<h2>
Measure of the angle between their courses is 95°</h2>
Step-by-step explanation:
Speed of submarine 1 = 25 knots = 28.77 mph
Speed of submarine 2 = 20 knots = 23 mph
Time taken = 3 hours
Distance traveled by submarine 1 = 28.77 x 3 = 86.31 miles
Distance traveled by submarine 2 = 23 x 3 = 69 miles
Distance between them is 100 nautical miles = 115.08 miles
Refer the figure
By cosine formula we have
![cosB=\frac{a^2+c^2-b^2}{2ac}](https://tex.z-dn.net/?f=cosB%3D%5Cfrac%7Ba%5E2%2Bc%5E2-b%5E2%7D%7B2ac%7D)
a = 86.31 miles
b = 115.08 miles
c = 69 miles
Substituting
![cosB=\frac{86.31^2+69^2-115.08^2}{2\times 86.31\times 69}\\\\cosB=-0.0867\\\\B=94.98^0=95^0](https://tex.z-dn.net/?f=cosB%3D%5Cfrac%7B86.31%5E2%2B69%5E2-115.08%5E2%7D%7B2%5Ctimes%2086.31%5Ctimes%2069%7D%5C%5C%5C%5CcosB%3D-0.0867%5C%5C%5C%5CB%3D94.98%5E0%3D95%5E0)
Measure of the angle between their courses is 95°
The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5
Step-by-step explanation:
Let,
Cost of each fried crab claw = x
Cost of each gumbo = y
According to given statement;
4x+4y=32 Eqn 1
2x+y = 12.5 Eqn 2
Multiplying Eqn 2 by 2
![2(2x+y = 12.5)\\4x+2y=25\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=2%282x%2By%20%3D%2012.5%29%5C%5C4x%2B2y%3D25%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 3 from Eqn 1
![(4x+4y)-(4x+2y)=32-25\\4x+4y-4x-2y=7\\2y=7](https://tex.z-dn.net/?f=%284x%2B4y%29-%284x%2B2y%29%3D32-25%5C%5C4x%2B4y-4x-2y%3D7%5C%5C2y%3D7)
Dividing both sides by 2
![\frac{2y}{2}=\frac{7}{2}\\y=3.5](https://tex.z-dn.net/?f=%5Cfrac%7B2y%7D%7B2%7D%3D%5Cfrac%7B7%7D%7B2%7D%5C%5Cy%3D3.5)
Putting y=3.5 in Eqn 2
![2x+3.5=12.5\\2x=12.5-3.5\\2x=9](https://tex.z-dn.net/?f=2x%2B3.5%3D12.5%5C%5C2x%3D12.5-3.5%5C%5C2x%3D9)
Dividing both sides by 2
![\frac{2x}{2}=\frac{9}{2}\\ x=4.5](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B9%7D%7B2%7D%5C%5C%20x%3D4.5)
The cost of each order of fried crab claw is $4.5 and cost of each cup of gumbo is $3.5
Keywords: linear equation, subtraction
Learn more about subtraction at:
#LearnwithBrainly
4 1/2-3 5/8=0.875 or 875/1000 or 35/40 or 7/8