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
============================================
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
Select the correct answer.
What is the slope of the linear relationship shown in this table of values?
a.-3
b.-2
c.2
d.3
Answer:
c
Step-by-step explanation:
A store sells candles. Each candle costs the same amount. During a sale, the store reduces the price of each candle by $1.70. Owen spends $11.96 on 4 candles at the sale price. what was the price of 1 candle before the sale?
Answer:
The regular sales price was $4.69
Answer:
4.69
Step-by-step explanation:
I had the maps test
Two parallel lines are cut by transversal x and a transversal Y so that x and y intersect at point Q as shown. Wong constructs the following argument : A) Reason 1: an alternating exterior angel with one angle in the triangle ...etc
Answer:
A
Step-by-step explanation:
Help ASAP Please. Working on this now. Look at picture for question and answer A, B, C. No Plagiarism Please. Will Mark Brainliest.
Answer:
Please check explanations for answer to the question
Step-by-step explanation:
The exponential relation can generally be represented as ;
y = I (1 + x)^n
where I is the initial value
1 + x represents the growth rate
n represents the time such as number of years
y represents the value after n count
a) The value 1200 represents the initial count of bacteria in the study
b) 1.8 represents the growth rate of the bacteria population in the culture
c) 1000 represents the initial bacteria population in the second function
The difference mean that the initial population in the first case study is greater than what we have in the second function
A women drives her car 168 miles in 3 hours. At this rate how far will she travel in 5 hours?
Answer:
280mph
Step-by-step explanation:
168 divided by 3 = mph
Times 5 = Answer
Patrick paid $18.70 for a pack of 10 notebooks. Individually, each notebook in the pack costs $ . PLS HELPPPPPP now
Answer:
$1.87
Step-by-step explanation:
Since the total cost was $18.70 and there are ten in the pack, to find the price of one notebook you just need to divide the total cost by the amount of notebooks there are. So 18.70 divided by 10 is $1.87 for each notebook.
what is 344.7234 to 1 decimal point
Answer: 344.7
Explanation:
344.7∣234
(Cut ^off point at the line)
The digit to the right of the cut of the point is less than 5. So the digit to its left (the 7) is not changed and all those to the right are changed to 0 gives you:
344.7000
Written as 344.7
Hope this helps and hope you have a wonderful day :)
Can you please help do not understand
The numbers - 12, -7, -2,3,... follow a pattern. What are the next three
numbers in this pattern?
Answer:
5
Step-by-step explanation:
Tyler needs to complete this table for his consumer science class. He knows that 1 tablespoon contains 3 teaspoons and that 1 cup contains 16 tablespoons. Write an equation that represents the number os teaspoons tcontAINED IN A CUP C.
Answer:
([tex]\frac{t}{3}[/tex])÷16=C
Evaluate | -65 | = ?
Answer:
65
Step-by-step explanation:
It's the absolute value of -65
Hope this helped, Have a Wonderful Day!!
What is a formula for the nth term of the given sequence? 50, -20,8...
Answer:
L = 50 * (-0.4)^(n - 1)
Step-by-step explanation:
r = t2/t1 = -20/50 = - 0.4
a = 50
L = 50 * (r)^(n - 1) Let's see if we can get the answer when n = 3
L=50 * (-0.4)^(3 -1)
L =50* (-0.4)^2
L = 50 * 0.16
L = 8 which is correct
Together, Lee and Joanna have 19 computer games. Joanna has 3 more games than Lee. Write and solve an equation to find the number of games each friend had.
Answer:
L=8 and J=11
Step-by-step explanation:
If Lee is L and Joanna is J we get: L+J=19.
And since Joanna has 3 more than Lee we get: J=L+3
When we substitute J for L+3 we get: 2L+3=19
When we solve we get: L=8
Finally, since J=L+3 we get: J=11
Page 2 I need help with this whole page! And be careful, my teacher said “think about what part of the equation deals with price “
Answer:
a) Already correct
b) If x represents each one dollar increase in price, than prices that are increased by $16 and $28
c) $6
d) Maximum Revenue would be $2,420
e) x = -5 but it's extraneous
(if we were using imaginary numbers then it would be 5i)
Step-by-step explanation:
How do I find where my potato chip went
Answer:
look around for it maybe it fell under your bed, couch etc just look
Step-by-step explanation:
Two adjacent sides of a parallelogram are 7cm and 10cm respectively.Find its perimeter
Answer:
[tex]Perimeter = 34cm[/tex]
Step-by-step explanation:
Given
Represent the adjacent sides with A and B
[tex]A= 7cm[/tex]
[tex]B = 10cm[/tex]
Required
Determine the perimeter
The perimeter is calculated as follows;
[tex]Perimeter = 2 * (L + B)[/tex]
[tex]Perimeter = 2 * (7cm + 10cm)[/tex]
[tex]Perimeter = 2 * (17cm)[/tex]
[tex]Perimeter = 2 * 17cm[/tex]
[tex]Perimeter = 34cm[/tex]
Need help ASAP!!
HELP!!!!!
Answer:
Option D
Step-by-step explanation:
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the formula,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the graph attached,
Since, the given line passes through two points (-3, 0) and (0, 2),
Slope of the line = [tex]\frac{2-0}{0-(-3)}[/tex]
= [tex]\frac{2}{3}[/tex]
y-intercept of the line is the point of intersection of the line and y-axis.
Therefore, y-intercept of the line given in the graph is,
y = 2 units
Option D is the answer.
- A box contains 7 apples and 5 oranges. The pieces of fruit are taken out of the box, one at a
time and in a random order. What is the probability that the bowl will be empty after the last
apple is taken from the box?
Answer:
The value is [tex]P( O \ and \ A ) = 0.583[/tex]
Step-by-step explanation:
From the question we are told that
The number of apples is [tex]A = 7[/tex]
The number of oranges is [tex]R = 5[/tex]
Generally the probability that the bowl will be empty after the last apple is taken from the box is mathematically represented as
The probability that 5 oranges and 7 apples are drawn in the 1st 11 draws
So
[tex]P( O \ and \ A ) = \frac{(^5 C_5) * (^7 C_6) }{^{12} C_{11}}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
[tex]P( O \ and \ A ) = \frac{(1 * 7 )}{12}[/tex]
=> [tex]P( O \ and \ A ) = 0.583[/tex]
Help..I’m useing all my points TELL ME ALL THE AWNSERS TO THE LOWER PART
Answers:
Lazy Butcher: M E A T L O A F E R
Rubber Raft: P L A Y B U O Y
Corn Salesman: S T A L K B R O K E R
T = 6(3*4 - 5) - 9*4 = 6
U = 4 - 8(-2 -6*-1) = -28
Y = -3*-3 + 2(-5 * -3 + 1) = 41
R = -7(7 +6) + 12 = 79
F = 4(8 + 5 * -2) + 2* -2 = -12
S = -5 -3(4 - 9) = 10
E = 7 - 6(-8 + 2 * -6) + -6 = 121
P = 8 * -8 - 9 * -8 + 2(-3 * -8 - 4) = 48
K = -4(4 + 7 * 2) + 5 + 3 * 2 = -61
B = 5(--5 - 3) + 4 * -5 - 10 = -20
M = -1 + 9(4 * -1 - 2) - 6 * -1 = -49
A = 6 - 2 * 3 - 6(-3 * 3 + 7) = 12
O = -8(9 + 2 * 6) + 8 * 6 + 6 = -114
L = -1 - 5 + 5(-5 * 1 + 9) = 14
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Write the following in point-slope form using the given information: Slope: 2 points
1/15; Point: (3,-5)
Answer:
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
Step-by-step explanation:
Given
[tex]m = \frac{1}{15}[/tex] -- Slope
[tex](x_1,y_1) = (3,-5)[/tex] --- Point
Required
Write an equation in point slope form
The point slope form of an equation is:
[tex]y - y_1 = m(x - x_1)[/tex]
Substitute values for y1, x1 and m
[tex]y-(-5) = \frac{1}{15}(x - 3)}[/tex]
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
Hence, the equation in point slope form is:
[tex]y+5 = \frac{1}{15}(x - 3)}[/tex]
can someone please help!?
Answer:
x = 44.4°
Step-by-step explanation:
Use SOHCAHTOA.
In this case, use sine trigonometric function formula
[tex] \sin(x) = \frac{o}{h} [/tex]
The opposite side of angle is 7.
The hypoteneuse is 10.
So,
[tex] \sin(x) = \frac{7}{10} \\ x = \sin ^{ - 1} ( \frac{7}{10} ) \\ x = {44.427}^{o} \\ x = {44.4}^{o} [/tex]
9514 1404 393
Answer:
44.4°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
sin(x) = 7/10
x = arcsin(7/10)
x = 44.4°
Help me out here pleaseeeeeeee
Answer:
if gray is what's left then it is C if white is what's left it is A
Step-by-step explanation:
Step-by-step explanation:
A because it shows the 2/3 of the pie colored meaning eaten
Is (-4,2) a solution of 4x+5y<-7
Answer:
(-4,2) is NOT a solution
Step-by-step explanation:
In this question, we have to see if the coordinate is a solution to the inequality.
To do this, plug in and solve:
4(-4) + 5(2) < -7
-16 + 5(2) < -7
-16 + 10 < -7
-6 < -7
Since -6 is not less than -7, this would be false.
Therefore, (-4,2) is NOT a solution.
coordinates are (-4,2)
equation :
[tex]4x + 5y < - 7[/tex]
substituting values of x and y in equation :
[tex]4( - 4) + 5(2)[/tex]
[tex] = - 16 + 10 \\ = - 6 > - 7[/tex]
which is not the required solution as - 6 is greater than -7
therefore (-4,2) is not the solution
Rolling a 2 on a number cube is
1. likely
2. unlikely
3. as likely as not (50/50)
4. impossible
5. certain
Answer:
2. unlikely
Step-by-step explanation:
The probability of rolling a 2 is 1/6, 0r 0.1666... .
Probabilities and their meanings:
0 - impossible
between 0 and 0.5 - from unlikely to almost as likely as not
0.5 - as likely as not
between 0.5 and 1 - from as likely as not to almost certain
1 - certain
This probability is 0.1666... which is in the category from 0 to 0.5. It is closer to 0 than to 0.5, so although it is not impossible, it is unlikely.
Answer: 2. unlikely
find the length of the top part of the window shown. The diameter of the Sun in my circle is 63 in in length. Round your answer to the nearest inch
Answer:
[tex]99\ inches[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\Diameter\ of\ the\ Sun\ or\ the\ Semi-Circular\ Window=63\ inches\\Hence\ in\ order\ to\ find\ the\ length\ of\ the\ top\ part,\ we\ need\ to\\ find\ the\ semi-circumference\ of\ the\ window.\\Hence,\\As\ we\ know\ that,\ in\ any\ circular\ figure,\\Radius=\frac{Diameter}{2} \\Hence\ here,\\Radius\ of\ the\ Semi-Circular\ Window=\frac{63}{2}\\Hence,\\As\ the\ Circumference\ of\ a\ circle= 2\pi r[/tex][tex]Hence,\\Semi-Circumference= \frac{Circumference}{2}\\Hence,\\ Semi-Circumference=\frac{2\pi r}{2}\\Semi-Circumference=\pi r\\Hence\ taking\ r=\frac{63}{2}\ and\ \pi =\frac{22}{7} ,\\The\ Semi-Circumference\ of\ the\ Semi-Circular\ Window=\pi *\frac{63}{2} \\The\ Semi-Circumference\ of\ the\ Semi-Circular\ Window= \frac{22}{7}*\frac{63}{2}\\[/tex]
[tex]The\ Semi-Circumference\ of\ the\ Semi-Circular\ Window= 11*9=99\ in\\Hence,\\The\ length\ of\ the\ top\ part\ of\ the\ window= 99\ inches[/tex]
Answer:34)63
Step-by-step explanation:
Find the commission on a $1250 sale with a commission rate of 5%
Answer:
He will have in total $1312.50
He earns a total of $62.50
Step-by-step explanation:
1250 x 1.05 = 1312.50
1250 x 0.05 = 62.50
Two doctors is % of 25 doctors
=_____%
Answer:
50
Step-by-step explanation:
Answer:
I believe it is 5 percent
Step-by-step explanation:
Hope it helps and is right.
6. Translate statement below. "One less than twice a number. A 1-n² B. 2-1 c. 1-2 D. 2n-1
12 yards = ______________ feet
Answer:
36 feet
Step-by-step explanation:
One yard is 3 feet.
12 yards * 3 feet = 36 feet
Answer:
36
Step-by-step explanation:
1 yard=3 feet so
12 yards = 3x12 feet
12 yards = 36 feet
Hope this helps! :)