Create a triangle starting with the length of 540 coming out of SF to LA bearing 140.
This looks like it leaves SF in IV quadrant and enters LA in II quadrant. The wind will take the plane more to the east (right). Therefore the pilot must aim to the west (left) in order for the wind to push it to the intended destination of LA. The second side of the triangle should come out of LA from the II quadrant bearing 290. The length of this side is 60t (60 km/h * t = time flying). The third side of the triangle connects the first two. There for it comes out of SF at some unknown angle > 140 and connects with the 60t side. The length of this third leg is 640t. (640 km/h * t = time flying). The angle between the 540 side and the 60t side is 30. This is found because the 540 side enters LA in 2nd quadrant as 130 angle . The 60t side enters LA in 2nd quadrant as 160 angle. Using law of sin's: sin 30/640t = sin x/60t. The t's cancel and you are left with sin x = 3/64. When solving for the angle x you get x = 2.6867 degrees. Adding this to the bearing of 140, the compass bearing should be 142.6867 or 142.7 degrees. To find the value of t, you use the law of sin's to get sin 30/640t = (sin (180 - 30 - 2.6867))/540. Solving for t gives you: t = .7811. This is in hours. To convert to minutes multiply by 60 to get t = 46.87 minutes. Add this to the 2pm departure time to get 2:47 pm arrival time.
Answer:
<h3>
Any of them.</h3><h2>
a ∈ R</h2>
Step-by-step explanation:
-5x - 4y = 2a 4x - 5y = 2
-4y = 5x + 2a -5y = -4x + 2
y = (5x + 2a):(-4) y = (-4x + 2):(-5)
y = -⁵/₄x - ¹/₂a y = ⁴/₅x - ²/₅
m₁ = -⁵/₄, b₁ = -¹/₂a m₂=⁴/₅, b₂= -²/₅
-⁵/₄ ≠ ⁴/₅
Different slopes means that two lines have one point of intercept (no mater what the b's are). That means that the system of linear equations has exactly one solution for any value of a.
2 5/8 × 4 = 10 1/2
Charlie does not have enough wood because 10 1/2 is also equal to 10 4/8 and Charlie only has 10 3/8
hope this helped
Answer:
28
Step-by-step explanation:
You want the smaller of the two factors of 896 that have the ratio 8:7.
<h3>Setup</h3>
Let x represent the smaller of the two factors (the one we want to find). Then the larger factor is (8/7)x, and their product is ...
x(8/7)x = 896
(8/7)x² = 896
<h3>Solution</h3>
Multiplying by the inverse of the coefficient of x², we have ...
x² = (7/8)(896) = 784
x = √784 = 28 . . . . . . . . take square root
The smaller of the two numbers is 28.
__
<em>Additional comment</em>
The larger is (8/7)(28) = 32.
