Problem 9, part a)
Compass bearings always have north as the starting point. This is where 0 degrees is situated, and 360 degrees as well. As the bearing angle increases, you'll turn to the right toward the eastward direction. Effectively you're sweeping out a clockwise rotation. The bearing 322 degrees is in a northwest position as the diagram shows (place the ship at the bottom right corner of the triangle). The bottom right acute angle of the triangle is 322 - 270 = 52 degrees. This is the reference angle we'll use for finding the distance d.
With respect to the reference angle of 52 degrees, the side 18.5 is the opposite side and d is the adjacent side. Use the tangent ratio to get...
tan(angle) = opposite/adjacent
tan(52) = 18.5/d
d*tan(52) = 18.5
d = 18.5/tan(52)
d = 14.4537840903742
The approximate value of d is 14.4537840903742 km
This rounds to 14.5 when rounding to one decimal place.
<h3>Answer: 14.5 km</h3>
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Problem 9, part b)
Recall that
distance = rate*time
where "rate" is another term for "speed" or "velocity"
We can solve this for the time to get
time = distance/rate
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We found the distance back in part a) above. We are given the rate of 48 km/h
So,
time = distance/rate
time = 14.4537840903742/48
time = 0.3011205018828
This is the time it takes in hours. Multiply by 60 to convert to minutes
0.3011205018828 hours = 60*0.3011205018828 = 18.067230112968 minutes
This rounds to the whole number 18
<h3>Answer: 18 minutes</h3>
Answer:
550
Step-by-step explanation:
We aren't given that they are consecutive so lets just pretend the numbers are x, y, z , and r.
We are given x+y+z+r=1320
We are also given that y+z+r=.4x+x
Simplifying my second equation gives us y+z+r=1.4x. I'm going to plug this into first equation giving me
x+1.4x=1320
2.4x=1320
So x=1320/2.4=550
Answer:
(d) 944 mm³
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the distance between bases.
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<h3>base area</h3>
Here, the base of the prism is a rectangle with a semicircle on top. The circle has a diameter of 9 mm, so a radius of 4.5 mm. The area of the semicircle is ...
A = 1/2πr² = 1/2π(4.5 mm)² ≈ 31.809 mm²
The area of the rectangle is the product of its length and width.
A = LW = (9 mm)(6 mm) = 54 mm²
So, the total base area is ...
31.809 mm² +54 mm² = 85.809 mm²
<h3>prism volume</h3>
The prism volume is this area multiplied by the length of the figure:
V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³
The volume of the figure is about 944 mm³.
Answer:
$12
Step-by-step explanation:
42 - 6 = 36
36/3
12
