eskansepehr
Calculators
General
Algebra
Geometry
Coordinate-geometry
Statistics
Calculus
Qna
Math
eskansepehr
eskansepehr
Home
General
Algebra
Geometry
Coordinate-geometry
Statistics
Calculus
Qna
Math
MATH SOLVE
Home
General
The rate of change is constant in each table. Find the rate of change. Explain what the rate of chan...
5 months ago
Q:
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. time (hours) 4, 6, 8, 10 distance (miles) 212, 318, 424, 530
Accepted Solution
A:
[tex]\bf \begin{array}{ccll} \stackrel{\stackrel{x}{hours}}{time}&\stackrel{\stackrel{y}{miles}}{distance}\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 4&212\\ \boxed{6}&\boxed{318}\\ 8&424\\ \boxed{10}&\boxed{530} \end{array}\\\\ -------------------------------[/tex]
[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ 318}})\quad % (c,d) &({{ 10}}\quad ,&{{ 530}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{530-318}{10-6}\implies \cfrac{212}{4} \\\\\\ \stackrel{\textit{average rate of change}}{\cfrac{53}{1}}[/tex]
recall the top is distance, and the bottom is hours, so 53 miles for every 1 hour.Β So the object or vehicle is moving at 53 mph on average.