Answer:
Step-by-step explanation:
a)
i)
<u>Use the law of cosines:</u>
ii)
<u>Use the law of sines:</u>
- sin ∠A / PB = sin ∠P / AB
- sin ∠A / 100 = sin 80 / 107.31
- sin ∠A = 100 sin 80 deg / 107.31
- sin ∠A = 0.92
- ∠A = arcsin 0.92
- ∠A = 67° (rounded)
iii)
<u>Bearing of B from A:</u>
b)
<u>PB is longer distance. Time to reach B:</u>
- t = d/s
- t = 100/20 = 5 hours
<u>The speed s of the slower ship:</u>
- s = d/t
- s = 60/5 = 12 km/h
Answer:
Step-by-step explanation:
The volume of a cylinder is:
where is the radius and is the height.
The height is 4 inches greater that the radius, so:
Substituting this in the formula for volume:
the volume is
thus:
Dividing everything between pi:
We can see that the solution for this is
since
We have the radius, now we find the height:
Answer:
The area of the shaded region is about 38.1 square centimeters.
Step-by-step explanation:
We want to find the area of the shaded region.
To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.
The given circle has a radius of 6 cm.
And the given sector has a central angle of 150°.
The area for a sector is given by the formula:
In this case, r = 6 and θ = 150°. Hence, the area of the sector is:
Now, we can find the area of the triangle. We can use an alternative formula:
Where a and b are the side lengths, and C is the angle between them.
Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.
And the angle C is 150°. Hence, the area of the triangle is:
The area of the shaded region is equivalent to the sector minus the triangle:
Therefore:
Use a calculator:
The area of the shaded region is about 38.1 square centimeters.
Answer:
225600
Step-by-step explanation:
Simple interest formula:
A = P(1 + rt)
A = final amount
P = initial principal balance
r = annual interest rate
t = time (in years)
So...
A = 600(1 +(75 x 5) )
75 x 5 = 375
1 + 375 = 376
600 x 376 = 225600
A = 225600
Answer:
2.2
Step-by-step explanation: