 + 2 × 0.50 + 3 × 0.25

Mean  = 1.95

Variance = (0 - 1.95)² + (1 - 1.95)² + (2 - 1.95)² + (3 - 1.95)²

Variance = 3.8025 + 0.9025 + 0.0025 + 1.1025

Variance = 5.81

Standard deviation = √(Variance)

Standard deviation = √(5.81)

Standard deviation = 2.41

Thus, the mean is 1.95 and the standard deviation is 2.41 for the given distribution.

Learn more about the standard deviation here:

brainly.com/question/16555520

#SPJ2

someone help pls thank u

Answers

A bc it is pie fjskdnsowiksnxbx
Option a is irrational

HELP PLZ 20 POINTSSSS

Answers

Answer:

cube................

Answer:

A)

Step-by-step explanations:

To begin a bacteria study, a petri dish had 2300 bacteria cells. Each hour since, the number of cells has
increased by 7.2%.
Lett be the number of hours since the start of the study. Let y be the number of bacteria cells.
Write an exponential function showing the relationship between y and t.
PLEASE HELP :)

Answers

Answer: [tex]y= 2300(1.072)^t[/tex]

Step-by-step explanation:

The exponential growth equation : [tex]y=A(1+r)^t[/tex] , where A=initial value, r= rate of growth , t= time.

Given: A = 2300,  r= 7.2% = 0.072  

Let t be the number of hours since the start of the study. Let y be the number of bacteria cells.

then, the exponential function showing the relationship between y and t will be:

[tex]y= 2300(1+0.072)^t\\\\\Rightarrow\ y= 2300(1.072)^t[/tex]

If you would help it would be life-saving

Answers

Answer:

waiting for the wishing well, put they hands put they hands to the wishing well still no ns but oh well they pain and they wishes in the wishing well.

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

2) [tex]y=\frac{3}{2}*64\\[/tex]

y = 3 * 32 = 96

[tex]3) x = \frac{2}{3}y\\\\x =\frac{2}{3}*39=2*13=26[/tex]

[tex]4)y=\frac{3}{2}x\\\\y=\frac{3}{2}*1=\frac{3}{2}[/tex]

Solve for X
1q - 2 x = 7
Help!

Answers

X=4
Hope this helps :)

Guys.. I’m going to get held back, I. Need. Help.

Answers

-12 and -6
Good night!!

Answer:

1).  -12

2).  -6

Hope this helps<3

Based on this triangle, which one of the following statements is true? (Note: the triangle is not drawn to scale)
[PLEASE LEAVE A SMALL EXPLANATION ILL MARK BRAINLIEST]

Answers

Answer:

A

Step-by-step explanation:

All triangles angles add up to 180°

Which points are solutions to the system of inequalities? Select ALL that apply.

(-2, 4)
(2, -1)
(3, 1)
(0, 0)
(0, -1)

Answers

Answer:

0,0

2,-1

-2,4

Step-by-step explanation:

What is the diameter of this circle? A) 2 cm B) 3.14 cm C) 4 cm D) 8 cm

Answers

Answer:

The answer is c

Step-by-step explanation:

Well, since the Circle is 8cm you can divide the circle by two to get 4

What is the value of 5k+m when k=-3 and m= -9

Answers

I think the answer is -6 Because 5 times-3 is negative 15 plus -9 that’s 6

Answer: -24

Step-by-step explanation:

Substitute k and m with -3 and -9 then solve.

Which is the equation for the line that passes through (5,-3) and has a slope of 6?

Answers

v=4/3[~]R^3 need 20 letters

So ummm. I kind of got this wrong, and I had to delete my answer, I swear, I am SOOOO sorry. If there is a way I can give your points back I will do so.

So um yeah, just ignore this.

Please answer

If it takes 4/5 hours to mow 1/4 of the lawn, how much time does it take to mow the entire lawn?

A. 5/16 hr

B. 5/8 hr

C. 21/20hr

D.16/5hr

Answers

Step-by-step explanation:

it will take 21/20hours

please find the Equations PLEASE ​

Answers

Answer:

9) y = -x

10) y = -3/2x + 12

11) y = 3/4x - 5

12) y = -2/3x

6y + 12x + 4y - 9x - 3x
Combining like terms
I need some help!

Answers

Answer:

10y

Step-by-step explanation:

solve the equation
58 = 9x - 5

Answers

Answer:

x=7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Let's solve your equation step-by-step.

58=9x−5

Step 1: Flip the equation.

9x−5=58

Step 2: Add 5 to both sides.

9x−5+5=58+5

9x=63

Step 3: Divide both sides by 9.

9x/9 = 63/9

x=7

WILL GIVE THE BRAINIEST AND 50 POINTS!!!

Walmart sells colored pencils for $0.75 a box, spiral notebooks for $3 each, and pencil boxes for $1.20 each.

a. If Jack and his two sisters all buy one of each item, what will be the total cost?

b. Their dad game them a total of $30.00. How much would they have left after they purchase these school supplies?

Answers

A. 14.85 (.75x3=2.25 3x3=9 1.20x3=3.60)
B. 15.15 (30.00-14.85=15.15)

Express the limit as a definite integral on the given interval. lim n→[infinity] n xi ln(1 + xi2) Δx, [2, 7] i = 1

Answers

Answer:

Step-by-step explanation:

[tex]Consider \ the \ following \ series[/tex]

[tex]\lim_{n \to \infty} \sum \limits ^n_{i=1} x_i \ In ( 1+ x_i^2) \Delta x , [2,7][/tex]

[tex]Let's \ recall \ the \ explanation \ of[/tex] d[tex]efinite[/tex] [tex]\ integral \ in \ terms \ of \ Riemann \ sum[/tex]

[tex]\int^b_a \ f(x) \ dx = \lim_{n \to \infty} \sum \limits ^n_{i=1} \ f(x_i) \Delta x , \ where \ \Delta x = \dfrac{b-a}{n}[/tex]

[tex]By \ efinition, \ the \ limit \ is \ then \ expressed \ as \ integral[/tex]

[tex]\lim_{n \to \infty} \sum ^a_{i=1} \ x_i \ In (1+x_i^2) \Delta x = \int^7_2 xIn (1+x^2) \ dx[/tex]

URGENT PLEASE HELP GIVE RIGHT ANSWER.

Answers

Answer:

its negative 8

Step-by-step explanation:

you can see it there

I NEED HELP ITS DUE IN A FEW MINUTES HHHHEEELLLLPPP

Answers

Answer:

Question 11 - B

Question 12 - C

Step-by-step explanation:

11). 4 chairs per table --> B

120/30 = 4

12). The 24 pack is a better buy (C).

12 pack - 0.3333 per can24 pack - 0.3125 per can <-- cheaper

You will drop the bottle/water mass so that it hits the lever at different speeds. Since an object in free fall is accelerated by gravity, you need to determine the heights necessary to drop the bottle to achieve the speeds of 2 m/s, 3 m/s, 4 m/s, 5 m/s, and 6 m/s. Use the equation Ht = v squared over 2 g. to calculate the height, where Ht is the height, v is the speed (velocity), and g is the gravitational acceleration of 9.8 m/s2. Record these heights in Table B. To achieve a speed of 2 m/s, the bottle must be dropped at m. To achieve a speed of 3 m/s, the bottle must be dropped at m. To achieve a speed of 4 m/s, the bottle must be dropped at m. To achieve a speed of 5 m/s, the bottle must be dropped at m. To achieve a speed of 6 m/s, the bottle must be dropped at m

Answers

Answer:2,3,4,5,6

Step-by-step explanation:

Answer:

0.20

0.46

0.82

1.28

1.84

Step-by-step explanation:

what is 30% as a fraction in simplest form and as a decimal to the nearest hundredtgh

Answers

Answer:

fraction-3/10

decimal-.3

Answer:

Step-by-step explanation:

There are a few ways you could look at this, but this is the way that I prefer:

A percent is essentially already a fraction out of 100. 100% = 1. Therefore, 30% = [tex]\frac{30}{100}[/tex].

To simplify this, divide the top and the bottom by 10. This equals [tex]\frac{3}{10}[/tex]. Because 3 is a prime number and 10 is not divisible by 3, this is completely simplified.

To find the percent of any fraction, the easiest way is to simply divide the top by the bottom.

3/10 = 0.3

This is your final answer, as there is no number in the hundredth place or beyond to concern yourself with.

please helllppp its in the picture and due in 5 mins​

Answers

Answer:

it is a it's a

Step-by-step explanation:

Answer:

D (I think)

Step-by-step explanation:

If you multiply -4 times -2 you get positive 8 and the five stays the same so it would be 8/5. If you multiply -4 times 3x you would get -12x. So the total equation would read 8/5 - 12x

* HELP QUICK I WILL MARK BRANLIEST* If the circumference of a circle is 10x inches, what is the area, in square inches, of
the circle?
1) 10 sq. in
2) 254 sq. in.
3) 50. sq. in.
4) 100 sq. in.

Answers

Answer:

100 Sq in.

Step-by-step explanation:

Please help me ASP please

Answers

lxw  so 3/4 x 4/5 then get ur answer

Bob is 17 years older than john. In 5 years, the sum of their ages will be 51. Find their current age

Answers

68 and 56 it’s not that hard

what is the slope for (-11,7),(15,-3)​

Answers

-5/13

Formula: Y2-Y1/X2-X1

Answer:

     m=-5/13

Explanation

Which triangles are congruent by SAS?

Answers

Answer: VTU and HGF

Step-by-step explanation:

PLZ help: The theoretical probability that a pop song plays on your MP3 player is 0.45. There are 80 songs on your MP3 player. How many of the songs are pop songs?

Answers

Answer:

36

Step-by-step explanation:

80 * .45 = 36

Answer:There are 36 pop songs on your playlist

Step-by-step explanation:

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