Alan

"Use a graphing calculator or other technology to answer the question.

Which quadratic regression equation best fits the data set?"

You can use the constant acceleration equation: v = u + a*t  where u = initial vertical velocity = 2.37*sin(56.6°) m/s here; v = final vertical velocity = -u (when she hits  the ground again); a = -9.8m/s² (acceleration due to gravity); t = time in the air:

 -2.37*sin(56.6°) = 2.37*sin(56.6°) - 9.8*t

t = 2*2.37*sin(56.6°)/9.8 s   

As follows:

Answer to 4_39:

"X/6 + X/3 =3

 If i make the denominator on the left 6, do I need to do the same on the right hand side?"

The simplest way is to multiply every term (on the RHS as well as the LHS) by the lowest common denominator of the 6 and the 3 (in this case that is just 6).

"another example is 5x/3 - 3x/4=11/6"

In this case multiply every term by the lcd of 3 and 4 (namely 12).

a. The top of the graph illustrated has a value of y = 4, so you need to solve the equation (x-2)² - 1 = 4 (this is a quadratic equation and will produce two values for x). 

b. Assuming this means the intersection of the curve with the horizontal line at y = 5, there will be two points of intersection.

c.  Since 'a' gives the y-coordinate of the vertex (lowest point), then when a>0 the curve will not intyersect the x-axis.

Like so:

\(\frac{x}{y}\times\frac{y}{z}=\frac{2}{3}\times\frac{7}{5}\\\frac{x}{z}=\frac{14}{15}\\\frac{z}{x}=\frac{15}{14}\)     

Exponential fit:

Notice that, because the fit was done using the log of y, we need to use the log version to determine the coefficient of determination.

Quadratic fit:

Linear fit: