7. An aircraft flies 400 km from a point O on a bearing of 025°
and then 700 km on a bearing of 080° to arrive at B.
a) How far north of O is B?
b) How far east of O is B?
Answers
Answer:
484 km north858 km eastStep-by-step explanation:
You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.
Coordinate transformationFor some distance r and bearing angle θ, the (north, east) coordinates will be ...
(north, east) = (r·cos(θ), r·sin(θ))
ApplicationFor the trip at hand, the final coordinates of the plane are ...
a)Distance north = (400 km)cos(25°) +(700 km)cos(80°)
= 362.52 km +121.55 km = 484.07 km
B is about 484 km north of O.
b)Distance east = (400 km)sin(25°) +(700 km)sin(80°)
= 169.05 km +689.37 km = 858.41 km
B is about 858 km east of O.
__
Additional comment
Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...
(x, y) = (r·cos(θ), r·sin(θ))
You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.
Related Questions
38 Points pls help Evaluate the expression (2 + 2) (3) × 5 - 3.
Answers
Answer:
4/9
Step-by-step explanation:
solving systems by substitution (algebra 2)
7x + y = 12
y = 4x - 21
Answers
Answer:
x = 3, y = -9
Step-by-step explanation:
plug y=4x-21 into 7x+y=12 to get
7x + (4x-21) = 12 -> 11x -21 = 12 -> 11x = 33 -> x = 3
plug x=3 into y=4x-21 to get
y = 4(3) - 21 = 12 - 21 = -9
7x+4x-21=12
add the common variables
11x-21=12
add 21 to 12 and -21
11x=33
divide 11 to 33 and itself
x=3
Which shows (3^2)^-2 in standard form
Answers
Answer:
1/81
Step-by-step explanation:
[tex](3^2)^{-2}=3^{-4}=\frac{1}{3^4}=\frac{1}{81}[/tex]
Jane is 3 years older than Mary. Mary is twice as old as Kay. If Kay is x years how old is jane
Answers
Mary = 2x
Jane = 2x+3
Jane is 2x+3 years old. (answer)
In this case, we can use Kay as the base/foundation in this problem. Kay is x years old. Mary is twice as old as Kay, making Mary 2 times x or 2x. We are solving for Jane. Jane is 3 years older than Mary, who we know is 2x. We can add on 3 years making the final expression for Jane's age: 2x+3. Since we do not know Kay's age, or x, we cannot solve this problem any further.
3 meters of cloth is the ratio of 3:7
Answers
When given 3 meters of cloth and it is to be divided in a ratio of 3:7 then one part will have 0.9 meters and the other will have 2.1 meters.
How to divide cloth by ratio?The first thing to do is to find the denominator of the ratio by summing the two numbers in the ratio:
= 3 + 7
= 10
The first part of the cloth would be:
= 3 / 10 x 3 meters
= 0.3 x 3 meters
= 0.9 meters
The second part of the cloth would be:
= 7 / 10 x 3 meters
= 0.7 x 3
= 2.1 meters
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6x + 4y = 36 when x
= 3 and y = 4 explain the solution satisfies the open sentence
Answers
Answer:
Undefined
Step-by-step explanation:
Plugging in 3 for x and 4 for y we get:
6(3) + 4(4) = 36
multiplying we get
18 + 16 = 36
34 = 36
which is not true.
if this was helpful pls give me brainliest <3
An online poll of 6,000 residents of Washington, DC showed that 79% agreed with the statement "Employers should be required to pay men and women the same salary for the same job." An online poll of 4,800 residents of Atlanta revealed that 74% agreed with the same statement.
A button hyperlink to the SALT program that reads: Use SALT
(b)
How many successes were there in the Washington sample?
How many failures were there in the Washington sample?
(c)
Calculate a 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement (DC − Atlanta). (Use a table or technology. Round your answers to three decimal places.)
Answers
Step-by-step explanation:
Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.
b. The number of successes in the Washington sample were 4740 .
The number of failures in the Washington sample is 1,260
c. the 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement "Employers should be required to pay men and women the same salary for the same job" is 0.018 to 0.068.
How do we calculate?(b) Number of successes and failures in the Washington sample:
Total number of respondents in the Washington sample: 6,000
Percentage who agreed with the statement: 79%
Number of successes = 79% of 6,000
= 0.79 * 6,000
= 4,740
Number of failures = Total - Number of successes
= 6,000 - 4,740
= 1,260
(c)
confidence interval = (p1 - p2) ± Z * √((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
p1 = Proportion of successes in the Washington sample
p2 = Proportion of successes in the Atlanta sample
n1 = Size of the Washington sample
n2 = Size of the Atlanta sample
Z = Z-score for the desired confidence level = 1.96
confidence interval = (0.79 - 0.74) ± 1.96 * √((0.79 * (1 - 0.79) / 6000) + (0.74 * (1 - 0.74) / 4800))
confidence interval = 0.05 ± 1.96 * √((0.79 * 0.21 / 6000) + (0.74 * 0.26 / 4800))
confidence interval = 0.05 ± 1.96 * √(0.00013815 + 0.0001244583)
confidence interval = 0.05 ± 1.96 * √(0.0002626083)
Lower bound of the confidence interval (DC - Atlanta)
= 0.05 - 0.0317226549
= 0.018
Upper bound of the confidence interval (DC - Atlanta)
= 0.05 + 0.0317226549
= 0.068
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Find the area of the triangle
3 m
8 m
Answers
area - 1/2 x 3 x 8
Answer:
3×8 =24
24÷2=12
Area of triangle=12m²
Step-by-step explanation:
3×8 =24
24÷2=12
PLEASE HELP I WILL GIVE BRAINLIST Graph the line with slope 1/3 passing through the point (2, -3)
Answers
Answer:
steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts
You measure a foam roller in the shape of a cylinder. The foam roller has a diameter of 5.9375 inches and a height of 53.5 inches. About how many cubic inches of foam were used to make the roller?
Answers
Answer:
Volume V ≈ 1481.3269 cubic inches
Step-by-step explanation:
Volume V of a cylinder is given by the formula
V = πr²h where r = radius of the base of the cylinder and h the height
Here we are given the diameter, d = 5.9375 inches
Radius r = d/2 = 5.9375/2 = 2.96875 in
Height h = 53.5 in
V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches
Answer V ≈ 1481.3269 cubic inches
An architectural company is trying to test the effectiveness of its promotional activity by looking at how many designs for
new buildings it sells each year.
Year Sales
2012 23
2013 18
The company assumes its promotional activity is less effective, which is why sales decreased. However, there could be many
confounding factors. Which of the following is not a possible confounding factor?
Answers
The factor that is not a possible confounding factor is B. the expected sales for the year 2014.
What is a confounding factor?A confounding factor is a third variable that influences or explains both the independent and dependent variables.
The independent variable here is the year while sales are the dependent variable.
However, confounding factors could include the number of new buildings constructed in 2013, which was not factored in by the architectural company and the state of the economy in 2013.
Thus, the expected sales for the year 2014 cannot be a confounding variable for the decreased sales in 2013 because it cannot explain the 2013 performance.
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Question Completion:A. the number of new buildings constructed
B. the expected sales for the year 2014
C the state of the economy
Please help I will give you brainliest
Answers
Answer:
$7.4
each bag of milk cost $7.4
Answer: $7.4
Step-by-step explanation: i did this and i remember it!
China generated 237.188 billion kilowatt-hours (kWh) of wind energy in 2018. The population in China in 2018 was 1.379 billion. What was the wind energy generated per capita? Give your answer to the nearest hundredth.
Answers
Answer:
172 kilowatts.
Step-by-step explanation:
Energy : 237.188 billion = 237,188,000,000 = 2.37188 × 10¹¹
People : 1.379 billion = 1,379,000,000 = 1.379 × 10⁹
Divide both values : 2.37188 ÷ 1.379 = 1.72; 10¹¹ ÷ 10⁹ = 10² ⇒ 1.72 × 10² or 172 kilowatts.
I just need the answer for C. Please answer quick this is due tmr morning!! worth 20 points and brainliest
Answers
Answer:
The answer is 7 for C.
Step-by-step explanation:
7+7=14 and 7x7=49
The diamond just asks for numbers that make up a pattern for the two given numbers.
Which fraction is greater, 35/109 or 36/104?? To explain your answer, use our definition of fraction along with reasoning other than finding common denominators, common numerators, cross-multiplying, or converting to decimals.
Answers
The fraction that is greater is 36/104 since 34.62% is greater than 32.11%
Percentages and ratioFractions are written as the ratio of two integers. For instance a/b is a fraction.
In order to determine which of the fractions is greater, we will express them as percentage as shown:
35/109 * 100
3500/109
32.11%
Similarly;
36/104 * 100
3600/104
34.62%
Hence the fraction that is greater is 36/104 since 34.62% is greater than 32.11%
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Hall dimensions 200m by 85m. Diagram office wall scale 1:40. What are the dimensions of floor space in cm
Answers
The dimensions of floor is 500 cm by 212.5 cm
HOW TO FIND DIMENSION OF HALL ?Multiply the width and length of each rectangle to find its area. The areas of each rectangle are then added up to determine the total area. In the event that your room is L-shaped, for instance, this can be split into two rectangles. Additionally, this method still works in a complicated room.
CALCULATION500 cm by 212.5 cm
Given :
The main arena hall has dimensions 200 m by 85 m.
On a large diagram on the office wall the scale is 1:40.
Length of arena hall = 200 m
Scale is 1:40
So, the length of the floor =
Since 1 m = 100 cm
So, 5 m = 100*5 = 500 cm
Width of arena hall = 85 m
So, width of floor =[tex]\frac{85 * 1}{40}[/tex] = 2.125m
Now 1 m = 100 cm
So, 2.125 m = 212.5 cm
Thus the dimensions of floor is 500 cm by 212.5 cm
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What are all the solutions to the equation 10x4 + 30x3 + 35x2 = 0? 0, StartFraction 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, StartFraction negative 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction negative 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, 6 + 2 i StartRoot 5 EndRoot, 6 minus 2 i StartRoot 5 EndRoot. 0, negative 6 + 2 i StartRoot 5 EndRoot, negative 6 minus 2 i StartRoot 5 EndRoot.
Answers
The solutions to the equation 10x⁴ + 30x³ + 35x² as required in the task content are; 0, (-3 + i√5)/2, and (-3 - i√5)/2.
What are all the solutions to the equation 10x⁴ + 30x³ + 35x² = 0 as given in the task content?It follows from the task content that the given equation is; 10x⁴ + 30x³ + 35x² = 0.
Hence, to find all the solutions of the equation, one must factorise the expression on the left hand side so as to obtain the factors as follows;
10x² (x² + 3x +3.5) = 0
Hence, we have;
10x² = 0; x = 0 OR
x² + 3x +3.5 = 0.
Hence, it follows from the quadratic formula that the roots/zeroes of x in the equation above can be evaluated as follows;
x = {-b±√(b²-4ac)}/2a
hence, by comparison, we have;
x = {-3±√(9-14)}/2
x = (-3 ± √-5)/2
x = (-3 ± i√5)/2
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can someone please explain this
Answers
Answer: x=-3-[tex]\sqrt{7}[/tex] or x=-3+[tex]\sqrt{7}[/tex]
Step-by-step explanation:
f(x)=x+1. g(x)=x+5
(f * g)(x)=
f(x)*g(x)=
(x+1)(x+5)=
x^2+5x+x+5=x^2+6x+5
x^2+6x+5=3
x^2+6x+9=7 ==> Add 4 on both sides of the equation
(x+3)^2=7
x+3=[tex]\sqrt{7}[/tex]
x=-3+[tex]\sqrt{7}[/tex]
x+3=-[tex]\sqrt{7}[/tex]
x=-3-[tex]\sqrt{7}[/tex]
One-stray Problem Solving
POSSIBLE POINTS: 5.88
A rectangular playground is to be fenced in using a wall on one side and 210 meters of fencing for the other three sides. The area A(z) in square meters
of the playground is a function of the length z in meters of the side parallel to the wall.
What is the area of the playground when z = 50?
square meters
Answers
b) A(x) = x(200 -2x)
c) 0 < x < 100
Step-by-step explanation:
b) The remaining fence, after the two sides of length x are fenced, is 200-2x. That is the length of the side parallel to the building. The product of the lengths parallel and perpendicular to the building is the area of the playground:
A(x) = x(200 -2x)
__
a) A(50) = 50(200 -2·50) = 50·100 = 5000 . . . . m²
__
c) The equation makes no sense if either length (x or 200-2x) is negative, so a reasonable domain is (0, 100). For x=0 or x=100, the playground area is zero, so we're not concerned with those cases, either. Those endpoints could be included in the domain if you like.
Factor as the product of two binomials. x 2 + 3 x − 4
Answers
Answer:
[tex](x-1)(x+4)[/tex]
Step-by-step explanation:
Given:
[tex]x^2+3x-4[/tex]
The best way to write a polynomial with three terms as a product of binomials is to FACTOR!
The middle number is 3 and the last number is -4.
Factoring means we want something like
[tex](x+?)(x+?)[/tex]
We need two numbers that...
ADD together to get 3 and
MULTIPLY together to get -4
Test the numbers -1 and 4:
[tex]-1+4=3\\(-1)4=-4[/tex]
These are the right numbers! Now, I can write them as factored binomials!
[tex](x-1)(x+4)[/tex]
Carlos is paid $17.90 per hour regularly. If he worked 45 hours last week, what was his gross pay? Carlos is paid at time-and-a-half for overtime.
Answers
Answer:
$ 850.25
Step-by-step explanation:
I will assume anything over 40 hours is 'overtime'
total pay will be
regular pay + overtime pay
17.90 * 40 hr + (17.90 * 1.5)(5hr) = $ 850.25
Find the quotient.
h6 ÷ h
Answers
Answer:
6
Step-by-step explanation:
Possibly 6 but if not let me know
Answer:
6
Step-by-step explanation:
the h's cancel out
Gabriel is deciding between 2 different movie streaming sites to subscribe to. Plan 1 costs $22 per month plus $1 per movie watched. Plan 2 cost $14 per month plus $3 per movie watched. Create a system of equations to represent this situation. Use the graph below and explain how many movies x would cause the 2 plans would have an equal monthly cost
Answers
Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The fixed cost is the intercept.The cost per movie is the slope.Hence the cost functions are given as follows:
C1(x) = 22 + x.C2(x) = 14 + 3x.The costs will be the same when:
C1(x) = C2(x).
Hence:
22 + x = 14 + 3x
2x = 8
x = 4.
4 movies would cause the two plans to have an equal monthly cost.
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6) Convert the following equivalent scales to ratios.
(i) 1cm=20m
Answers
Answer:
[tex]1cm = 20 \times 100 \\ = 2000cm \\ 1cm = 2000cm[/tex]
Need help with this problem
Answers
Answer:
I could be wrong, but I think you got right in the beginning 107°, but go with your gut feeling. Wish you the very best <3
Answer: x=73 degrees, z=73 degrees, y=107 degrees
Step-by-step explanation:
y=107 degrees because y and 107 degrees are congruent angles
z=x because z and x are congruent angles
x+y=180 ==> x and y are supplementary angles that are placed on a straight line(the straight line is 180 degrees and is called a straight angle.)
x+107=180
x=73 degrees
z=x
z=73 degrees
3x + 1 > 2x - 3 > x - 13
Answers
Answer:
x> - 4
Step-by-step explanation:
In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them.
18x - 3
6 + 25x
does anyone know?
Answers
2. 6+25x=31
Need help asap math !
Answers
Answer:
7/10 = 0.7 = 70%
25/100 = 0.25 = 25%
56/100 = 0.56 = 56%
Step-by-step explanation:
based on the equation 5×x+860=2×x+380, you can say
Answers
The value of x is -160.
An equation in which the power of any variable is not more than one is called a linear equation.
Here, we are given a linear equation as follows-
5 × x + 860 = 2 × x + 380
⇒ 5x + 860 = 2x + 380
Let us solve the given equation-
Subtracting 2x from both sides, we get
5x - 2x + 860 = 2x - 2x + 380
3x + 860 = 380
Subtracting 860 from both sides-
3x + 860 - 860 = 380 - 860
3x = -480
dividing both sides by 3,
3x/3 = -480/3
x = -160
Thus, the value of x comes out to be -160.
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what is the value of x?
help would be so appreciated
Answers
Answer:
x = 23
Step-by-step explanation:
The two angles are supplementary angles.
Supplementary angles sum 180°
(6x+4) + 38 = 180
6x + 42 = 180
6x = 180 - 42
6x = 138
x = 138/6
x = 23
Check:
6*23 + 4 + 38 = 180
138 + 42 = 180
Answer:
x = 23Step-by-step explanation:
We know that the sum of angles of a linear pair is always equal to 180°. These angles are also known as supplementary angles.
[tex]\bf 6x+4+38^o=180^o[/tex] (Add numbers)
[tex]\bf 6x+42=180[/tex] (Simplify)
[tex]\bf 6x+42-42=180-42[/tex](Subtract both sides by 42)
[tex]\bf 6x=138[/tex] (Simplify)
[tex]\bf \cfrac{6x}{6}=\cfrac{138}{6}[/tex] (Divide both sides by 6)
[tex]\bf x=23[/tex]
Therefore, x = 23.
_____________________
Hope this helps!
Have a great day!