Jerrad's Junkyard of Math
These are problems that are slightly difficult,and I have provided the logical solutions for them.  

IT"S A WALK IN THE PARK!!! 
 

 
There are a range of equations, including, literal, standard, and others. 

STANDARD EQUATION: 

y-y+ y- y= y 
   2   3  4    5 
 

60(Y+ Y - Y) = (Y)60 
     2    3    4        5 

60Y - 30Y + 20Y - 15Y = 12Y 

(-12Y)+  35Y=12Y-(12Y) 
 

 23Y=  0 
  23     23 

Y=0 
 

  Difficulty Rating: 

First, multiply by the LCD (least common denominator). In this case 60. 
 

Add your like terms. 
 

Subtract 12Y from both sides. 

Divide by 23 on both sides. 
 

Y=0 AND YOU WIN!!!! 

 
 
Next, we move on to a function for a line. 
It's not hard. 
We will write it in standard form, slope-intercept form, and point-slope form. 
 
Difficulty Rating
 
 
 
Define a line through point (-2,7) and perpendicular to 
y = 2x+5 
 

Y1- Y2= m(X1-X2)

Y1-7= -1(X1+2)
            2
 

Y= -1 X+b
        2

7= (-1 )-2+b
        2

(-1)+7= 1+b+(-1)

6=b

Y=-1 X + 6
       2
 

(2)(Y)=(-1X + 6)(2)
               2

(-X)+2Y=X+6-(X)
 

(-1)(-X+ Y) =(6)(-1)
 
 

X-Y=-6
 
 

 We have a point and the means to fine the slope, so it is easiest to start in point-slope form. 

The slope of a perpendicular line is the negative reciprocal of the original. The negative reciprocal of 2 is -1/2 
  
So in slope intercept form this function is.

There's one

Next we move to slope intercept form.

We know the slope still.

The Y-intercept is easy to attain.  Simply use (-2,7) as your point

SOLVE.

There you go.
 

The last one is standard form. Simply solve again

First we multiply by two, because we would have to do it later anyway, and it's tough to type fractions.

Subtract X
 

The X can not be negative so we multiply by -1.
 

THATS ALL THREE OF THEM!!!
 
 
 
Last, and probably most, we tackle a 
 
 

serious literal equation.  Just remember, the rules of algebra still apply.
Difficulty Rating:
V2=u2 + 2as      :U

(-2as)+ V2=u2 + 2as-(2as)
 
 

(V2-2as)1/2=(u2)1/2
 
 
 
 
 

(V2-2as)1/2 = (u2)1/2
 

 We're solving this equation for U.

This is the formula for velocvity squared, it seems like it will be hard, but I can do it in two steps.

First subtract 2as.
 

Now all we have to do is square root both sides.  Pretty darn simple huh.
 
 

***Raising something to a half power is the same as taking a square root.

There you have it.
 
 

 

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