An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location in the sea. It then flies 483 miles from the sea at a bearing of S 55° W to another location. Finally, the aircraft flies straight back from the second location to its base. What is the total distance it flies, rounded to the nearest mile?
A.
550 miles
B.
1,033 miles
C.
1,583 miles
D.
1,692 miles
E.
2,210 miles
Answers
============================================
Explanation:
A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram
Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.Plot the points E and F, which are north and south of point B.Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.The diagram below shows all of this visually summarized. We have the segments
AB = 550 milesBC = 483 milesAC = x milesAnd we have these angles
Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)Angle ABC = 79 degrees (red)Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.
------------------------------
Once the diagram is set up, we'll use the law of cosines to find x.
Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.
The interior angles of triangle ABC are
A = 46 degreesB = 79 degreesC = 55 degreesThe sides opposite the angles are
a = 483 (opposite angle A)b = x (opposite angle B)c = 550 (opposite angle C)Now we can apply the law of cosines
b^2 = a^2 + c^2 - 2*a*c*cos(B)
x^2 = 483^2 + 550^2 - 2*483*550*cos(79)
x^2 = 434412.180756441
x = sqrt(434412.180756441)
x = 659.099522649229
x = 659
Side AC, or CA, is roughly 659 miles long.
------------
To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)
Distance Traveled = AB + BC + CA
Distance Traveled = 550 + 483 + 659
Distance Traveled = 1692 miles
Related Questions
Which line is perpendicular
to the line passing through
the points (-4, 2) and (4,--4)
Answers
Answer:
The line is 4/3x
Step-by-step explanation:
I graphed it
13(9−6m)+14(12m−8) =
Answers
Answer:
90m + 5
Step-by-step explanation:
Distribute 13 to (9-6m) and distribute 14 to (12m -8)
13*9 - 13*6m + 14*12m - 14*8 =
117 - 78m + 168m - 112 =
put like terms together
117-112 -78m + 168m =
5 + 90m
please give thanks by clicking the heart button :)
Jaron walked 15 blocks north and then 3 blocks west to school. Marisol walked 3 blocks east and then 15 blocks south to school. Write an expression to show that each traveled the same distance.
Answers
Answer:
sqrt(15² + 3²) = sqrt(15² + 3²)
Step-by-step explanation:
Using Pythagoras:
15 blocks North = 15 blocks south (direction opposite to each other)
3 blocks west = 3 blocks east (directions opposite to each other)
Hence distance traveled (d) :
JARON
D = sqrt(15² + 3²)
MARISOL:
D = sqrt(15² + 3²)
Hence ;
sqrt(15² + 3²) = sqrt(15² + 3²)
A function is initially defined by the set of coordinate pairs ((-3,7), (1,5), (4,13)). Which coordinate pair below, if added to this set, prevents the set from representing a function?
1) (2,5) 2) (5,0) 3) (-1,8) 4) (1,4)
Answers
Answer:
(1,4)
Step-by-step explanation:
Given
[tex]\{(-3,7), (1,5), (4,13)\}[/tex]
Required
Which pair makes the relation not a function?
A function is defined as:
[tex]\{(x_1,y_1), (x_2,y_2), (x_3,y_3)..... (x_n,y_n)\}[/tex]
Where each x values (domain) are unique and different from one another.
In the given function, the x values (domain) are: -3, 1 and 4
To get a pair that makes the relation, not a function; we have to select from the given options, any option that has either of -3, 1 and 4 as its x values.
From the list of given options.
4) (1,4) has an x value of 1
Hence, the solution to this question is (1,4)
Solve the following systems of equations by graphing. Write your answer in the form of (x, y).
y = x + 8 and y = 5x + 4
Answers
Answer:
(x,y) = (1,9)
Step-by-step explanation:
y = x + 8 and y = 5x + 4
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
c
Step-by-step explanation:
Answer:
C) c = 5 ( 3.5b + 10 )
Step-by-step explanation:
This is because the shop will charge a flat rate of $10 per visit. Then it will charge $3.5 per bowl. Hence the equation; (3.5b + 10) is formed. Finally, if one goes there 5 times, they will have to multiply this equation by 5 to find the total cost. Henceforth, C) is the only correct answer.
Triangle ABC is formed by the vertices A(1,2,-1), B(-3,-6,2)and C(3,-2,0).
If D is the midpoint of BC, the the length (distance) of AD.
write the midpoint
write the distance
Answers
Answer:
Point D: [tex](0,-4, 1 )[/tex]
d = √41
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightPre-Calculus
Midpoint Formula [3D]: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}, \frac{z_1+z_2}{2} )[/tex]Distance Formula [3D]: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point A(1, 2, -1)
Point B(-3, -6, 2)
Point C(3, -2, 0)
Step 2: Find Point D
Simply plug in your coordinates B and C into the midpoint formula to find midpoint
Substitute [MF]: [tex](\frac{-3+3}{2},\frac{-6-2}{2}, \frac{2+0}{2} )[/tex]Add/Subtract: [tex](\frac{0}{2},\frac{-8}{2}, \frac{2}{2} )[/tex]Divide: [tex](0,-4, 1 )[/tex]Step 3: Find distance d
Simply plug in the 2 coordinates A and D into the distance formula to find distance d
Substitute [DF]: [tex]d = \sqrt{(0-1)^2+(-4-2)^2+(1+1)^2}[/tex]Subtract/Add: [tex]d = \sqrt{(-1)^2+(-6)^2+(2)^2}[/tex]Exponents: [tex]d = \sqrt{1+36+4}[/tex]Add: [tex]d = \sqrt{41}[/tex]please help ill give BRAINLIEST
Answers
Answer:
B and D
Step-by-step explanation:
A player chooses one of the numbers 1 through 4. After the choice has been made, two regular four-sided (tetrahedral) dice are rolled, with the sides of the dice numbered 1 through 4. If the number chosen appears on the bottom of exactly one die after it is rolled, then the player wins If the number chosen appears on the bottom of both of the dice, then the player wins If the number chosen does not appear on the bottom of either of the dice, the player loses What is the expected return to the player, in dollars, for one roll of the dice
Answers
Answer: [tex]=\frac{-1}{16}[/tex]
Step-by-step explanation:
given data:
number to be chosen from = 1,2,3,4.
Solution:
ways the number can show
[tex]2*3*1=6[/tex] ways for your number to appear once.
[tex]1*1=1[/tex] ways for your number to appear twice.
[tex]3*3=9[/tex] ways for your number not to appear at all
[tex]= \frac{6(1) + 1(2) - 9(1)}{16}[/tex]
[tex]= \frac{6+2-9}{16}[/tex]
[tex]=\frac{-1}{16}[/tex]
expected return of the player is [tex]=\frac{-1}{16}[/tex]
please help!! if ur not gonna then, dont answer pls
Answers
Martina used 3/4 of a bottle of conditioner in 7/12 of a year. How much conditioner would she use in a full year
Answers
Step-by-step explanation:
7 months = 3/4
1 month = 3/4 ÷ 7
= 3/28
12 months / 1 year = 3/28 x 12
= 9/7
not sure if its correct
Answer: 1 2/7
trust me it just worked for me on IXL
Determine whether the statement below is true or false. Justify the answer. An orthogonal matrix is invertible. Choose the correct answer below. A. The statement is false. Only nonzero orthogonal matrices are invertible. B. The statement is false. Only orthogonal matrices with orthonormal rows are invertible. C. The statement is true. An orthogonal matrix is a square invertible matrix U such that . D. The statement is true. An orthogonal matrix is a square invertible matrix U such that
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Answer:
not so sure about this one
What is the relationship between the ratios?
8/11 and 24/33
Drag and drop to correctly complete the statement.
The ratios are ________.
Enter your answer in the box.
Answers
Answer:The ratios are _Equivalent_______.
Step-by-step explanation:
Step 1
Equivalent ratios are ratios that have the same value even though they look different. When we divide or multiply a given ratio by the same number ( in the numerator and denominator )we get anther equivalent ratio.
Step 2
In the given ratios
8/11 and 24/ 33
8/ 11 x 3/ 3 = 24/ 33
also
24/33 ÷ 3/3 = 8/11
This shows that the relationship between the ratios are equivalent.
Which ordered pair is a solution of this equation? x - 7y = -3
Answers
Answer:
Step-by-step explanation:
(-3,0)
Question in picture below Will give brainly
Answers
Answer:
J 120
Step-by-step explanation:
6.
Triangles TUV and TWV are congruent triangles.
Angles U and W are corresponding angles, so they are congruent.
m<U = m<W
7x + 15 = 8x
Subtract 7x from both sides.
15 = x
m<U = 7x + 15 = 7(15) + 15 = 8(15) = 120
Answer: J 120
WILL GIVE BRAINLIEST IF CORRECT!!
Adam and Simon start on bicycle trips from the same point at the same time. Adam travels east at 8mph and Simon travels south at 6mph. After how many hours are they 60 miles apart?
Answers
Answer:
4 miles
Step-by-step explanation:
Answer:
6 hours
Step-by-step explanation:
pythagroeom therom
Kung and So Lee offered $87,000
on a home that had been priced
at $96,500. The seller agreed to the
offer. A 20 percent down payment
is required. What is the amount of
the down payment? What is the
amount of the mortgage loan
needed to financethe purchase the purchase
Answers
Answer:
Down payment = $17,400
Amount of mortgage loan = $69,600
Step-by-step explanation:
Given that :
Cost of home = $87,000
Down payment = 20%
Amount of down payment :
20% of the cost of home
(20/ 100) * $87,000
0.2 * 87000 = $17,400
The cost of mortgage loan required to finance the purchase :
Cost of home - downpayment
$87,000 - $17,400
= $69,600
Solve this 40 pointsssss
Answers
Answer:
2
Step-by-step explanation:
Answer:
6 because the pattern on the 3 rows is remove 1 on each of the starting and end point of the pattern, therefore, 6 for the 4th row, 4 for the 5th row 2 for the last row
Question 4 of 5
Find the length of side a
O A 1
O B. 25
O C. 5
O D. V313
Answers
Answer: 5
Step-by-step explanation:
It’s half
Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
-1, 2, 4
Answers
9514 1404 393
Answer:
f(x) = x³ -5x² +2x +8
Step-by-step explanation:
If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:
f(x) = (x -(-1))(x -2)(x -4)
= (x +1)(x -2)(x -4)
= (x² -x -2)(x -4)
f(x) = x³ -5x² +2x +8
sum of 23.5 , 2.1, 6.07 , and 0.893
Answers
Help me I’ll give you stars
Answers
Answer:answer choice 2
Step-by-step explanation:
Select all values that satisfies the inequality 2f >–8
options-
4
4
0
-6
3.5
-2.25
-100
Answers
Step-by-step explanation:
2f > -8
f > -4
The values greater than -4 here are 4, 0, 3.5 and -2.25.
The public debt of a fictional country is 8,127,650,198,774 units of its
currency, while its gross domestic product (GDP) is 23,476,117,934,187 units
of its currency. What is the country's debt-to-GDP ratio?
Answers
Step-by-step explanation:
just divide 8,127,650,198,774 by 23,476,117,934,187
by calculator
Mrs. Browning bought ice cream treats for 6 children. Each child picked either a sundae or a milkshake. The sundaes cost $2 each and the milkshakes cost $5 each. If Mrs. Browning spent a total of $21, how many of each type of treat did she buy?
Please help me please !!!
Answers
Answer:
3 milkshakes and 3 sundaes
Step-by-step explanation:
3 * 5 = $15 + 3 * 2 = $21
Any help please I appreciate it thank you on 1 and 2 plzzzz!!!
Answers
Answer:
1. angle Y, angle XYZ, and angle ZYX
2. angle PQR, angle SQR, and angle PQS
Step-by-step explanation:
1. The 3 ways to name the given angle are:
✔️The use of an alphabet of the vertex: angle Y
✔️The use of the three alphabets can be named in two ways with the middle alphabet representing the vertex:
angle XYZ
angle ZYX
2. The three different angle in the diagram consist of two adjacent angles that share the same side: angle PQR and angle SQR,
and the bigger angle that sums up the two internal angles, which is angle PQS
A map of two cities is plotted on a coordinate grid. One city is centered at (-60,40), while the other is at (40, 20). A rest station lies at the midpoint of a straight road joining the centers of each city. What is the location of the rest station? (1 point)
Answers
Answer:
( - 10, 30 )
Step-by-step explanation:
A( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) , B( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
Coordinates of midpoint are
( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
~~~~~~~~~~~~~~~~~~~
A( - 60, 40)
B(40, 20)
The location of the rest station is
( [tex]\frac{-60+40}{2}[/tex] , [tex]\frac{40+20}{2}[/tex] ) = ( - 10, 30 )
Answer:
(-10,30)
Step-by-step explanation:
i just took test
Please make me Brainliest
Pls hurry I need the answer
Answers
=============================================
Work Shown:
Apply the law of cosines
a^2 = b^2 + c^2 - 2*b*c*cos(A)
10^2 = 13^2 + 11^2 - 2*13*11*cos(A)
100 = 290 - 286*cos(A)
100-290 = -286*cos(A)
-190 = -286*cos(A)
190 = 286*cos(A)
286*cos(A) = 190
cos(A) = 190/286
A = arccos(190/286)
A = 48.368620460647
A = 48
Make sure your calculator is in degree mode.
two planes travel a constant speed. plane A travels 2.800 miles in 5 hours plane B travels 3.885 miles in 7 hours. which plane is faster?
Answers
Have a good day!!!
Which equations are equivalent to −4(3d−2)−7minus, 4, left parenthesis, 3, d, minus, 2, right parenthesis, minus, 7 ?
A) −12d−15
B)12d−15
C)None of the above
Please help me !!!
Answers
Answer:
She/He is right it's C. Tysm!
The correct answer is:
A) −12d−15 (None of the options provided are equivalent to the given expression.)
How to determine the equivalentTo simplify the expression −4(3d−2)−7, we can apply the distributive property by multiplying -4 to each term inside the parentheses:
−4(3d−2)−7 = -4 * 3d + (-4) * (-2) - 7
This gives us:
-12d + 8 - 7
Combining like terms:
-12d + 1
So the expression is equivalent to -12d + 1.
Therefore, the correct answer is:
A) −12d−15 (None of the options provided are equivalent to the given expression.)
Learn more about expression at https://brainly.com/question/1859113
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