Radio tower M 2 is located 200 miles due west of radiotower M 1 . The situation is illustrated in the figure shown, where a coordinate system has been superimposed. Simultaneous radio signals are sent from each tower to a ship, with the signal from M 2 received 500 microseconds before the signal from M 1 . Assuming that radio signals travelat 0.186 mile per microsecond, determine the equation of thehyperbola on which the ship is located.
Radio tower M 2 is located 200 miles due west of radiotower M 1 . The situation is illustrated in the figure shown, where a coordinate system has been superimposed. Simultaneous radio signals are sent from each tower to a ship, with the signal from M 2 received 500 microseconds before the signal from M 1 . Assuming that radio signals travelat 0.186 mile per microsecond, determine the equation of thehyperbola on which the ship is located.
Solution Summary: The author calculates the standard equation of a hyperbola: ca2a=500times 0.186
Radio tower M2 is located 200 miles due west of radiotower
M
1
. The situation is illustrated in the figure shown, where a coordinate system has been superimposed. Simultaneous radio signals are sent from each tower to a ship, with the signal from M2 received 500 microseconds before the signal from
M
1
. Assuming that radio signals travelat 0.186 mile per microsecond, determine the equation of thehyperbola on which the ship is located.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
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ANALYZING RELATIONSHIPS Describe the x-values for which (a) f is increasing or decreasing, (b) f(x) > 0 and (c) f(x) <0.
y Af
-2
1
2 4x
a. The function is increasing when
and
decreasing when
By forming the augmented matrix corresponding to this system of equations and usingGaussian elimination, find the values of t and u that imply the system:(i) is inconsistent.(ii) has infinitely many solutions.(iii) has a unique solutiona=2 b=1
if a=2 and b=1
1) Calculate 49(B-1)2+7B−1AT+7ATB−1+(AT)2
2)Find a matrix C such that (B − 2C)-1=A
3) Find a non-diagonal matrix E ̸= B such that det(AB) = det(AE)
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