Natasha is 50 m due east of Michelle. Natasha walks 20 m due north, and Michelle walks 10 m due
south. Find the distance and bearing of Michelle from Natasha now.
Please use diagrams to explain.
Answers
Answer:
Let's define East as the positive x-axis and North as the positive y-axis.
If Michelle's initial position is (0, 0)m
We know that Nathasha is 50m due East of Michelle.
Then the position of Natasha is (50, 0)m
Now we know that Natasha walks 20m due North, then the new position of her's is:
(50, 0 + 20)m = (50, 20)m
While Michelle walks 10m due South (South would be the negative y-axis, then we subtract 10 meters)
Michelle's new position will be:
(0, 0 - 10)m = (0, -10)m
Now we want to know the distance and bearing of Michelle from Natasha.
First, remember that the distance between two points (a, b) and (c, d) is given by:
Distance = √( (a - c)^2 + (b - d)^2)
Then the distance between Michelle and Natasha is:
Distance = √( (50m - 0m)^2 + (20m - (-10m))^2)
Distance = √( (50m)^2 + (30m)^2) = 58.31m
Now to find the bearing you can see the image below:
Point B is Michelle's position and point A is Natasha's position.
To find the bearing, we can make a triangle rectangle as the one shown in the image:
Also remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus).
Where the opposite cathetus is the difference between the x-values of each position, this is:
opposite cathetus = 50m - 0m = 50m
And the adjacent cathetus is the difference between the y-values, this is:
adjacent cathetus = 20m - (-10m) = 30m
Then:
Tan(a) = 50m/30m
Tan(a) = 5/3
Now if we apply the inverse Tan function to both sides, Atan(x) we get:
Atan(Tan(a)) = Atan(5/3)
a = Atan(5/3) = 59°
So the bearing is of 59°.
Related Questions
Which equation represents the parabola shown on the graph?
y2 = 1.5x
x2 = 1.5y
y2 = 6x
x2 = 6y
Answers
The equation represents the parabola is x² = 6y.
What is Equation of Parabola?Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.
The general equation of a parabola is given by y = a(x – h)² + k
We have equations.
The graph's parabola is a vertical parabola that is open vertically and has its vertex at the origin.
So, the equation of the parabola is equal to
x² = 4ay...............(1)
and, the equation of the directrix is y= -a.
her, the directrix is y= -1.5
Now, the equation for the parabola is
x² = 4(1.5)y
x² = 6y
Learn more about Equation of Parabola here:
https://brainly.com/question/9583416
#SPJ5
Surveys, observational studies, and experiments are examples of
Answers
Answer: B data gathering
Step-by-step explanation:
all of those examples are examples of gathering data
In the year 2006, a person bought a new car for $18000. For each consecutive year after that, the value of the car depreciated by 15%. How much would the car be worth in the year 2009, to the nearest hundred dollars?
Please i need answer now
Answers
Answer:
Step-by-step explanation:
Use the exponential function
[tex]v(t)=a(b)^t[/tex] where a is the initial value of the car, b is the rate of decay, and t is the time in years. For us, a = 18000, b = (1 - .15), so the model for this car is:
[tex]v(t)=18000(.85)^t[/tex] We can use this model now to find the value, v(t), of the car after 3 years has gone by (from 2006 to 2009 is 3 years):
[tex]v(t)=18000(.85)^3[/tex] and simplifying a bit:
v(t) = 18000(.614125) so
v(t) = 11054.25
Round however you need to.
Calculate the distance of line segment AB.
1 pm
B
A
24 cm
10 cm
с
14
O 25
O 28
0 26
O 31
Answers
Answer:
26 cm
Step-by-step explanation:
[tex]a^{2} +b^2=c^2[/tex]
[tex]24^2+10^2=c^2[/tex]
576 + 100 = 676
[tex]\sqrt{676}[/tex] = 26 cm
Suppose the 100 people in society X all know the same 10 facts, while the 10 people in society Z specialize, with each person knowing 5 unique facts as well as 5 facts also known by the other 9 members of the society. If the standard of living is roughly equivalent to the average number of social facts known per person, which society has a higher standard of living
Answers
Answer:
29 times
Step-by-step explanation:
Given :
Society X ;
Population = 100
Number of facts known = 10
Average fact known per person = known fact / population = 10 / 100 = 0.1
Society X:
Population = 19
Common fact known by 9 = 5
Specialized fact, known by 10 = 5 * 10 = 50
Total facts = common + specialized = 55
Average fact known per person = 55 / 19 = 2.8947368 fact per person
Number of times society Z is better :
2.8947368 / 0.1 = 28.947 times
Approximately 29 times
In triangle ABC, A = 38° and B = C. Find B.
A)71
B)26
C)142
Answers
Answer:
A) because b=c it is an equlateral triangle.
The interior Angles of a triangle is always equal to 180 .
Therefore 180-38 =142
because B=C
142÷2 =71
Anyone know how to do this
Answers
Answer:
77
Step-by-step explanation:
3+2*49-24
3+98-24
101-24
77
Good luck
Answer:
77
Step-by-step explanation
3+2X7^2-4X6
First complete the exponent
3+2X49-4X6
Then multiply
3+2X49-24
Multiply
3+98-24
Calculate the rest of the equation
101-24=77
Therefore the answer is 77.
Please don't be mad if this is incorrect
Also the x's are multiplication symbols and NOT variables
help please and thank you
Answers
Answer:
40° D. is your answer to this question
if GJ = 11a and IJ = a + 10, find the value of a that makes quadrilateral FGHI a parallelogram
Answers
Note: Consider J is the intersection point of diagonals of quadrilateral FGHI.
Given:
[tex]GJ=11a[/tex]
[tex]IJ=a+10[/tex]
To find:
The value of a that makes quadrilateral FGHI a parallelogram.
Solution:
We know that the diagonals of a parallelogram bisect each other.
If FGHI is a parallelogram and J is the intersection point of diagonals, then
[tex]GJ=IJ[/tex]
[tex]11a=a+10[/tex]
[tex]11a-a=10[/tex]
[tex]10a=10[/tex]
Divide both sides by 10.
[tex]a=\dfrac{10}{10}[/tex]
[tex]a=1[/tex]
Therefore, the required value of a is 1 units.
The points (6, 9) and (0, 6) fall on a particular line. What is its equation in slope-intercept form?
Answers
Answer:
[tex]y = \frac{1}{2}x + 6[/tex]
Step-by-step explanation:
[tex]Let \ (x _1 y _ 1 ) = ( 6 , 9 ) \ and \ (x _ 2 , y _ 2 ) \ = ( 0 , 6 )\\\\[/tex]
Step 1 : Find slope, m
[tex]slope, m = \frac{y _ 2 - y _ 1}{x_ 2 - x_ 1 } = \frac{6 - 9}{0 - 6 } = \frac{-3}{-6} = \frac{1}{2}[/tex]
Step 2 : Find the equation
[tex](y - y _ 1 ) = m ( x - x_ 1) \\\\( y - 9 ) = \frac{1}{2} (x - 6 ) \\\\y = \frac{1}{2}x - 3 + 9 \\\\y = \frac{1}{2}x + 6[/tex]
Answer:
y = 1/2x + 6
Step-by-step explanation:
y = mx + b is the formula. m is the slope and to calculate that you use the slope formula y2 - y1/ x2 - x1.
(6, 9) is the first coordinate so 6 is x1 and 9 is y1. Similarly in (0, 6), x2 is 0 and y2 is 6. Now if we put that into the slope formula it would look something like this: 6-9/0-6. that comes to -3/-6. simplify and cancel out the negatives and you get 1/2 which is the m ( slope).
The b is the y-intercept, which is the y value for where the x is 0. In this question, they already give you the coordinate where x is 0. (0, 6). x is 0 and y is 6. therefore the b (y-intercept) is 6.
Put all of this into y =mx +b, and you get y= 1/2x + 6.
If you want to make sure you did it right, just plug in one of the coordinates into this equation. Let's use (6, 9).
9 = 1/2 (6) + 6
9 = 3 + 6
9 = 9. It works out, therefore the equation right.
Hope this helps
What is parallel to y=-5+4.2x
Answers
You walk 1/4 miles to a grocery store. Then you walk another 1/5 miles to a clothing store. How many miles have you walked in all?
Answers
Answer:
3/4 of a mile
Step-by-step explanation:
.5+.25=.75
14cm and 31cm and 34cm equal
Answers
Answer:
if its addition then it will be 79cm
Michals basketball team practiced for 2hours 40 minutes yesterday and 3 hours 15 minutes today how much longer did the team practice today than yesterday
Answers
Answer:
35 minutes
Step-by-step explanation:
The is calculated using the Subtraction operation
The number of minutes longer the team practiced today than yesterday =
Number of minutes they practiced today - Number of minutes they practiced yesterday
Number of minutes they practiced today = 3 hours 15 minutes
Number of minutes they practiced yesterday = 2hours 40 minutes
The number of minutes longer the team practiced today than yesterday =
3 hours 15 minutes - 2hours 40 minutes
= 35 minutes
Therefore, the team practiced 35 minutes longer today than yesterday
PLEASE ANSWER DUE IN 30 MINUTES IM GONNA FAIL ITS GRADE 7 WORK EZ HAP
1.Why were rivers very important to Canada’s
development and history?
2. What rivers run near to where you live? How are they
important to you?
Answers
Answer:
Rivers helped Canada in so many ways! One of the ways was it helped Canada travel trading goods with the waterways. Also 7% of the worlds fresh water come from Canada Rivers. Im from Toronto and the rivers here are super important. They provide me, my friends and family and everyone around me fresh water. and there are some beautiful sceneries from them to!
Step-by-step explanation:
Hope this gave you some ideas and helped please mark brainliest :)
Answer:
Certain heritage rivers, such as the Kazan River in Nunavut, are designated for their natural heritage. These pristine waterways are valued for their undisturbed Fall Caribou Crossing, Parks Canada / Passage-de-Caribous-en-Automne, Parcs Canadabeauty and have been designated to ensure that their natural integrity is protected... https://www.historicplaces.ca/en/pages/17_heritage_rivers-rivieres_patrimoniales.aspx I got you!
Step-by-step explanation:
please help confused tyy
Answers
You want to set the angles equal to 90°
So it would look like this
(6d+8)+(3x+1)=90
then you would solve
Hope this helps ;)
(3d+1)+(6d+8)=90
3d+1+6d+8=90
9d+9=90
-9 -9
9d=81
divide by 9 on both sides
d=9
Explanation: In order to solve for d, you will need to remove the parentheses, then combine like variables. Then, subtract 9 from both sides. Finally, divide by 9 on both sides. You should get d=9.
find the measure of the exter angle.
Answers
I think this should be the answer but I’m not so sure so good luck!!
Divide *° -3x– 10x+ 24 by X-2
Answers
Answer:
[tex] - 13 - \frac{2}{x - 2} [/tex]
Step-by-step explanation:
[tex] \frac{ - 3x - 10x + 24}{x - 2} [/tex][tex] \frac{ - 13x + 24}{x - 2} [/tex][tex] - 13 - \frac{2}{x - 2} [/tex]
Hope it is helpful...help me pls pls pls pls pls pls
Answers
11 is -30
12 is 1
And I don’t know 9 sorry
the angle of elevation of the top of an elevator pole to a man standing 10m from it is 60°. find the height of the pole
Answers
Answer:
10√3m
Step-by-step explanation:
Given :-
Angle of elevation = 60° Distance between man and pole = 60°We need to find the height of the pole . We are given here base. Therefore using ratio of tan ,
=> tan 60° = p/b
=> √3 = h / 10 m
=> h = 10 m× √3
=> h = 10√3 m
Name the kind or kinds of symmetry the following figure has: point, line, plane, or none. (o)
Answers
Answer is Line
which choices are equivalent to the expression below? check all that apply. rad -9 A.3i B.-3 C.irad-9 D.-rad9
Answers
Given:
Consider the expression is:
[tex]\sqrt{-9}[/tex]
To find:
The equivalent expression.
Solution:
We have,
[tex]\sqrt{-9}[/tex]
It can be written as:
[tex]\sqrt{-9}=\sqrt{-1\times 9}[/tex]
[tex]\sqrt{-9}=\sqrt{-1}\times \sqrt{9}[/tex]
[tex]\sqrt{-9}=i\times 3[/tex] [tex][\because \sqrt{-1}=i][/tex]
[tex]\sqrt{-9}=3i[/tex]
The expression [tex]3i[/tex] is equivalent to the given expression.
Therefore, the correct option is A.
PLS HELP THIS IS DUE TODAY
Answers
Answer:
Draw a C plane and plot the dots if the coordinates
Answer:
it's a triangle draw the chart
Nick has an album that holds 800 coins each page of the album holds eight coins is 82% of the album is empty how many pages are filled with coins
Answers
Answer:
18 Pages are filled with photos because you do 800÷8 and you get 100 coins then since it says 82% of the album is empty since the album has 100 coins it makes it easy and you subtract 82 from 100 therefore you get 18 coins that are filled
Step-by-step explanation:
Because you do 800÷8 and you get 100 coins then since it says 82% of the album is empty since the album has 100 coins it makes it easy and you subtract 82 from 100 therefore you get 18 coins that are filled
Help on this too Guys
Answers
Answer:
radius is 6 diameter is 2 don't know the other one tho
Find the value of x.
Answers
Answer:
8
Step-by-step explanation:
6x+1 = 9x-23
add 23 to both sides
subtract 6x from both sides
3x=24
x=8
Answer:
8 =x
Step-by-step explanation:
The angles are the same so
6x+1 = 9x-23
Subtract 6x from each side
6x+1-6x = 9x-6x-23
1 = 3x-23
Add 23 to each side
1 +23 = 3x-23+23
24 = 3x
Divide by 3
24/3 = 3x/3
8 =x
The answers are
A.9
B.25
C.18
D.15
PLEASE HELPPPP
Answers
Answer:
9
Step-by-step explanation:
Because I don't know but I think I'm correct.
PLEASE HELP PLEASE IT EASY PLEASE HELP
Answers
Answer:
$3x
Step-by-step explanation:
Trust me.
Write an equation that represents the line
Answers
(0,2) and (4,3)
can someone help me match these too?
Answers
ANSWER:
A is number 3
B is number 2
Step-by-step explanation:
The left side is A and B (order)
the right side is 1,2,3,4 (order)
explanation: A is number 3 because as said in A the tram already has 5 people which is what we start with a1 = 5 and we add 11 at each stop as shown in the equation.
B is number 2 for the same reason as it started with 2 but added 4 inches of rain each time.
