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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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.
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a1= blank (simplify your answer)
Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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radius (r)=3.4m
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now
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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]
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Step-by-step explanation:
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Answers
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S
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
2
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Answers
Answer:
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15y
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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
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Step-by-step explanation:
Let the whole pizza =1whole
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Answers
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Consider the function f(x). Select all of the following that include a horizontal compression of f(x).
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D) f(0.4x) - 1
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Answers
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Step-by-step explanation:
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Answers
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Answers
Answer:
6
Step-by-step explanation:
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Answers
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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
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-Aphrodite