A village R is 10km from a point P on a bearing 025° from P. Another village A is 6km from P on a bearing 162°.calculate the distance R from A and the bearing of R from A
Answers
Answer:
9.75
Step-by-step explanation:
10-0.25=9.75
The distance R from A and the bearing of R from A 15 km and 189° respectively.
What are sine and cosine rules?The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.
Given that, a village R is 10 km from a point P on a bearing 25° from P. Another village A is 6 km from P on a bearing 162°.
We need to calculate, the distance R from A and the bearing of R from A
We will use the Cosine Rule to determine the distance of R from A (p);
From Cosine Rule;
b² = a² + c²– 2ac Cos B
p² = a² + r² – 2ar Cos P
a= 10 km
Cos P = Cos 137
r = 6 km
p = ?
p² = a² + r² – 2ar Cos P
p² = 10² + 6² - 2 (10) (6) Cos 1370
p² = 100 + 36 – 120 (- 0.7314)
p² = 136 + 87.76
p² = 223.76
p = 14.95 = 15 km (approximated to the nearest km)
To find the bearing of the R from A,
we will apply Sine Rule;
From Sine Rule;
15Sin Ø = 10Sin 137 = 6.82
Sin Ø = 6.82/15 = 0.4547
Ø = ArcSin 0.4547 = 27°
Therefore, the bearing of R from A will be
∠ PRA = 180 – 137 – 27 = 160
The alternating angle to 25° at R is 65°
Then, the bearing of R from A = 270 -65-16 = 189°
Hence, the distance R from A and the bearing of R from A 15 km and 189° respectively.
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Related Questions
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A pack of 5 of board games costs $75.
If there is a direct proportion between the price (y) and number of board games (2), which equation represents the
situation?
y = 75.2
By = 52
C y = 2
Dy = 152
Answers
Answer:
one board game cost 15 dollars
75/5=15
15y
y = number of board games and 15= the price of each board game
so to calculate any number of board games bought just input the number of board games bought for y in the expression 15y and you will get the price.
Step-by-step explanation:
Why is 3 x 1/10 less than 3 x 10?
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Answer:
The value of 1 tenth is less than the value of 1 ten.
Step-by-step explanation:
Answer:
Because 3 x 1/10 = 3/10
whereas 3 x 10 = 30
and 3/10 < 30
Also b/c 1/10 < 10 and they are multiplied by the same value (3)
Step-by-step explanation:
C. A circle has a center at (3,−2) and radius of 4. Does the point (3,2) lie on the circle, inside the circle or outside the circle?
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To add the fractions 3/4 and 7/12 what must be done first?
A. reduce the fractions to lowest terms
B. change to improper fractions
C. make the numerators the same
D. find a common denominator
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Answer:
Step-by-step explanation:
S
Step-by-step explanation:
[tex] = \frac{(2c {}^{2} + c - 2) }{(c + 1)} \\ rationalise \: the \: denominator \\ = \frac{(2 {c}^{2} + c - 2)(c - 1)}{(c + 1)(c - 1)} \\ = \frac{(2 {c}^{3} - 2 {c}^{2} + {c}^{2} - c - 2c + 2) }{( {c}^{2} - {1}^{2} )} \\ = \frac{(2 {c}^{3} - {c}^{2} - 3c + 2 )}{( {c}^{2} - 1) } [/tex]
One equalion for finding the volume of a cylinder is V=Bh, where B represents the area of the base of the cylinder and h represents the height of the cylinder. Which expression could be used to find the volume of the cylinder in cubic meters ?
Answers
Answer:
we have
diameter {d}=6.8m
radius (r)=3.4m
height]h}=8.5
now
volume of cylinder=πr²h=π([6.8]/2)²×8.5=
π(3.4)²(8.5) is your answer
Step-by-step explanation:
Diameter of the cylinder=6.8m
Radius=Diameter/2=6.8/2=3.4
We know that[tex]\boxed{\sf Volume=\pi r^2h}[/tex]
[tex]\\ \tt \mapsto \:Volume_{(Cylinder)}=\pi(3.4)^2\times 8.5 units^3[/tex]
Hence option B is correctthe mean of 5 numbers is 8.
one more number is added to the group.
the mean of the numbers is 9.
what number was added to the group
Answers
Answer:
14
Step-by-step explanation:
Sum of the first five numbers = 40
The sum of the six numbers should equal 9 x 6 = 54
So, you would do 54 - 40 = 14
Hope that helps! :)
-Aphrodite
According to this diagram, what is tan 62°?
A 17/15
B 8/17
C 15/17
D 8/15
E 17/8
F 15/8
Answers
Tangent is Opposite/Adjacent so 15/8
Hope this helps! :)
Help Please!!!
A group of friends are going to a local pizzeria. One medium pizza costs $12.50. The friends spent less than $55. They purchased two pitchers of soda for a total of $8.99. How many medium pizzas could the group purchase? Write and solve an inequality. Show your work.
Answers
Answer:
8.99 + 12.50x < 55 and x = 3
Step-by-step explanation:
The cost of their pitchers of soda ($8.99) and the cost of x number of pizzas ($12.50x), is less than 55.
If jerome has 3 watermelons and 4 oranges, how fast was the train to his right going
Answers
Answer:
70 km/h
Step-by-step explanation:
Toby and Ahmed are eating pizza. Toby eats 1/2 of the pizza and Ahmed eats 1/4 of the pizza. How much of the total pizza have they eaten? 1 point
Answers
Answer:they have eaten 3/4 of the total pizza
Step-by-step explanation:
Let the whole pizza =1whole
Amount eaten by Toby =1/2
Amount eaten by Ahmed =1/4
Total Amount eaten by both of them =1/2 +1/4 = 2+1/ 4=3/4
Therefore, they have eaten 3/4 of the total pizza
Triangle ABC has vertices A(-2,0), B(2,5), C(3, 1). The reflection of the image of triangle ABC is triangle A'B'C' with vertices A(-2,0), B12, -5), C73.
-1). What is a rule that describes the reflection?
Answers
Answer: Reflection about x-axis
Step-by-step explanation:
Given
Initially, vertices are [tex]A(-2,0), B(2,5),C(3,1)[/tex]
After reflection they become [tex]A(-2,0),B(2,-5),C(3,-1)[/tex]
It is clear that the x coordinate remains unchanged and the y coordinate changes its sign. It occurs when reflection is done about the x-axis.
For example, when (a,b) is reflected about the x-axis, it becomes (a,-b).
So, here reflection is being done about the x-axis.
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28 blue cars out of 63 cars
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Answer:
What's the question?
Step-by-step explanation:
I need help on this ASAP
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Answer:
That other person was such a troll but it by 43! Could you please mark me branllest? Only if you want to :)
Step-by-step explanation:
Solve.
a-5/a+4=5/4
a=0
a=-1
a=-9
a=-40
Answers
Answer:
-1
Step-by-step explanation:
hzhsuxbsjsisnduxidnwhdicjdbe
essay on kim jong un
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Answer:
Step-by-step explanation:
From late 2010, Kim Jong-un was viewed as successor to the leadership of North Korea. Following the elder Kim's death in December 2011, state television announced him as the "Great Successor". Kim holds the titles of General Secretary of the Workers' Party of Korea,[7] Chairman of the Central Military Commission, and President of the State Affairs Commission. He is also a member of the Presidium of the Politburo of the Workers' Party of Korea, the highest decision-making body. In July 2012, Kim was promoted to the highest rank of Marshal in the Korean People's Army, consolidating his position as Supreme Commander of the Armed Forces. North Korean state media often refers to him as "the Marshal" or "Dear Respected Leader". He has promoted the policy of byungjin, similar to Kim Il-Sung's policy from the 1960s, referring to the simultaneous development of both the economy and the country's nuclear weapons program.
Please help. How many play sports year round?
Answers
3 because 2 of them played during spring and winter. 6 of them played during spring and fall. and 13 played during fall and winter. but your asking for year round which is all three seasons meaning only 3 played year round.
A computer program randomly selects a month of the year. What is the sample space for this experiment?
Answers
Answer:
The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1.
Step-by-step explanation:
i need help, ASAP!! i have 12 mins left
Answers
Answer:
x = 18
Step-by-step explanation:
So since a || b,
7x + 11 = 10x - 43
3x = 54
x = 18
My brainy brother and sister added their ages together and got 15. When they multiplied their ages together, they got 54. How old is the older one between the two of them?
Answers
Given:
Sum of ages of brother and sister = 15
Product of their ages = 54
To find:
How old is the older one between the two of them?
Solution:
Let x be the age of brother and y be the age of sister.
Sum of ages of brother and sister = 15
[tex]x+y=15[/tex]
[tex]x=15-y[/tex] ...(i)
Product of their ages = 54
[tex]xy=54[/tex]
[tex](15-y)y=54[/tex] [Using (i)]
[tex]15y-y^2=54[/tex]
[tex]0=54-15y+y^2[/tex]
Splitting the middle term, we get
[tex]54-15y+y^2=0[/tex]
[tex]54-9y-6y+y^2=0[/tex]
[tex]9(6-y)-y(6-y)=0[/tex]
[tex](6-y)(9-y)=0[/tex]
Using zero product property, we get
[tex](6-y)=0\text{ and }(9-y)=0[/tex]
[tex]y=6\text{ and }y=9[/tex]
If [tex]y=6[/tex], then using (i), we get
[tex]x=15-6[/tex]
[tex]x=9[/tex]
If [tex]y=9[/tex], then using (i), we get
[tex]x=15-9[/tex]
[tex]x=6[/tex]
Therefore, the age of older one is 9, the age of younger one is 6 and the difference between their ages is 3.
you have three sides and three angles what am i
Answers
How would you solve y=3/4x+9
Answers
Answer: i took a screen shot of the answer hope this helped
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Step-by-step explanation:
Which inequality correctly compares 1/2, 3/4, and 2/3?
Answers
PLZ HELP What is the mode interval for the histogram? Science Test Scores Frequency No Бел о об - 1 50-59 60-69 70-79 80-89 90-100 Scores (out of 100) 0 80 - 89 O 50 - 59 O 10 90 - 100
Answers
Answer: You are correct. The mode is between 90 and 100
This is because the tallest bar corresponds to this interval. The mode is the most frequent value.
Step-by-step explanation:
i am not sure but i hope this can help you
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Consider the function f(x). Select all of the following that include a horizontal compression of f(x).
A) 2f(x)
B) f(3x)
C) -f(x)+1
D) f(0.4x) - 1
E) f(6x) +9
F) -f(0.12x)
Answers
Answer: B, E
Step-by-step explanation:
You are at a bookstore and you are allowed to buy 9 books. You have already selected 3 books. Find the possible amount of books you can still select.
Answers
Answer:
6
Step-by-step explanation:
9 - 3 = 6
15 is which percent of 30?
A. 450%
B. 200%
C. 50%
D. 1/2%
E. 2%
Answers
Answer:
answer: 50%
Step-by-step explanation:
The answer is 50% because 15 is half of 30 because 15 + 15 = 30 so 15 is half of 30 50%
The answer is C because
30-15= 15
I need help cand someone help me find this answer
Answers
Answer:
725.7 m²
Step-by-step explanation:
A=2πrh
r=16 1/2 ÷ 2 = 8 1/4
A= 2π(8.25)(14)=725.7
find a1 for the geometric sequence with the given terms.
a5=96 and a7=384
a1= blank (simplify your answer)
Answers
Answer:
6
Step-by-step explanation:
r = √(384/96) = √4 = 2
so, a1 = 96/ (2)⁴ = 96/16 = 6