Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands
on the ground above. The path of the rock can be modeled by the equation y = 0.005x + 0.41x 5.1, where x is the horizontal distance of the rock, in feet, from Landon and y is the height, in feet, of the rock above the ground. How far horizontally from Landon will the rock land?
1 answer:
We can model the path of the stone as shown in the diagram below. The horizontal distance is shown between the two point on the x-axis which values we can find by solving the quadratic equation
The easiest method to use is the Quadratic Formula
Substitute a, b, and c into the formula, we obtain
and 
and the distance in between is 162.6 ft
The easiest method to use is the Quadratic Formula
Substitute a, b, and c into the formula, we obtain
You might be interested in
Answer:
The rectangles that have exactly 100 squares are 1 by 100 4 by 11 and 5 by 8
Step-by-step explanation:
The given parameters are;
A 2 by 3 rectangle contains 8 squares
A 3 by 4 rectangle contains 20 squares
A 4 by 6 rectangle contains 50 squares
We note that the number of squares varies proportionately to the increase in the dimension of the rectangle, that is we have;
2 by 3 rectangle contains 8 squares
3 by 4 rectangle contains 20 squares increase by 12 = 3 × 4
4 by 5 rectangle contains 40 squares increase by 20 = 4 × 5
The number of squares formed can therefore be arranged in a matrix as follows(please see attached matrix);
Column, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
Row
1
2
3
4
5
6
7
8
9
10
11
It will be observed that after reaching a point where the row and column are equal, (x, x) the rate of increase in the number of squares become constant and equal to x × ((x - 1) × 0.5) + 1) = x × (x + 1)/2
From the matrix, the rectangles that have exactly 100 squares are 1 by 100 4 by 11 and 5 by 8 and there are no more as presented in the attached matrix, the number of squares formed keeps increasing for each column and row added.
