The course for a boat race starts at point A and proceeds in the direction of S52'E for 1 hour at 8 knots to point B and then in the direction S50°W for 1 hour at 4.5 knots to point C and finally back to A. Find the total distance of the race and find the compass bearing from point A to point to the nearest whole degree.

20.823 nautical miles

S20°E

Step-by-step explanation:

I assume you mean ° (degrees), not ' (minutes).  There are 60 minutes in 1 degree.

S52°E means "south, 52° east", or 52° east of south.

S50°W means "south, 50° west", or 50° west of south.

1 knots = 1 nautical mile / hour, so the boat first travels 8 nautical miles from A to B, then 4.5 nautical miles from B to C, then finally back to A.

If we say A is at the origin, then the coordinates of B are:

(8 sin 52°, -8 cos 52°)

And the coordinates of C are:

(8 sin 52° − 4.5 sin 50°, -8 cos 52° − 4.5 cos 50°)

(2.857, -7.818)

So the distance from A to C is:

x = √(2.857² + (-7.818)²)

x ≈ 8.323

And the total distance of the race is:

d = 8 + 4.5 + 8.323

d = 20.823

The compass bearing from A to C is:

θ = atan(2.857 / 7.818)

θ ≈ S20°E

answer: standard form is ax^2 + bx + c = 0

step-by-step explanation:

standard form is ax^2 + bx + c = 0

(2x + 1)(x - 2) = 0

distribute to get into standard form

2x^2 - 4x + x - 2 = 0

2x^2 - 3x - 2 = 0

a = 2, b= -3, c = -2

a is your answer

if she was to only spend a dollar she can get 1lb

step-by-step explanation: