Answer:
<em>A.</em>
<em>The student made an error in step 3 because a is positive in Quadrant IV; therefore, </em>
<em />
Step-by-step explanation:
Given



Required
Where and which error did the student make
Given that the angle is in the 4th quadrant;
The value of r is positive, a is positive but b is negative;
Hence;

Since a belongs to the x axis and b belongs to the y axis;
is calculated as thus

Substitute 


Rationalize the denominator


So, from the list of given options;
<em>The student's mistake is that a is positive in quadrant iv and his error is in step 3</em>
Given :
Nathan smiled at 50 people one day and recorded that 36 people smiled back at him.
To Find :
How many people should Nathan expect to return a smile if he smiles at 650 people over a period of time.
Solution :
Ratio of people smiled by total number of people is :

Now, it is given that we have to use the given conditions.
Therefore, ratio will be same :

Therefore, number of smiles Nathan expect to return is 468.
3x - 2y = 1
2x + 2y = 4
Add the second equation to the first
5x = 5
2x + 2y = 4
Divide the first equation by 5
x = 1
2x + 2y = 4
Subtract the first equation from the second
x = 1
x + 2y = 3
Subtract the first equation from the second again
x = 1
2y = 2
Divide the second equation by 2
x = 1
y = 1
<h3>
So, the solution is x = 1 and y = 1 {or: (1, 1)} </h3>
<span>Let the number of nickles be x
Let the number of pennies be y
Value Value
Type Number of of
of of EACH ALL
coin coins coin coins
-------------------------------------------
nickles x $0.05 $0.05x
pennies y $0.01 $0.01y
-------------------------------------------
TOTALS 56 ----- $1.52
The first equation comes from the second column.</span>