A drone flies in a circular path around an object that is 100 feet east and 50 feet north of the drone operator. The drone's path takes it over a point that is 40 feet east and 30 feet south of the drone operator. Find an equation for the drone's path. Does the drone cross a north-south line through the operator's position? If so, where? If not, explain why. Suppose the drone operator is facing the object. Is the drone ever "behind" the drone operator? Why/why not?

See below

Step-by-step explanation:

Let's plot the points for visibility

The path makes a line. The equation in slope-intercept form:

Slope:

y -intercept:

The equation:

Questions:

Does the drone cross a north-south line through the operator's position?

Suppose the drone operator is facing the object. Is the drone ever "behind" the drone operator?

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

55? i think maybe

step-by-step explanation: