Hi there
So, if the track is 1/8 of a mile, let's call every lap a "one-eighth mile" run. We know John ran 24 laps, or that he ran 24 "one-eighth miles," just consecutive, one right after another. Let's stop worrying about rates or tricks or math for a second, and just ask: how many real miles is 24 "one-eighth" miles? We know it's less than 24---a lot less, since you have to go around 8 times just to get to 1 mile. Well wait, if we go around 8 times, we get 1 mile. That means if we go around 28, or 16 times, we get 2 miles; And let's just think to the next full mile---if we go 38, or 24 times, we get 3 miles. He did go around 24 times, so he must have run 3 miles on a 1/8 track.
Division and multiplication are inverses of each other. So we solved this by looking for an intuition for how many full miles corresponded to how many laps, with a bunch of steps of multiplication. But you can cut right to the chase and solve it faster with division---24 laps * 1 mile per 8 laps, means:
total distance = 24 Lap (1 mi / 8 Lap) total distance = 24/8 total distance = 3
Answer:
45 degrees
Step-by-step explanation:
A straight line is an angle with a measure of 180°, but becasue it looks like we have two angles that create the 180° angle, therefore, it is a supplementary angle.
Knowing this
2X = 90° (right angle)
so (2X) + (2X) = 180° (supplementary angle)
Therefore, to find X you can do
2X = 90
divide by 2 on both sides (to isolate the variable we are trying to find which is X)
and you get....
X= 45 becasue 2 times 45 equals 90
answer: X=45°
Answer:
-3, 1
Step-by-step explanation:
f(x) = 3(x − 1)(x + 3)
To find the x intercepts, set the equation equal to zero
0 = 3(x − 1)(x + 3)
Using the zero product property
x-1 = 0 x+3 =0
x=1 x=-3
Answer:
The drift angle is approximately 7.65° towards the East from the plane's heading
Step-by-step explanation:
The speed of the plane = 350 mph
The direction in which the plane flies N 40° E = 50° counterclockwise from the eastern direction
The speed of the wind = 40 mph
The direction of the wind = S 70° E = 20° clockwise from the eastern direction
The component velocities of the plane are;
= (350 × cos 50)·i + (350 × sin 50)·j
= (40 + cos 20)·i - (40 × sin 40)·j
The resultant speed of the plane = + = 265.915·i +242.404·j
The direction the plane is heading = tan⁻¹(242.404/265.915) ≈ 42.35°
Therefore, the drift angle = Actual Angle - Direction of the plane = 50 - 42.35 ≈ 7.65° towards the East
