A car travels 22 km due south and then 28 km in a direction 60° east of south. Find the Direction of the car's resultant vector. PLEASE HELP

Answers

Answer 1

A car travels 22 km due south and then 28 km in a direction 60° east of south. Find the Direction of the car's resultant Remember that any  can be written as a coordinate like this: (AcosΘ,AsinΘ) where A is the magnitude of the object and Θ is the directional angle. So for the car travelling 20km north, that vector can be written as: (20cos90°, 20sin90°) Then when the car drives northwest at 60 degrees, that vector can be written as: (35cos150°, 35sin150°) (do you see why I it's 150°?) Then, simply calculate each of these coordinates, add them up, and then that resulting coordinate is the coordinate of the resulting displacement vector. (20cos90°, 20sin90°) = (0, 20) (35cos150°, 35sin150°) = (-30.31, 17.50) Displacement vector (x, y) = (-30.31, 37.50) With this, we can calculate the magnitude which is \displaystyle \sqrt{x^2+y^2}  x  2 +y  2  ​ . Thus: Magnitude = \displaystyle \sqrt{(-30.31)^2+(37.50)^2}=48.2km  (−30.31)  2 +(37.50)  2  ​ =48.2km The resulting directional angle is then \displaystyle \tan^{-1}(\frac{y}{x})+\pitan  −1 (  x y ​ )+π. Adding \displaystyle \piπ is only necessary when x < 0 in order to put us in the proper quadrant. Thus: Direction = \displaystyle \tan^{-1}(\frac{37.50}{-30.31})+\pi=2.25\ radians=128.9°tan  −1 (  −30.31 37.50 ​ )+π=2.25 radians=128.9° ges ok HOPE THIS HELPS :):0

Related Questions

jerome completes 8 extra credit problems and then 4 problems each day until the worksheet is done.28 problems is on the worksheet.

Answers

Answer:It will take 5 days
Explosion:28-8=20 20/4=5

PLEASE ANSWER ASAPEnter the equation of the line in slope-intercept form. Slope is − 2 3 , and (−6, −5) is on the line. The equation of the line is y =

Answers

Step-by-step explanation:

there seems to be something missing.

I assume the slope of the line is -2/3.

the slope of a line is always the factor of x in the equation.

the slope is the y/x ratio indicating how many units y changes, when x changes by a certain amount of units (e.g. when going from one point on the line to another).

the equation for the line looks like this then :

y = (-2/3)×x + b

to get b we use the provided point (-6, -5) and it's x and y values.

-5 = (-2/3)×-6 + b = 4 + b

b = -9

so, the full equation of the line is

y = (-2/3)×x - 9

need help on proportions question urgently!!!!!!

Answers

Answer:

SSS~

RQP

Step-by-step explanation:

36/15 = 2.4

48/20 = 2.4

72/30 = 2.4

Triangles are similar by SSS~.

triangle JKL is similar to triangle RQP

If line m is perpendicular to line n, and the slope of line m is -5/3, what is the slope of line n? Write in simplest form.

Answers

Answer:

Step-by-step explanation:

Slope of perpendicular line = [tex]\frac{-1}{m}[/tex]

       = -1 ÷ [tex]\frac{-5}{3}[/tex]

        [tex]= -1 *\dfrac{-3}{5}\\\\=\dfrac{3}{5}[/tex]

Anyone willing to help? I have to submit it tmr

Answers

Answer:

here's your answer

hope it helps

(look at attachment)

sam buys a rare stamp for his stamp collection at an auction. he buys the stamp for 920£ the stamp increased in value by 7% in each of the first 2 years decreased in value by 4% in the third year

Answers

The value of the stamp at the end of the third year is £976.31.

How to calculate the value?

From the information, Sam buys a rare stamp for his stamp collection at an auction. he buys the stamp for 920£ the stamp increased in value by 7% in each of the first 2 years.

First year value:

= 920 + (2% × 920)

= 938.4

Second year value:

= 938.4 + (2% × 938.4)

= 957.168

Third year value:

= 957.168 + (2% × 957.168)

= £976.31

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Complete question

sam buys a rare stamp for his stamp collection at an auction. he buys the stamp for 920£ the stamp increased in value by 7% in each of the first 2 years decreased in value by 4% in the third year. What is the cost by the end of. the third year?

If the volume of the cube was 27 (each side length is 3 units), what would the new volume be if each side length of the cube was reduced to 2 units?

Answers

clapped

Step-by-step explanation:

The new volume would be 8 because 2 by 2 by 2 equals 8.

Please help me this is due please help

Answers

Step-by-step explanation:

so levt's label the video games as "P"

if 6P=207.54$

1P= X

1P × 207.54$ = 6P × X

1P × 207.54$ = 6P × X => P eliminates P on the right side

6P 6P. => 6P eliminates 6P on the left side

207.54$ = X

6

X = 34.59$

Step-by-step explanation:

Let the cost of 1 video game = x

6 video games = $207.54

1 video game = x........cross multiply

6x = 207. 54............ divide both sides by 6

x = 34.59

therefore, 1 video game costs $34.59

What is the equivalent ratio to 14:10 ?

?:30

Answers

Answer:

42:30

Step-by-step explanation:

10 x 3 = 30

14 x 3 = 42

The answer is 42.

10 is 3 times to get to 30

So 3 times 14 gets to ?

14:10
42:30

7.836 - 937 + 2.846 =.....​

Answers

Answer:

Hi There,

Your answer is -926.318

find T1 and T2, if a 60 N load is hanged and in equilibrium position.​

Answers

Answers:

T1 = 59.5677879151077 N

T2 = 45.7583538175564  N

The values are approximate. Round the values however you need to.

=========================================================

Explanation:

Refer to the diagram below. I have added red and blue lines to break up each tension vector into the x and y components. For tension T1 in red, we have x1 and y1 as the horizontal and vertical components respectively. Note that x1 points to the left and y1 points upward.

For T2 in blue, we have x2 point to the right and y2 point upward. The horizontal components x1 and x2 must be equal, and point in opposite directions, so that we have horizontal balance. Otherwise, the object would accelerate to one side rather than be stationary.

Applying a bit of trig, we can say

cos(angle) = adjacent/hypotenuse

cos(45) = (x1)/(T1)

x1 = T1*cos(45)

and also

sin(angle) = opposite/hypotenuse

sin(67) = (x2)/(T2)

x2 = T2*sin(67)

----------------------

Again, the x1 and x2 vectors must be equal in magnitude, allowing us to say this

x1 = x2

T1*cos(45) = T2*sin(67)

T1 = T2*sin(67)/cos(45)

which we'll use later.

----------------------

Doing a bit more trig set up, we know that

sin(45) = (y1)/(T1)

y1 = T1*sin(45)

and

cos(67) = (y2)/(T2)

y2 = T2*cos(67)

Adding those two y components together will yield the total upward force that the ropes apply

y1+y2 = T1*sin(45)+T2*cos(67)

y1+y2 = (T2*sin(67)/cos(45))*sin(45)+T2*cos(67)

y1+y2 = T2*( sin(67)*sin(45)/cos(45) + cos(67) )

y1+y2 = T2*( sin(67)*tan(45) + cos(67) )

y1+y2 = T2*( sin(67)*1 + cos(67) )

y1+y2 = T2*( sin(67) + cos(67) )

This combined upward pull must be equal to 60 newtons or else we wouldn't have vertical equilibrium. If the upward pull was smaller than the downward pull, then the object would be falling. If the other way around, then the object would be pulled upward at some accelerated speed (think of a spring action).

So we'll set y1+y2 equal to 60 and solve for T2

y1+y2 = 60

T2*( sin(67) + cos(67) ) = 60

T2 = 60/( sin(67) + cos(67) )

T2 = 45.7583538175564

That value is approximate. The units for T2 are in newtons. This is the amount of pull or force along the T2 line in the upper right direction.

Side note: make sure your calculator is in degree mode.

----------------------

The last thing to do is to compute T1

T1 = T2*sin(67)/cos(45)

T1 = 45.7583538175564*sin(67)/cos(45)

T1 = 59.5677879151077

That value is approximate as well. The units are also newtons here. This represents the amount of pull in the upper left direction as the diagram shows.

----------------------

Finding such values for T1 and T2 is useful to determine if a rope can handle a certain stress load. Let's say we had a rope that was rated for only 40 newtons. Anything beyond 40 N for this hypothetical rope would mean the rope breaks. We found T1 and T2 beyond this threshold which would indicate that such a rope isn't up to the task of holding this object up (at least not with the angles shown in the diagram).

please explain how to solve this
(12+5i) - (9-2i)
i have answers but dont understand

Answers

Answer: 3 + 7i

Step-by-step explanation:

Equation expanded: 12 + 5i - 9 + 2i // now simplfy

12 - 9 = 3

5i + 2i = 7i

// together, we get

3 + 7i

Answer:

10i

Step-by-step explanation:

(12+5i) - (9-2i)

(17i) - (7i)

10i


Express the equation In y = 5 in exponential form.
TIMED HELP PLEASE

Answers

Answer:

log

2

(

y

)

=

5

2

5

=

y

y

=

32

Step-by-step explanation:

Josie used 1/2 of the milk for pancakes this morning. If her brother and sister divided what was left to eat cookies with their movie, what fraction of the milk did each drink?

Answers

Answer:

1/4 cup of milk

Step-by-step explanation:

= 1/2 ÷ 2

= 1/2 × 1/2

= 1/4

3 sss, aas, sas, or not enough information

Answers

Answer:

AAS

Step-by-step explanation:

I'm pretty sure its this, but im sorry if im wrong!

The equation of the cables for a suspension bridge is modeled by the equation
y-48 = 0.0025x2, in feet. How far is the lowest point of the cables above the bridge?
The lowest point of the cables is
feet above the bridge.

Answers

The lowest point of the cables above the bridge is 48 feet above the bridge.

The statement give us a parabola equation in standard form, the vertical distance of the lowest point above the bridge is determined by the y-coordinate of the vertex. Hence, the lowest point of the cables above the bridge is 48 feet above the bridge.

We kindly invite to check this question on parabolae: https://brainly.com/question/8495869

A watch worth Rs. 5400 is offered for sale at Rs. 4590 , then the percent of discount offered during the sale is

Answers

Answer:

15%

Step-by-step explanation:

4590 = 5400 - D% × 5400

4590 = 5400 - D/100 * 5400

4590 = 5400 - 54D

54D = 5400 - 4590

D = 810 / 54

D = 15%

Dont forget to give me the brainliest.

0.4(-1.08) = ?

what is the product?

Answers

Answer: -0.432

Step-by-step explanation:

0.4*1.08 would be 0.432 add the negative sign to get -0.432

The product of 0.4 and -1.08 is -4.240.

What is Multiplication?

Multiplication is a method of finding the product of two or more numbers

To multiply 0.4 and 1.08, we need to follow few steps

first multiply as if there is no decimal.

Next, count the number of digits after the decimal in each factor.

Finally, put the same number of digits behind the decimal in the product.

   0.40

    1.08

___________

     240

   000+

 040++

____________

    4.240

As there is a negative sign infront if 1.08, we will put minus sign to the product value

So 0.4(-1.08) is -4.240

Hence the product of 0.4 and -1.08 is -4.240.

To learn more on Multiplication click:

https://brainly.com/question/5992872

#SPJ2

is 3 a rational answer

Answers

Answer:

YES!!

Step-by-step explanation:

All rational numbers can be expressed as a fraction whose denominator is non-zero. Here, the given number, 3 can be expressed in fraction form as 3⁄1. Hence, it is a rational number.

Yup 3 is a rational number.
A rational number is any number that can be written as a fraction, like x over y.

. Ramu took a loan of 50000 rupees from a bank which charges 10% interest, compounded an- nually. He repaid 10000 rupees after one year and 15000 rupees after two years. How much should he pay at the end of three years to settle the loan?​

Answers

Answer:

= 30,550 rupee owed

Step-by-step explanation:

yr1 = 50000 x 0.10^1 = 5000

5000 - 10000 = 5000 credit from debt.

yr 2 = 50000 x 1.10^2 = 500 debit from debt = 5000-15000= 10,000 credit from debt

yr 3 = 50000 x 1.10^3 = 50 debit from debt

5000 + 500 = 15000 where 50,000 owed initially and yr1 and yr 2 paid in full interest of 5500 and we deduct this from his payment = 25000-5500 =

19500 paid of initial and nothing owed on interest.

50000-19500= 30,500 rupees owed + 50 rupee interest.

= 30,550 rupee owed

The amount he should pay at the end of the three years to settle the loan is; 41,550 Rupees

Compound Interest

We are given;

Investment = 50000 rupees

Annual Interest Rate = 10% = 0.1

Since the interest is compounded annually, then number of times of compounding = 3

Thus;

Amount to pay after 3 years is;

A = 50000(1 + 0.1)³

A = 50000 × 1.1³

A = 66500 Rupees

Now, we are told that he has already paid 10000 rupees after one year and 15000 rupees after two years. Thus, amount he now owes to settle the loan = 66500 - (10000 + 15000) = 41,550 Rupees

Read more on Compound Interest at; https://brainly.com/question/2455673

identify the congruence transformation shown as a reflection, translation or rotation

Answers

Answer:

Counterclockwise rotation 90°

Step-by-step explanation:

first quadrant graph -> 2nd quadrant

Counterclockwise rotation 90° : (x,y) -> (-y , x)

Help WITH THE MATH PLEASE QUICK

Answers

Answer:

Step-by-step explanation:

2x - 3 = 135    {Corresponding angles are congruent}

2x = 135 + 3

2x = 138

Divide both sides by 2

x = 138/2

x = 69

[tex]\small\boxed{\begin{array}{cc} \hline\sf \normalsize {Math \: \: \: Question}\\ \hline\end{array}}[/tex]

=================================

2× - 3 = 135

2× = 135 + 3

2× = 138

× = 138/2

× = 69

=================================

[tex]\begin{gathered}\begin{gathered}\tiny\boxed{\begin{array} {} \red{\bowtie}\:\:\:\: \red{\bowtie}\\。◕‿◕。\end{array}}\end{gathered}\end{gathered}[/tex]:BrainliestBunch

What is an equation in point slope form for the line perpendicular to..

Answers

Answer:

b

Step-by-step explanation:

And since we're perpendicular to y is equal to 3x plus 9, we know the slope of the two lines that are perpendicular

K times 3 is minus 1, so k is minus 1/3,

Only b and c match. Plug in the point negative 6,5.

The answer is b.

Complete the equation. ( − 4 ) 2 =

Answers

Answer:

-16

Step-by-step explanation:

multiply 4x4 and then determine if its negative or positive

-8 This is what I believe it is hopefully this helps

Please help. I'll mark the answer as brainliest.​

Answers

thanks for the points

Step-by-step explanation:

hehe

-2×(-2)³×(-2)×3+(-2)×3×(-1)³

Answers

Answer:

-90

Step-by-step explanation: I hope its the right answer. If not I'm sorry.... I'm just a kid...

helppp
what is the slope

Answers

-1/2 I think is the slope

The slope is [tex]-\frac{3}{7}[/tex]

Find the difference. 8.6 − 2.87

Answers

Answer:

5.73

Step-by-step explanation:

The difference is 5.73.

The product of three whole numbers is 120 how many different possibilities are there for the three whole numbers

9 different possibilities

Answers

Answer:

z. sjshshdbd.d.difffjfjfjf

please answer this question

Answers

Answer:

3rd option

Step-by-step explanation:

a point (0, y ) lies on the y- axis

a point (x, 0 ) lies on the x- axis

a point (x, y ) lies in I quadrant

a point (- x, y ) lies in II quadrant

a point (- x, - y ) lies in III quadrant

a point (x, - y ) lies in IV quadrant

Then

point (2, - 5 ) lies in IV quadrant

-----------------------------------------------------------------

We require 2 equations with the repeating digit 7 placed after the decimal point.

let x = 0.427777... ( multiply both sides by 100 and 1000 )

100x = 42.777..... (1)

1000x = 427.777.... (2)

Subtract (1) from (2), thus eliminating the repeating digits

900x = 385 ( divide both sides by 900 )

x = [tex]\frac{385}{900}[/tex] = [tex]\frac{77}{180}[/tex]

Other Questions
MY PAPER IS DUE IN AN HOUR!!!Your challenge- Write a paper on how to build, construct, and engineer a faster roller coaster. You essay must contain 5 paragraphs minimum. Each paragraph must be 3 sentences minimum.Potential energy, Kinetic energy, Thermal energy and friction, speed, velocity, and acceleration, and the law of conservation of energy must be the main ideas of your paragraphs what is the minimum mass in Mol. of plutonium 234 needed to reach a critical mass nuclear reaction? An object has a gravitational force of 111N acting on it. If it had 4 times more mass, what would the force on it be? Which series of transformations will not map figure Q onto itself? (x + 2, y 2), reflection over y = x 1 (x 2, y + 2), reflection over y = x + 3 (x + 0 y 4), reflection over y = x 1 (x 3, y 3), reflection over y = x + 1 solve plsw brainliest Which of the following is reflected in the way you use your time?Your likes and dislikesYour stress levelYour important classes and other activitiesYour goals and priorities if my gentiles fall off am I no longer part of the bois? How does the human immune system work In ASL, the position in which certain signs are completed indicates A-ability to sign B-age of speaker C-place of action D-time of event H hw r dg td what is the mean of a standard normal distribution? Please help me with this math probelm ASAP!! Will give brainliest!! :) Solve 4(x5)=6x. You must SHOW EACH STEP for full credit. Please help me with this and no link plsssss Ill mark you BRAINLY how has parris changed? why doesnt the news that abigail and mercy have left town affect the decision of the court? how is danforth a victim of his own logic? Assertion(A):-India is the seventh largest country in the worldReason(R):-Canada is smaller than India which part of human heart carry oxygenated blood........ Hi i need help with this work Explain what is happening below solve for f. f-(-4)=-1