An airplane flies at 400 mph with a direction of 120° relative to the air. The plane experiences a wind that blows 40 mph with a direction of 50°.
Part A: Write each of the vectors in linear form. Show all necessary calculations. (6 points)
Part B: Find the sum of the vectors. Show all necessary calculations. (2 points)
Part C: Find the true speed and direction of the airplane. Round the speed to the thousandths place and the direction to the nearest degree. Show all necessary calculations.
Answers
Answer:
caveat: your grader may expect <E, N> coordinates, reversed from these
A. <N, E> = <-200, 346.410> (plane) and <25.712, 30.642> (wind)
B. resultant <N, E> = <-174.288, 377.052>
C. resultant = 415.385∠115°
Step-by-step explanation:
The necessary calculations for vector arithmetic are handily carried out by a suitable calculator. The attached shows a TI-84 work-alike, but there are many other possible choices.
The necessary calculations for doing this "by hand" (without a calculator that does vectors or complex numbers) are ...
a∠b = a·cis(b) = (a·cos(b) +i·a·sin(b))
a +i·b = √(a²+b²)∠arctan(b/a) . . . . . with attention to signs and quadrant
__
Ordinarily, bearings are measured clockwise from North, and angles in the x-y or complex plane are measured counterclockwise from +x (East). If you use bearing angles without any translation, the resulting (complex plane) coordinates from rectangular/polar conversion are ...
(North + i·East)
Coordinates in this system can be added and subtracted in the usual way. When the result is converted back to a distance and direction, that direction can be considered to be a bearing angle. In short, we can use bearing angles in our math with no special treatment, provided we are consistent in that usage.
__
A.The airplane speed vector in <north, east> coordinates is ...
400∠120° = 400cos(120°) +i·400·sin(120°) = <-200, 346.410>
Similarly, the wind speed vector is ...
40∠50° = 40cos(50°) +i·40sin(50°) = <25.712, 30.642>
__
B.The sum of the vectors is found from the sum of their components:
plane + wind = <-200 +25.712, 346.410 +30.642> = <-174.288, 377.052>
__
C.Converting this vector in linear form back to a magnitude and direction gives ...
magnitude = √((-174.288)² +377.052²) = √172544.644542
magnitude ≈ 415.385 . . . mph
direction = arctan(-377.052/174.288) . . . . . 90° < θ < 180°
direction ≈ 115°
_____
Additional comment
As we discussed above, the vector coordinates used here are <N, E> coordinates. If you translate the bearing angles to Cartesian plane angles (measured CCW from +x), the corresponding coordinates will be <E, N> coordinates. That is, rectangular coordinates will be reversed from those shown here. If you're filling in an answer box, you may want to be aware of that fact.
Related Questions
f(x)=3x^2+x f(x)=3x 2 +x \text{Find }f(-5) Find f(−5)
Answers
So the equation given is: [tex]3x^2+x[/tex]
What do we find: f(-5)
To find f(-5), we must plug '-5' into the equation in place of the 'x'
[tex]f(-5) = 3(-5)^2+(-5) = 3 * 25 -5=75-5=70[/tex]
Answer: f(-5) = 70
Hope that helps!
Yvette paid $921 for tires for her car. She got special financing with a 0% interest rate if she paid off the tires in 6 months. How much will she have to pay each month in order to pay off the tires before she will have to pay interest?
a
$183.50
b
$153.50
c
$76.75
d
$92.10
Answers
Answer: B
Step-by-step explanation:
In 6 months she will have to pay $921
In 1 month she has to pay [tex]\frac{921}{6}[/tex] = $153.50
Each month, Yvette has to pay $153.50 in order to pay off the tires before she will have to pay interest
Therefore, B is the correct answer
please help and tysm!! :)) <3
Answers
Answer:
39
Step-by-step explanation:
above 50 it's nearest 100.
Please mark me as a brainliest
Answer:
38.98
Step-by-step explanation:
Step 1: look at the number after the hundredths place, in this problem being 7
Step 2: Indecate wither thr number is larger than 5 or smaller than 5. If larger you would round up, if smaller you'd round down.
In this problem you would round up.
Step 3: When rounding up you go to the hundredths place and add one to that place. When rounding down, you delete all the values after the hundredths place.
which recurring decimal is equivalent to the Fraction shown ? 9/11
equals a) 0.8 b) 0.18 c) 0.18 d) 0.18'
Answers
Using a calculator would show that
[tex]9/11 = 0.818181\ldots = 0.\overline{81}[/tex]
The horizontal line over top means the "81" repeats forever.
You can use long division as an alternative method to getting the answer above.
Pls help I’ll give 30 points
Answers
Answer:
C
Step-by-step explanation:
30, 32, 33, 33, 34, 37, 39, 41, 43, 47, 49, 52, 53, 57
Middle numbers: 39 + 40 = 80/2 = 40
Highest number: 57
Lowest number: 30
I hope this helps!
Ted makes an hour delivering pizzas. if he gets a 5% raise, how much will he make delivering pizzas for 4 hours?
Answers
The amount Ted would make from delivering pizzas for 4 hours would be $42.
How much would Ted make?The first step is to determine the increase in Ted's income after the raise: (1.05) x $10 = $10.50
The second step is to determine the total income for 4 hours of work: 10.50 x 4 = $42
Here is the complete question:Ted makes n$10 hour delivering pizzas. if he gets a 5% raise, how much will he make delivering pizzas for 4 hours?
To learn more about multiplication, please check: https://brainly.com/question/3385014
(redo for the mistake) + 5 points (also how do I delete may last mistake)
The picture below shows rhombus ABCD with side length 3.16. EC=1 and ED=3.
Find the area of ABCD
Answers
Answer:
6
Step-by-step explanation:
The Rhombus is made up of 4 right triangles. To find the area of a right triangle, you have to multiply the length and width and divide it by 2.
1 triangle; 1.5
all triangles; 6
The Area of the Rhombus is 6!
Hope This Helps! :) Please give brainliest if you can!
Find the missing angle.
Answers
Answer:
32 degrees
Step-by-step explanation:
The angle supplementary with the 122 degree angle measures 180-122=58 degrees.
So, the triangle has interior angles of f, 90, and 58 degres.
Since the angles in a triangle add to 180 degrees, f+180-90-58=32 degrees
Draw an illustration using the given information below (you don't need to answer the question itself and assume that the buildings, ladders, etc. are all on the ground)
• A bird sits on top of a 5-meter lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35º.
Answers
Step-by-step explanation:
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Please help me with this thank you
Answers
Answer:
-11x² +14x -11
Step-by-step explanation:
When one polynomial is subtracted from another, each of the terms of the subtrahend is subtracted from the corresponding term of the minuend.
(-2x² +4x -10) -(9x² -10x +1)
= (-2 -9)x² +(4 -(-10))x +(-10 -1)
= -11x² +14x -11
Paul bought 4 DVDs for $9.95 each. What was his total cost?
$39.90
$40.80
$39.80
$38.80
Answers
Answer:
$39.80
Step-by-step explanation:
just 9.95 x 4
The answer would be $39.80
Which of the following are solutions to the equation below?
Check all that apply 25x(squared) - 16 = 0
Answers
[tex]~~25x^2-16=0\\\\\implies (5x)^2 -4^2 =0\\\\\implies (5x+4)(5x-4)=0\\\\\implies x = -\dfrac{4}5, ~~~x=\dfrac 45[/tex]
If the probability that the Islanders will beat the Rangers in a game is 85%, what is the probability that the Islanders will win exactly three out of five games in a series against the Rangers? Round your answer to the nearest thousandth.
.138
.037
.158
.232
Answers
The probability that the Islanders will win exactly three out of five games in a series against the Rangers is mathematically given as
P(x=3)=0.26367
What is the probability that the Islanders will win exactly three out of five games in a series against the Rangers?Generally, the equation for the probability is mathematically given as
P(x=3)=nC3 (P)^r (q)^{n-r}
Therefore
P(x=3)=5C3 (0.75)^3 (0.25)^{5-3}
P(x=3)=10 (0.75)^3 (0.25)^{5-3}
P(x=3)=0.26367
In conclusion, The probability of the islander
P(x=3)=0.26367
Read more about probability
https://brainly.com/question/795909
y= x^2-2x+2 complete the square to determine the vertex and maximum or minimum value. Determine the number of x-intercepts.
Answers
Answer:
Step-by-step explanation:
y = x^2 - 2x + 2
y = (x - 1)^2 - 1 + 2
y = (x - 1)^2 + 1
Vertex is at (1, 1) and minimum value is 1.
What is the product of -1−1 and-8−8?
Answers
Answer:
32
Step-by-step explanation:
I need an answer for all those please!
Answers
Kristine wants to do hardwood flooring for her room. A floor plan of the room (in feet) is shown. How much hardwood flooring does she need?
Answers
Kristine would require at least 116ft of hardwood flooring for her room.
The answer is arrived at by using simple calculations of the area of a square - a polygon.
How do we arrive at the answer above?Note that there are missing portions on the shape of the floor. (See a more elaborate version attached).
The side labeled F = 12ft
The side labeled CDE comprises three sides: 8, 2, and 2 respectively. This is also equal to 12.
With this information, we can calculate the area of the square assuming it was full.
The area of a square is given as:
Length x Breadth or L²;
that gives us: 12 x 12 or 12² = 144ft.
Now we get the total actual area by removing the areas of the missing segments.
Section Ax and Ay is also a square. because the length and the breadth are equal.
hence the area of AxAy = 16ft.
We also have the area of the section labeled D,Dx. This section is a rectangle. The formula for the area of a rectangle is:
Length x Breadth.
Hence, we have
6 x 2 = 12ft.
Total area of missing sections are:
12 + 16 = 28ft.
The total area of the square less the missing areas is:
144 - 28 = 116ft.
Hence the total amount of Hardwood that Kristine would require in square ft is 116ft.
See the attached images and learn more about areas of polygons at:
https://brainly.com/question/10567784
Alice has 2290 dollars, Cindy has 987 more than Alice
What is the amount of money combined with Alice and Cindy?
Answers
Answer: 3,277
Step-by-step explanation: all you have to do is add 2290 and 987 toghther
Answer:
5567 $.
Step-by-step explanation:
The amount of money Alice has = 2290 $.
Cindy = Amount of money Alice has + 987
= 2290 + 987
= 3,277.
Now,
The amount of money combined = 2290 + 3277
= 5567 $.
I need help with this question.
Answers
Step-by-step explanation:
the volume of a cylinder is as for any regular shaped object
ground area × height
here the ground area is a circle, so we get
pi×r²×h
with r being the radius (half the diameter), and h the height.
therefore,
pi×(2.7/2)²×10 = 3.14×1.8225×10 = 57.25552611... cm³
so, the first option is correct.
there are 56 customer in a shop 24 of them are men the rest of the customer are women find the ratio of the number of men to the number of women in the shop
Answers
There are 32 women in the shop.
A swimming pool measures 10 feet by 8 feet by 5 feet. What is the volume of the swimming pool
Answers
Answer:
400 ft^3
Step-by-step explanation:
To find volume you simply do length x width x height
So, 10 x 8 x 5 which equals 400 ft; We make it have a power of 3 (cubed) because it is 3 dimentional object.
Hope this helps!
Prove: An even times an even is
an even.
Answers
Answer: 4
Step-by-step explanation:
i just guessed and it was right, sorry i don't have a better explanation than that
How many whole groups of 63 go into 504?
I will mark brainliest answer!
Answers
Answer: 8
504÷63= 8
I hope this helps! :)
Mia opens a new savings account with $675 from her birthday last week.
* The bank pays 8% annual simple interest
* She makes no other deposits or withdrawals
What would be her total interest in her account, at the end of 4 years?
Answers
Answer:
$891
Step-by-step explanation:
This is Your Answer: $891, Steps below
In January, Mr. Cooper started a new exercise plan weighing 200 pounds. In March, he found his weight had increased by 5% because the exercise had increased his muscle mass. He added some work on the treadmill to his exercise routine found in May that he had dropped 6% from his March weight.
Answers
Step-by-step explanation:
100%+5%=105%
105/100*200=210
100%-6%=94%
94/100*210
A six-sided number cube has sides labeled 1, 1, 2, 2, 3, and 3. What is known about the probability model for this situation? Select all correct answers.
The probability model for this situation is uniform.
The probability model for this situation is non-uniform
. The probabilities of the individual outcomes are the same.
The probabilities of the individual outcomes are not the same.
Answers
Answer:
The probabilities of the individual outcomes are the same.
The probability model for this situation is uniform.
Step-by-step explanation:
There is 2 of each number so there is an equal chance. when there is an equal chance that is uniform.
Answer:
i hope this helped :)
Step-by-step explanation:
help me please quick!!!
Answers
Answer:
y is 12 degrees
x is 30 degrees
Step-by-step explanation:
If angle ABC is equal to angle MNC, that means 5y equals to 60 degrees. 60 divided by 5 equals 12. So, y equals 12 degrees
2x and 4x equals 180 degrees. So, 180 divided by 6 equals to 30. So x equals 30 degrees
Answer:
x = 30, y = 12
Step-by-step explanation:
2 similar equilateral triangles, each corner is 60 degrees.
2x = 60 degrees
divide by 2
x = 30 degrees
5y = 60 degrees
divide by 5
y = 12 degrees
This can be verified by checking 4x + 2x which gives you 180 degrees forming that straight line angle.
your answer should be a polynomial in standard form. -t(-4t^3+8t^2)=
Answers
is there any answer choices
giving brainiest and 85 points!
Answers
Answer:
12 560 cubic feet
Step-by-step explanation:
radius of circular cross section = 20ft/2 = 10ft
Area of circular cross section = πr²
= 3.14 x 10 x 10
= 314 square feet
Volume of cylindrical tank = 314 ft² x 40ft
= 12 560 ft³
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
Final answer -
[tex]Area \: of \: figure = 60 \: m {}^{2} [/tex]
hope helpful :D