You’ve explored a variety of trigonometric applications and studied different coordinate systems in the process, namely the Cartesian (rectangular), the polar, and the complex coordinate systems. What do these coordinate systems have in common, and how is each system unique? How are the absolute value of an imaginary number, the magnitude of a force, and the distance between two points related to one another? What are the advantages and disadvantages of each system?

Following are the solution to the given points:

Step-by-step explanation:

Its cartesian method, often named global positioning structure, could be applied on two axes of coordinate named x-axis and y-axis that are parallel to each other In the lengthy curve or velocity curves on the perpendicular reference axis could be drawn of the length of y-axis or period of its x-axis.

Polar Coordination System- let's use an instance to grasp this. They find the equation for a circle of the center at origin (0,0).

. Throughout the rectangle method, the positions on the circle shall have the shape (x,y) however the point mostly on sphere throughout the situation of the linear form (rcosθ,rsinθ) where 'r'

will be the circle diameter, can be indicated. They can change the equation of the cycle provided for polar coordinates of rectangular cordons by removing the point x=rcosθ and y=rsinθ. Throughout the case of a difficult coordinate, since we realize an impose tariffs comprises a true and false element where the real component is placed on the x-axis as well as the imaginary element on the y-axis. The descriptive statistics of the differential equation has been its distance from the center.

The common feature of its three coordinates is they're all parallel to one another on the co-ordinate axis. Its unique thing is that the rectangular co-ordinating system involves figures, whereas the triangular co-ordinates system contains a direction of the direction, because as co-ordinates (rcosθ,rsinθ)  will be of the shape.

In such a complex co-ordination system, it appears like such a cartesian co-ordination scheme because as the imagination component is tracked to a vertical axis, the actual component to be tracked to both the x plane measurement is comparatively easier with different co-ordinate horizontal plane, and representation of the specific issue is easier that may be one of the advantages.

a negative exponent is translated as follows:

so, we have

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct