Solution - Properties of a straight line

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "t2"   was replaced by   "t^2". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     h*(t)-(160*t-16*t^2)=0 

Step  1  :

Equation at the end of step  1  :

  ht -  (160t -  24t2)  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   ht + 16t² - 160t  =   t • (h + 16t - 160) 

Equation at the end of step  3  :

  t • (h + 16t - 160)  = 0 

Step  4  :

Theory - Roots of a product :

 4.1    A product of several terms equals zero. 

 When a product of two or more terms equals zero, then at least one of the terms must be zero. 

 We shall now solve each term = 0 separately 

 In other words, we are going to solve as many equations as there are terms in the product 

 Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

 4.2      Solve  :    t = 0 

  Solution is  t = 0

Equation of a Straight Line

 4.3     Solve   h+16t-160  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  h+16t-160  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when h = 0 the value of t is 10/1 so this line "cuts" the t axis at t=10.00000

  t-intercept = 160/16  =  10 

Calculate the X-Intercept :

When t = 0 the value of h is 160/1 Our line therefore "cuts" the h axis at h=160.00000

  h-intercept = 160/1  = 160.00000 

Calculate the Slope :

Slope is defined as the change in t divided by the change in h. We note that for h=0, the value of t is 10.000 and for h=2.000, the value of t is 9.875. So, for a change of 2.000 in h (The change in h is sometimes referred to as "RUN") we get a change of 9.875 - 10.000 = -0.125 in t. (The change in t is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = -0.125/2.000 = -0.062 

Geometric figure: Straight Line

1.   Slope = -0.125/2.000 = -0.062
2.   h-intercept = 160/1 = 160.00000
3.   t-intercept = 160/16 = 10
4.  t = 0