There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of B, 7 miles away. What is the bearing needed to navigate from island B to C? Round to the nearest degree
Answers
Answer:
The bearing needed to navigate from island B to island C is approximately 38.213º.
Step-by-step explanation:
The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:
[tex]AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta[/tex] (1)
Where:
[tex]AC[/tex] - The distance from A to C, measured in miles.
[tex]AB[/tex] - The distance from A to B, measured in miles.
[tex]BC[/tex] - The distance from B to C, measured in miles.
[tex]\theta[/tex] - Bearing from island B to island C, measured in sexagesimal degrees.
Then, we clear the bearing angle within the equation:
[tex]AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta[/tex]
[tex]\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}[/tex]
[tex]\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)[/tex] (2)
If we know that [tex]BC = 7\,mi[/tex], [tex]AB = 8\,mi[/tex], [tex]AC = 5\,mi[/tex], then the bearing from island B to island C:
[tex]\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right][/tex]
[tex]\theta \approx 38.213^{\circ}[/tex]
The bearing needed to navigate from island B to island C is approximately 38.213º.
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What is 8x^6 divided by 4x^3
Answers
Answer:
2x^3
Step-by-step explanation:
Which statement is true? Ill mark brainlest
−6.5>6.55
−6.5≥6.55
−6.5<6.55
−6.5=6.55
Answers
Answer:
6.5 < 6.55
Step-by-step explanation:
since
6.5 can be written as 65/10
6.55 can be written as 655/100
when we take LCM of 100 and 10 we get 100.
so we will multiply 65/10 with 10 on both numerator and denominator.
we get 650/100 and 655/100 .
since denominators are same we can say that 650<655.
Hence,
6.5 < 6.55
For a remodeling job, an architect suggested increasing the sides of a square patio by 5 feet per side. This made the new area of the patio 144 square feet. What was the area of the original patio?
Answers
Answer:
49 sq ft.
Step-by-step explanation:
The area of a square is calculated by multiplying the length by the width which, since it is a square, are both the same value. Therefore, since we are given the area of the new patio we can simply square root that area to find the value of the length/width
[tex]\sqrt{144}[/tex] = 12 feet
Since the new sides of the patio are 5ft more than the original we need to subtract 5 feet.
12 - 5 = 7 feet
Now we can multiply the original width/length together to calculate the original area of the patio.
7 * 7 = 49 sq ft.
What is the x-intercept of y=1/3x-5
Answers
Answer:
x = 15
Step-by-step explanation:
To find the x-intercept(s), substitute in 0 for y and solve for x.
0 = 1/3 x − 5
Solve the equation.
x = 15
This is so it makes more sense for u
Hope this Helps (✿◠‿◠)
IT WOULD BE HELPFUL IF YOU GUYS CAN HELP ME WITH THIS!
The temperature at sunrise is 28°F. Each hour, the temperature rises 7°F.
Write an equation that models the temperature y, in degrees Fahrenheit, after x hours.
Answers
Answer:
y=6x+24
Step-by-step explanation:
your temperature at the y-intercept is 24 degrees, and your slope being 6/1, so that would be your line equation. You can just plug in to solve after that
Remember that for your graph your dependent variable is always on the x-axis, and your independent variable is always on the y-axis. So because the temperature depends on time, the x-axis is the time of day in hours, and your y-axis is the temperature in Fahrenheit.
Answer:
28=(7)x+b
Step-by-step explanation:
y=mx+b right?
starts at 28, so plug that into y
28=mx+b
the rate of change is 7, so you plug that into m
28=(7)x+b
(I'm sorry if this is wrong, this is just my understanding of this)
What is the length of a right rectangular prism that has a volume of 1,071 cubic centimeters, a width of 17 centimeters, and a height of 3 centimeters?
Answers
Answer:
hi mom love you
Step-by-step explanation:
A student answers 9 questions
correctly out of 12 total
questions on a test. What
percent is this?
Answers
Explanation:
To find the answer you would divide 9/12 and you get .75, then you move the decimal point to the right twice to get your percentage
I have been stuck on this and don’t know what the answer is
Answers
Answer:
x= -1 or x= -11
Step-by-step explanation:
Answer:
i think its D. Im not fully sure
Step-by-step explanation:
Eighth grade
> G.2 Compare numbers written in scientific notation RHT
Which sign makes the statement true?
6.3600 x 10^10
? 5.360 x 10^11
>
<
=
Answers
Answer:
>.6.3600×10power 10 is the answer.it is bigger than the other numbers
Answer:
6.3600 x 10^10 is GREATER THAN (>) 5.360 x 10^11
Step-by-step explanation:
6.3600 x 10^10 = 63,600,000,000
5.360 x 10^11 = 536,000,000,000
Therefore it is simply seen that 5.360 x 10^11 is larger than 5.360 x 10^11.
Since 536,000,000,000 is larger than 63,600,000,000.
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Answer:
Step-by-step explanation:
1) Divide 50 by 7
2) Take that number and multiply it by 6.5 km
This works because the result of dividing 50/7 multiplied by 7 will give you 50, and if you multiple the result by 6.5 you will get your answer!
what is the slope of the line ?
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Answer:
-1,-2
Step-by-step explanation:
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Answer:
C
Step-by-step explanation:
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Answer:
ik the answer
Step-by-step explanation:
Solve for m
Find the measure of angle MHL
Please help me!!!!!!
Answers
∠MHL and ∠MHJ are supplementary angles that is some of the measure of both angle is 180°, because these angle are on a line.
∠MHL + ∠MHJ = 180°
substituting values.
⟹ (2m + 10)° + (5m + 100)° = 180°
⟹ 5m + 2m + 10 + 100 = 180°
⟹ 7m + 110 = 180°
⟹ 7m = 180° - 110°
⟹ 7m = 70°
⟹ m = 70/7
⟹ m = 10
m = 10°
measure of ∠MHL is
⟹ (2m + 10 )°
⟹ 2(10°) + 10°
⟹ 20° + 10°
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[tex]\red{\large\boxed{Mark\: Brainleist\: please ! }}[/tex]
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Find the output of the function y = x - 16 if the input is -28.
Help please
Answers
Answer:
-44
Step-by-step explanation:
If the input is -28, that means x = -28, so we plug -28 in for x and solve for y, which is the output:
y = x - 16
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Answer:
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Step-by-step explanation:
Answer:
they're corresponding
Step-by-step explanation:
If y= -7 when x= -28, find y when x=20
Answers
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Answers
Answer:
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Step-by-step explanation:
When ordering tickets online, a collage theater charges a $5 handling fee no matter how large the order. Tickets to a comedy concert cost $58 each. If you had the line showing the total cost, y, of buying tickets, x, what would the slope of your line be? Explain your thinking.
Answers
Answer:
58
Step-by-step explanation:
Given that :
Handling fee = $5
Cost of ticket to comedy concert = $58 each
The total cost y of buying ticket x ;
Using the slope - Intercept relation
y = mx + c
m = slope ; c = intercept
The constant handling fee = $5 = c = intercept
Cost of x tickets = (cost per ticket * number of tickets) = 58 * x = 58x
Hence,
y = 58x + 5
Comparing with the intercept slope equation :
Slope (m) =58
A math teacher graded 45 problems in
3
5
of an hour. At that rate, how many problems can she grade in 1 hour?
Answers
3/5 of an hours is 36 minutes you can then do 45 over 36 mins and set it equal to x over 60 mins then you do 45 times 60 which equals 2700 then you divide 2700 by 36 and you get 75
If a town with a population of 1,500 doubles in size every 21 years, what will the population be 42 years from now?
Answers
Answer:
In 42 years from now the population would be 6,000
Step-by-step explanation:
Answer:
6,000
Step-by-step explanation:
well if the population doubles every 21 years and it already has 1,500 and 42 years / 2 = 21 the population is going to double twice. 1,500*2=3,000
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I said certified freak
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Answer:
7 days a week
Step-by-step explanation:
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
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Step-by-step explanation:
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A student plays a total of 20
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Scissors. He wins 75% of
them. How many rounds did
he win?
Answers
Answer: The student wins 15 rounds.
Step-by-step explanation:
The number of rounds the student won is required.
The number of rounds the student won was 15.
The total number of rounds played is [tex]20[/tex].
The percentage the student wins is [tex]75\%[/tex]
The number of times he won was
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The number of rounds the student won was 15.
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Find the volume given cylinder. 8in,8in. Use 3.14 for pi and round to the nearest tenth.
A.1607.7in*3
B.2845.7in*3
C.6430.7in*3
D.401.9in*3
2.Find the volume of a rectangular prism with the following dimensions: L=5mm B=7mm H=3mm
142mm*3
105mm*3
126mm*3
130mm*3
3.Find the volume of the given pyramid. 7yd,7yd,9yd
147yd*3
175yd
Answers
Answer:
1. [tex]V =1607.7\ in^3[/tex]
2. [tex]V = 105mm^3[/tex]
3. [tex]V = 147yd^3[/tex]
Step-by-step explanation:
Solving (1):
Given
[tex]Radius, r =8\ in[/tex]
[tex]Height, h =8\ in[/tex]
Required
Determine the volume
Volume (V) of a cylinder is calculated as thus:
[tex]V =\pi r^2h[/tex]
[tex]V =3.14 * 8^2 * 8[/tex]
[tex]V =1607.7\ in^3[/tex]
Hence, the volume of the cylinder is [tex]1607.7\ in^3[/tex]
Solving (2):
Given
[tex]Length, l = 5mm[/tex]
[tex]Width, B = 7mm[/tex]
[tex]Height, H = 3mm[/tex]
Required
Determine the volume (V) of the rectangular prism
Volume (V) of a rectangular prism is calculated as thus:
[tex]V = LBH[/tex]
[tex]V = 5mm * 7mm * 3mm[/tex]
[tex]V = 105mm^3[/tex]
Hence, the volume of the prism is [tex]105mm^3[/tex]
Solving (3):
Given
[tex]Length, l = 7yd[/tex]
[tex]Width, B = 7yd[/tex]
[tex]Height, H = 9yd[/tex]
Required
Determine the volume (V) of the pyramid
Volume (V) of a pyramid is calculated as thus:
[tex]V = \frac{1}{3} *LBH[/tex]
[tex]V = \frac{1}{3} * 7yd * 7yd * 9yd[/tex]
[tex]V = \frac{1}{3} * 441yd^3[/tex]
[tex]V = 147yd^3[/tex]
Hence, the volume of the pyramid is [tex]147yd^3[/tex]
Waiter or waitress , earning $2.35 per hour plus $60 tips each week, working 24 hours per week.
Answers
Answer:
$116.40
Step-by-step explanation:
