A "super ball" dropped from a height of x feet bounces to a height y that is 80% of x.
Can anyone please teach me how to find its numerical, algebraic, and graphical representations? Thanks a lot!!!
After n bounces, y(n) = X(0)*0.8^n
where X(0) is the initial height from which it is dropped
Since they don't tell you what X(0) is, you could make a graph of y/X(0) vs n.
can you please tell me the differences and examples of the numerical,algebraic, and graphical representations?
Numerical could be a table of n and y(n)/X(0) values
Algebraic could be the formula y(n)/X(0) = (0.8)^n
Graphical could be a graph of y(n)/X(0) vs n
2cos*2x-cosx=1 find all solutions to the equation on the domain [0,2ð]
i got ð/4, 7ð/4, 3ð/4, and 5ð/4 but only got two out of four points... what did i do wrong?
Certainly! Let's break it down into numerical, algebraic, and graphical representations.
Numerical Representation:
To find the numerical representation, we need a specific value for the height. Let's suppose the height of the ball, x, is 10 feet. According to the given information, the ball will bounce to a height, y, that is 80% of x.
So, y = 0.8 * x
Plugging in the value of x as 10, we get:
y = 0.8 * 10
y = 8
Therefore, when the height of the ball is 10 feet, it will bounce to a height of 8 feet.
Algebraic Representation:
To find the algebraic representation, we need to represent the relationship between the height of the ball before and after the bounce.
Let's use the variables x for the initial height and y for the height after the bounce. According to the given information, y is 80% of x. We can write this relationship as the following equation:
y = 0.8x
This equation represents the algebraic representation of the relationship between the height of the ball before and after the bounce.
Graphical Representation:
To visualize the relationship graphically, we can plot a graph with the height before the bounce (x) on the x-axis and the height after the bounce (y) on the y-axis.
Since we have an equation y = 0.8x, we can plot multiple values of x and find the corresponding values of y.
Let's choose a few values for x, such as 5, 10, 15, and 20 feet. We can now substitute these values into the equation and plot the corresponding points on the graph.
For example, when x = 5 feet, y = 0.8 * 5 = 4 feet. So, we would plot the point (5, 4) on the graph.
Similarly, we can compute the values of y for the other chosen values of x and plot the corresponding points on the graph. Connecting these points will give us a straight line.
The resulting graph will be a line passing through the origin (0,0) with a slope of 0.8. Every point on this line represents the height of the ball before and after the bounce, satisfying the given relationship.
I hope this helps to provide a comprehensive explanation of the numerical, algebraic, and graphical representations of the "super ball" bounce scenario!