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2 years ago

A water ballon is launched straight up. The balloons flight is modeled by the function h(t)=16t^2+192t

Mathematics

1 answer:

lubasha [3.4K]2 years ago

7 0

Answer:Step by Step Solution

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Rearrange:

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

h*(t)-(16*t^2+192*t)=0

STEP

Equation at the end of step 1

ht - (24t2 + 192t) = 0

STEP

Pulling out like terms

3.1 Pull out like factors :

ht - 16t2 - 192t = t • (h - 16t - 192)

Equation at the end of step

t • (h - 16t - 192) = 0

STEP

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-192 = 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-192 = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when h = 0 the value of t is 12/-1 so this line "cuts" the t axis at t=-12.00000

t-intercept = 192/-16 = 12/-1 = -12.00000

Calculate the X-Intercept :

When t = 0 the value of h is 192/1 Our line therefore "cuts" the h axis at h=192.00000

h-intercept = 192/1 = 192.00000

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 -12.000 and for h=2.000, the value of t is -11.875. So, for a change of 2.000 in h (The change in h is sometimes referred to as "RUN") we get a change of -11.875 - (-12.000) = 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

Slope = 0.125/2.000 = 0.062

h-intercept = 192/1 = 192.00000

t-intercept = 192/-16 = 12/-1 = -12.00000

t = 0

Step-by-step explanation:

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