Step-by-step explanation:
The wind has a speed of w and a direction α with the vertical. The x component of that speed is w sin α. The y component is -w cos α.
In order to stay on the north trajectory AB, the plane must have a horizontal speed of -w sin α. The plane's speed is v, so using Pythagorean theorem, the y component of the plane's speed is:
v² = (-w sin α)² + vᵧ²
v² = w² sin²α + vᵧ²
vᵧ = √(v² − w² sin²α)
The total vertical speed is therefore √(v² − w² sin²α) − w cos α.
If a is the length of AB, then the time is:
t = a / [√(v² − w² sin²α) − w cos α]
To rationalize the denominator, we multiply by the conjugate.
t = a / [√(v² − w² sin²α) − w cos α] × [√(v² − w² sin²α) + w cos α] / [√(v² − w² sin²α) + w cos α]
t = a [√(v² − w² sin²α) + w cos α] / (v² − w² sin²α − w² cos²α)
t = a [√(v² − w² sin²α) + w cos α] / (v² − w²)
They will have the same solution because the first equation of system b
is obtained by adding the first equation of system a to 4 times the
second equation of system a.
Answer: 250 mi
Step-by-step explanation:
Here we can think in a triangle rectangle:
The distance from Birmingham to Atlanta is roughly 150 mi, and this is one of the cathetus.
And the distance from Birmingham to Nashville is roughly 200 mi, this is the other cathetus of the triangle.
Now, the distance from Atlanta to Nashville will be the hypotenuse of this triangle rectangle.
Now we can apply the Pythagorean's theorem:
A^2 + B^2 = H^2
Where A and B are the cathetus, and H is the hypotenuse:
Then:
H = √(A^2 + B^2)
H = √(150^2 + 200^2) mi = √(62,500) mi = 250 mi
Then the estimated distance from Atlanta to Nashville is 250 mi
The answer is 7i because if you add 4+3i together as an absolute value, it equals to 7 plus the i is 7i
C, always go with supervisors
