Bearings Problem Solving Question:
From a lighthouse two boats can be sighted. Boat 1 on a bearing of 60° at a distance of 2km and Boat 2 on a bearing of 340° at a distance of 3km.
a) If Boat 1 is in need of assistance, what bearing would Boat 2 need to travel on to reach it?
b) Assuming Boat 1 does not move, how far would Boat 2 have to travel?
Answers
9514 1404 393
Answer:
a) 123.4°
b) 3.3 km
Step-by-step explanation:
In (N, E) coordinates, Boat 1 is located relative to the lighthouse at ...
2(cos(60°), sin(60°)) = (1.0, 1.732) . . . . . km
Boat 2 is located at ...
3(cost(340°), sin(340°)) = (2.819, -1.026) . . . . . km
So, relative to Boat 2, Boat 1 is located at ...
(1, 1.732) -(2.819, -1.026) = (-1.819, 2.758) . . . . . km
This is at a bearing of ...
arctan(2.758/-1.819) = 123.4°
and a distance of ...
√(1.819² +2.758²) ≈ 3.304 . . . . . km
a) Boat 2 would need to travel on a bearing of 123.4°.
b) Boat 2 would need to travel 3.3 km.
_____
Additional comment
We use (North, East) coordinates so we don't have to do the mental gyrations necessary to translate to and from (E, N) coordinates. The latter would correctly orient a map relative to the X-Y Cartesian plane. The former are equivalent to flipping the map over and looking at it from the back side. This is a "rigid transformation", so angles and distances remain unchanged.
Related Questions
HELP DUE IN 10 MINS! Determine whether the triangle described is right, obtuse, or acute. Show work to justify your answer.
7, 10, 13
This triangle is a obtuse, acute, right triangle?? because blank number is equal to, greater than, or less than another number??
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What is the range of the graph?
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Answer:
D
Step-by-step explanation:
the graph is forever extending to infinity, so there's no definite range
What does x equal in this problem
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Brookwood High School is considering adding co-ed soccer to the sports program for the fall
season. In order to get an unbiased sample of interest in soccer, who should the school survey?
A. girls in PE class
B. members of the soccer team
C. every fifth student entering the cafeteria
D. students in freshman homerooms
Answers
Answer:
B
Step-by-step explanation:
Pierce removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 10x2 −17x + 3, where x is the time in minutes. Choose the appropriate form of the expression that would reveal the time in minutes when the trough is empty.
10(x − 3)2 − 1
10(x − 1)2 − 3
(5x − 1)(2x − 3)
10(0)2 − 17(0) + 3
Answers
Answer:
(5x - 1)(2x - 3)
10x^2 - 17 + 3 = (5x - 1)(2x - 3)
Answer:
C.(5x − 1)(2x − 3)
O 91.7 miles
O 55.5 miles
O 41.7 miles
O 63.8 miles
Answers
Answer:
* 55.5 miles
Step-by-step explanation:
17² + b² = 23²
289 + b² = 529
b² = 240
b = 15.491 ≈ 15.5
17 + 23 + 15.5 = 55.5
You can also simply notice B is the only answer with a .5 decimal and thus don't have to add.
Steven warms a cup of a coffee to a temperature of 195°F and then leaves it to cool in a room that is 75°F. This equation represents the
temperature, T, of the coffee in the cup after x minutes.
T = 75 + 120e-0.051
After how many minutes will the temperature of the coffee be approximately 141°F?
Answers
Answer:
12 minutes
Step-by-step explanation:
First substitute 141°F for T in the given equation.
Then isolate the exponential term.
Now rewrite the equation as a natural log, and solve for x.
After 12 minutes will the temperature of the coffee be approximately 141°F.
What is temperature?Temperature is the degree of hotness or coldness expressed in terms of any of numerous scales, such as Fahrenheit and Celsius. Temperature suggests the route wherein heat strength will spontaneously flow—i.e., from a warmer body (one at a better temperature) to a less warm frame (one at a lower temperature).
diploma measures of temperature are typically expressed with the ° temperature scale: The sample became heated to 80 °C.
Substitute the 141°F in the equation
⇒T = 75 + 120e-0.051
⇒ 141 = 75 + 120x - 0.051
⇒ 120x = 141 -75 + 0.051
⇒120x = 66.051
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Simplify the Expression
Answers
A pet home owner wants to keep the ratio of cats to dogs at 3:5. She has 21 cats, how many dogs are there in the pet home?
Answers
35 dogs
Step-by-step explanation:
The ratio of cats to dogs can also be written as
3/5 = 21/x
x = 35
1/8 to decimal number
Answers
Answer: 0.125
Step-by-step explanation:
Which expression is equivalent to (18x + 9k) + (2x + 6k)?
16 x + 3 k
20 x + 15 k
20 x + 16 k
36 x + 54 k
Answers
20x + 15k is the answer we just have to remove the bracket and add the terms
hope it helps
Answer:
20x + 15K
Step-by-step explanation:
just add like variables (x and Y)
Find the equation of the line between the points (10, – 5) and ( - 2,0).
Answers
Answer (assuming it can be in slope-intercept form):
[tex]y = -\frac{5}{12} x-\frac{5}{6}[/tex]
Step-by-step explanation:
1) First, find the slope of the line between the two points by using the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(0)-(-5)}{(-2)-(10)} \\m = \frac{0+5}{-2-10} \\m=\frac{5}{-12}[/tex]
Thus, the slope of the line is [tex]-\frac{5}{12}[/tex].
2) Next, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.
Since [tex]m[/tex] represents the slope, substitute [tex]-\frac{5}{12}[/tex] in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:
[tex]y-(0)=-\frac{5}{12} (x-(-2))\\y-0 = -\frac{5}{12} (x+2)\\y = -\frac{5}{12} x-\frac{5}{6}[/tex]
X(-9x^2-5x+9)
..................
Answers
hope it helps
Find the value of x.
Answers
Answer:
66
Step-by-step explanation:
subtract each external angle by 180 to find the interior angle.
Since you know that all of the interior angles add up to 540 because 180(n-2)
with n is how many sides in the polygon
so 180(5-2)=540
now take each value and subtract it by 180
180-(45)=135
180-(40)=140
180-(x)=180-x
180-(77)=103
180-(2x)=180-2x
135+140+180-x+103+180-2x=540
738-3x=540
x=66
hope that helps :)
Please give brainliest
6. Mr. Walthour is building a storage shed in a conical shape. The base of the shed is 4 meters in diameter and the height of the shed is 3.8 meters. What is the volume of the shed? Round to the nearest tenth. (Example 2)
Answers
I think it helps you..............
What is the value of the expression below when x=10x=10 and y=4y=4?
8x-7y
8x−7y
Answers
Answer:
Step-by-step explanation:
8(10) - 7(4)
8X10 - 7X4
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52
Simplify
12d divided by 2
Answers
Answer:
6d
Step-by-step explanation:
Find the rate of change given the following solutions: (6, 2) and (1, 12).
Answers
Answer:
The rate of change is -2
Step-by-step explanation:
f(b)-f(a) 12-2 10
---------- = ------------ = -------- = -2
b-a 1-6 -5
Please help me pls plsss
Answers
Answer:
c is correct
Step-by-step explanation:
If you look at it, 2x is the slope. Always remember the formula y = mx + b
The mx is your slope. And the whole number is your b or y - intercept
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Name the interval on which the function graphed below is
increasing.
1. X>1.5
2. X<1.5
3. X>0
4. -1
Answers
Answer:
Step-by-step explanation:
x > 1.5
The price of a book, which regularly sells for $24, was marked down by 25%. A coupon reduced the price by another 10%. What was the final selling price?
Answers
Answer:
$16.20
Step-by-step explanation:
24.00 × 25%= 6.00
24.00 - 6.00 = 18.00
18.00 × 10%=1.80
18.00 - 1.80 = 16.20
A percentage is a way to describe a part of a whole. The final cost of the book will be $16.2.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given the cost of the book is $24. Therefore, the cost of the book after a 25% discount is,
Cost of book after discount = $24×(100%-25%) = $18
Now, the cost after the 10% counpon will be,
Cost after the 10% counpon = $18×(100%-10%) = $16.2
Hence, the final cost of the book will be $16.2.
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And angle measures 54° more than the measure of its complementary angle what is the measure of each angle
Answers
The measure of the angles are 72 degrees and 18 degrees
Step-by-step explanation:
we know that
If two angles are complementary, then their sum is equal to 90 degrees
Let
x -----> the measure of an angle
y-----> the measure of he other angle
we know that
x+y=90 -----> y=90-x -----> equation A
x=y+54 ----> equation B
substitute equation B in equation A and solve for y
y=90-(y+54)
y=90-y-54
2y=36
y=18°
Find the value of x
x=y+54 -----> x=18+54=72°
therefore
The measure of the angles are 72 degrees and 18 degrees
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find the area of the composite figure
Answers
Answer:
12 x 13 = 156
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A.3
B.8
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Answer:
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Step-by-step explanation:
Answer:
yea for sure the third one
Step-by-step explanation:
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Answers
Answer:
x=3
Step-by-step explanation:
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Answer:
X=3
Step-by-step explanation:
-6(-2x -y + 4)
It also says to use the distributive property
Answers
Answer:
The answer is 12x+6y-24
Step-by-step explanation:
Answer:
12x + 6y -24
Step-by-step explanation:
What is the degree measure of
A
310
34
58
D
Answers
Answer:
34
Step-by-step explanation:
A triangle always has a sum of 180 degrees
First, let us find the right angle
180-149=31
Now find v
180=31+115+x
180-146=x
x=34
(50 points really need help on this it's the last question)
Answers
Answer:
Pretty sure it's C
Step-by-step explanation:
trUst mE
A,C,E
Step-by-step explanation:
I got it right on my test