A car travels 32 km due north and then 46 km in a direction 40° west of north. Find the direction of the car's resultant vector. [?] Round to the nearest hundredth.

Answers

Answer 1

Answer:

Step-by-step explanation:

This requires some serious work before we even begin. First off, we will convert the km to meters:

32 km = .032 m

46 km = .046 m

And then we have to deal with the angle given as 40 degrees west of north. An angle 40 degrees west of north "starts" at the north end of the compass and moves towards the west (towards the left in a counterclockwise manner) 40 degrees. That means that the angle that is made with the negative x axis is a 50 degree angle. BUT the way angles are measured in standard form are from the positive x-axis, therefore:

40 degrees west of north = 50 degrees with the negative x axis = 130 degrees with the positive x axis. 130 is the angle measure we use. Phew! Now we're ready to start. Adding vectors requires us to use the x and y components of vectors in order to add them.

[tex]A_x=.032cos90.0[/tex] so

[tex]A_x=0[/tex] (the 90 degrees comes from "due north")

[tex]B_x=.046cos130[/tex] so

[tex]B_x=-.030[/tex] and if we add those to get the x component of the resultant vector, C:

[tex]C_x=-.030[/tex]   And onto the y components:

[tex]A_y=.032sin90.0[/tex] so

[tex]A_y=.032[/tex]

[tex]B_y=.046sin130[/tex] so

[tex]B_y=.035[/tex] and if we add those together to get the y component of the resultant vector, C:

[tex]C_y=.067[/tex]  Note that since [tex]C_x[/tex] is negative and [tex]C_y[/tex] is positive, the resultant angle (the direction) will put us into QII.

We find the magnitude of C:

[tex]C_{mag}=\sqrt{(-.030)^2+(.067)^2}[/tex]

We will round this after we take the square root to the thousandths place.

[tex]C_{mag}=.073m[/tex] and now for the angle:

[tex]\theta=tan^{-1}(\frac{.067}{-.030})[/tex] which gives us an angle measure of -67, but since we are in QII, we add 180 to that to get that, in sum:

The magnitude of the resultant vector is .073 m at 113°


Related Questions

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!

Answers

The correct answer is A

Answer:

I believe it is A. 1,1150.6cm^3

Step-by-step explanation:

To solve for the volume of a cone:

[tex]V = \pi radius^{2} \frac{height}{3}[/tex]

Write 0.2 repeating as a fraction in simplest form (The 0.2 is repeating, so the 2 has the repeating bar above it, just need someone to solve this, it would help a lot thanks.)

Answers

If x is the number 0.222…, then 10x = 2.222…. Subtracting x from 10x eliminates the fractional part, so that

10x - x = 2.222… - 0.222…

==>   9x = 2

and solving for x gives x = 2/9.

Justin is saving money to buy a stereo. He has $25 saved in the bank right now. He earns $40 each week delivering newspapers.

Let y = the total amount of money Justin has, and x is in weeks.

Answers

Y=40x+25 y is the total he has, 40x is he makes 40 per week, and 25 he already has

Vanessa and her friends are watching three movies consecutively. The first movie is 2 hours and 17 minutes long. The second movie is 84 minutes long, and the last movie is 99 minutes long. How much time will they spend watching the movies?

Answers

Answer:

320 minutes (5 hours and 20 minutes).

Step-by-step explanation:

2 hours and 17 minutes = 137 minutes

137 + 84 + 99 = 320

Therefore, they will spend 320 minutes (5 hours and 20 minutes) watching movies.

Two teams are playing basketball. At the end of the game,
Team A scores 72 points and Team B's score is 125% of Team
A's. How many points does Team B score?

Answers

Team B score will be 162 points

Answer: 90 points

Step-by-step explanation:

Team A's score = 72 points

Team B's score = 125% of A's

= 90 points

please click thanks and mark brainliest if you like :)

Mr. Johnston needs a shelf to hold a set of textbooks, each 1 3/4 in. Wide. How many books will fit on a 35-in.-long shelf?

Answers

Answer:

20 books

Step-by-step explanation:

35/1.75

20

Find the missing value.
Hint: Use the number line to find the missing value.
-5 = -8-
H
-15
-10
-5
0
5
10
15
Stuck? Review related articles/videos or use a hint.


Answers

Answer:

-3

Step-by-step explanation:

-8 - x =-5

I hope this helped! :)

arshad's father bought x sweets .(x-4)were eaten by children and 20 were left.how many sweets did his father bring

Answers

Answer:

24

Step-by-step explanation:

20+4

simple

x-4=20

x=20+4

x=24

mark me as brainliest

Answer:

24 sweets

Step-by-step explanation:

Remaining sweets = 20

x - 4 = 20

Add 4 to both sides.

x = 20 +4

x = 24

FIND THE AREA OF THE SHADED REGION.

Answers

This problem can be a bit confusing, so let's break it down:

First, let's take the area of the square (A = b · h):

A = 15 · 15

A = 225 cm²

Now comes the confusing part:

We can tell that the non-shaded area is 1/4 of a circle, so, if we take 1/4 of the area of a circle, we can subtract its area from the area of the square:

A = πr²

A = 15²π

A = 225π

1/4 A = 225π / 4

New Area = 56.25π

Or... about 176.7

Since we have both of the areas, all we have to do is subtract:

225 - 176.7 =

48.3.

Your final answer is 48.3 cm²

How much of a circle does a 100-degree angle turn through?
A.1
B.100/180
C.50/360
D.100/360

Answers

Answer:

100/360

Step-by-step explanation:

A circle is 360 degrees

100/360

10/36

5/18

use the ratio of a 45-45-99 triangle to solve for the variables.​

Answers

hopefully this answer can help you to answer the next question.

help me, thank you!!!

Answers

Answer:

Step-by-step explanation:

i don't understand this language but i think you want to simplify  it.

[tex]\frac{3x-3\sqrt{x} -3}{x+\sqrt{x} -2} -\frac{\sqrt{x} +1}{\sqrt{x} +2} +\frac{\sqrt{x} -2}{1-\sqrt{x} } \\=\frac{3x-3\sqrt{x} -3}{x+2\sqrt{x} -\sqrt{x} -2} -\frac{\sqrt{x} +1}{\sqrt{x} +2} -\frac{\sqrt{x} -2}{\sqrt{x} -1} \\=\frac{3x-3\sqrt{x} -3}{\sqrt{x} (\sqrt{x} +2)-1(\sqrt{x} +2)} -\frac{(\sqrt{x} +1)(\sqrt{x} -1)+(\sqrt{x} +2)(\sqrt{x} -2)}{(\sqrt{x} +2)(\sqrt{x} -1)} \\=\frac{3x-3\sqrt{x} -3}{(\sqrt{x} +2)(\sqrt{x} -1)} -\frac{(x-1)+(x-2)}{(\sqrt{x} +2)(\sqrt{x} -1)} \\[/tex]

[tex]=\frac{3x-3\sqrt{x} -3-2x+3}{(\sqrt{x} +2)(\sqrt{x} -1)} \\=\frac{x-3\sqrt{x} }{(\sqrt{x} +2)(\sqrt{x} -1)}[/tex]

Help fast!
Describe at least two ways to find or
estimate the year the population of the town
will be 40 thousand. (You don't have to
actually find the value.)

Answers

Plug in 40,000 for p(n), then use algebra. First step divide by 18. Then you have 2222.222222=e^0.035n.
Take the natural logarithm (Ln) on your calculator of both sides:
Ln(2222.2222)=Ln(e) 0.035n
Ln2222.2222 just gives you a number and Ln(e) cancel each other so you have:
Ln(2222.222222)= 0.035n, divide both sides by 0.035 and you will find “n”(the number of years after 2000).

The second method is trial and error, keep plugging in numbers for n starting at “1” and see what number gets you closest to 40,000 when you calculate the equation

On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞

Answers

Answer:

F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Step-by-step explanation:

The minimum value of the curve = (1.9, -5.7),

The maximum value = (0, 2)

The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)

The point the function crosses the y-axis (the y-intercept) = (0, 2)

The given points can be plotted using MS Excel, from which we have;

F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5

The correct option is therefore, F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5)

Answer:

A. F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).

Step-by-step explanation:

what is 2/3 divide by 2/9

Answers

Answer:

3

Step-by-step explanation:

(2/3)/(2/9) = (2/3) * (9/2) = 3

HELP! A semi circle of radius 6 is centered at the origin as shown. A rectangle has two of its vertices at (5,0) and (-5,0) and the other two vertices on the semi-circle. What is the exact area of the rectangle? What is the equation of the semi circle?

Answers

The Area of rectangle is "[tex]30 \ unit^2[/tex]" and the equation of the semi circle is "[tex]y = \sqrt{36-x^2}[/tex]".

According to the question,

The vertices of rectangle,

(5, 0) and (-5, 0)

Length,

l = 10 unit

Breadth,

b = 3 unit

Radius of semi circle,

r = 6

Centre of origin,

(0, 0)

As we know,

→ The Area of rectangle is:

= [tex]Length\times Breadth[/tex]

= [tex]10\times 3[/tex]

= [tex]30 \ unit^2[/tex]

and,

→ The Equation of semi circle is,

[tex]y = \sqrt{r^2-x^2}[/tex]

by substituting the values, we get

  [tex]=\sqrt{(6)^2-x^2}[/tex]

  [tex]= \sqrt{36-x^2}[/tex]

Thus the above is the correct answers.

Learn more about Area of rectangle here:

https://brainly.com/question/14383947

PLEASE HELP ASAP Please?

Answers

Answer:

c

Step-by-step explanation:

First, from A to B, x=6, but y ranges from 8 to -8. From B to C, y=-8, but x ranges from 6 to -6. From C to D, x=-6, but y ranges from -8 to 8. From D to A, y=8, but x ranges from -6 to 6.

The ranges are as follows:

- x goes from -6 to 6

- y goes from -8 to 8

There are no x values less than -6, no x values greater than 6, no y values less than -8, and no y values greater than 8. x is always greater than or equal to -6 and less than or equal to 6. y is always greater than or equal to -8 and less than or equal to 8. We can write these as inequalities as follows:

x ≥ -6

x ≤ 6

y ≥ -8

y ≤ 8

The answer that is not in these 4 is c. y ≤ -8. y is never less than -8, so this is wrong

(6 1/4)^4

Answer fast or i will report you

Answers

Answer:6

Step-by-step explanation: The rules of exponential says (a^x)^y=a^xy.

Therefore you will multiply 1/4 with 4 to get an exponent of 1. So the answer is 6^1 which is also written as 6

What are the x- and y-intercepts of g(x) = 4 - X2?

Answers

Answer:

g(x) = 4 - x^2

at x-intercept, y=0

0=4-x^2

x^2=4

x = ± 2

=> two x- intercepts, (-2,0) and (2,0)

at y-intercept, x = 0

g(x) = y = 4 - 0 = 4

y-intercept = (0,4)

The x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).

What is an intercept?

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

g(x) = 4 - x²

At x-intercept, y = 0

0=4-x²

x² = 4

x = ± 2

Two x- intercepts, (-2,0) and (2,0)

at y-intercept, x = 0

g(x) = y = 4 - 0 = 4

y-intercept = (0,4)

Therefore, the x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).

To know more about an intercept follow

https://brainly.com/question/1884491

#SPJ2

Alec pulled a couch 3 meters, using a force of 400 N. The couch weighed 200 N. How do you calculate the work done by Alec?

A . Add 400 to 200

B . Divide 400 by 3

C . Multiply 200 by 3

D . Multiply 400 by 3

Answers

Answer:

D

Step-by-step explanation:

It is because work is done when a force cause an object to move in the direction of the applied force.

so work is equal to force × distance

In the figure below j ll h find the values of x and y

Answers

Answer:

26

Step-by-step explanation:

Given: Lines J and H are parallel lines. O intersects both lines equally.

Since two angles equal 180, that will be what  (4y + 12) and 64 will be equal to.

(4y + 12) + 64 = 180

76 + 4y = 180

-76          -76

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

    4y = 104

      y = 26

x and y is both 26 because they are vertical angles.

Hope this helped.

what must be added to a + b to get a​

Answers

Answer:

we have to add (-b) to get (a)

Step-by-step explanation:

a+b+(-b)=a

a+b-b=a

a=a

Hence verified.

Hope this helps you. Have a nice day^_^

solve for the measure of a

Answers

Answer:

Step-by-step explanation:

The supplement of the exterior angle is 180 - 75 = 105

In a cyclic quadrilateral (a four sides figure where all the vertices touch the circumference of a circle), the opposite angles are supplementary. Therefore <a = 180 - 105 = 75

But I think you already knew that.

which equations have a leading coefficient of 3 and a constant term of -2?

Answers

Answer: the answer to this is 3x-2

Step-by-step explanation:

How to find interquartilte range

Answers

Answer:  Choice C) 8.5

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

Explanation:

Each x represents a data point location.

So, for example, having an x over 60 means 60 is part of the set.

The set of values we're working with is

{59,60,61,63,63,64,66,68,70,71,71,73}

The repeated values are due to the fact we have a stack of two 'x' markers, and they occur at 63 and 71.

To find the IQR (interquartile range), we'll first need to find the median of this set. That's the middle most value.

Count out the number of values to find that there are n = 12 values.

The list splits into two halves that are n/2 = 12/2 = 6 items each

Between slots 6 and 7 is where the median is located.

The value in slot 6 is 64 and the value in slot 7 is 66. Average those two items to get (64+66)/2 = 65

The median is 65

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

Next, we'll form two groups L and U such that

L = set of items lower than the median

U = set of items larger than the median

Because n is even, we simply just break the original set into two equal groups (6 items each)

L = {59,60,61,63,63,64}

U = {66,68,70,71,71,73}

The values of Q1 and Q3 represent the medians of L and U in that order.

The median of set L is (61+63)/2 = 62, so Q1 = 62

The median of set U is (70+71)/2 = 70.5, which is Q3

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

To summarize everything so far, we have found

Q1 = 62Q3 = 70.5

Subtract those items to get the IQR

IQR = Q3 - Q1

IQR = 70.5 - 62

IQR = 8.5 which points us to choice C as the final answer.

Slope -1/4, passes through (12,-4)​

Answers

Answer:

y = - [tex]\frac{1}{4}[/tex] x - 1

Step-by-step explanation:

Assuming you require the equation of the line

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{4}[/tex] , then

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute (12, - 4) into the partial equation

- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1

y = - [tex]\frac{1}{4}[/tex] x - 1 ← equation of line

RS=7y+4, ST=3y+6, and RT=90

Answers

Answer:

If it is a straight line then ;

RT= RS+ST

90=(7y+4) + (3y+6)

90 = 10y + 10

10y= 90 – 10

10y = 80

y= 80 / 10

y =8

ST = 3y+6= 3(8)+6= 24 +6 = 30

RS = 7y +4 = 7(8) + 4 = 56 +4 = 60

I hope I helped you^_^

What is 8j - 3k + 6 - 7j + 3k - 4 simplified

Answers

Answer:

j+2

Step-by-step explanation:

combine like terms

3k - 3k = 0

8j - 7j = 1j or j

6 - 4 = 2

put it all together

j + 2

Answer:

j + 2

Step-by-step explanation:

= 8j - 3k + 6 - 7j + 3k - 4

= 8j - 7j - 3k + 3k + 6 - 4

=j + 2

Answer from Gauth math

Find the area of the shape:

Answers

Answer:

(8×6)+2×((14+6)×6)

=48+2×(20×6)

=48+240

=288

Step-by-step explanation:

please mark me as brainliest

In XYZ, what is the cosine ratio of X?

Answers

Answer:

c) 12/15 = 4/5

Step-by-step explanation:

imagine we mirror the triangle up, so that Z is on top.

then you can clearly see that 6 is cos(X) times r (and r is then 7.5).

XY is sin(X)×7.5

and again, 7.5 is r (the line making the X angle).

so, the cosine ratio of X is

6 = cos(X)×7.5

cos(X) = 6/7.5 or then 12/15. or simplified 4/5.

yea the person on top is right, bc I also got that correct on my test LMFOAOA
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