Finding the Actual Speed and Direction of an Aircraft ABoeing 747 jumbo jet maintains a constant airspeedof 550 miles per hour (mph) headed due north. Thejet stream is 100 mph in the northeasterly direction.(a) Express the velocity va of the 747 relative to the air andthe velocity vw of the jet stream in terms of i and j.(b) Find the velocity of the 747 relative to the ground.(c) Find the actual speed and direction of the 747 relative tothe ground.
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
Finding the Actual Speed and Direction of an Aircraft A
Boeing 747 jumbo jet maintains a constant airspeed
of 550 miles per hour (mph) headed due north. The
jet stream is 100 mph in the northeasterly direction.
(a) Express the velocity va of the 747 relative to the air and
the velocity vw of the jet stream in terms of i and j.
(b) Find the velocity of the 747 relative to the ground.
(c) Find the actual speed and direction of the 747 relative to
the ground.
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