For a person of height h (in inches), a healthy weight W (in pounds) is one that satisfies this system of inequalities:

W is greater than or equal to (19h^2)/703 and W is less than or equal to (25h^2)/703

Graph the system for 0 is less than or equal to h which is less than or equal to 80. What is the range of healthy weights for a person 67 inches tall? **Note** ^ means "to the power of."

we have

19h^2/703 <= w <= 25h^2/703

If h=67, we have

121.3 <= w <= 159.6

Personally, I think that the formula is bogus, even in principle, since volume goes up as the cube of the height, not the square.

To graph the system of inequalities, we need to plot the functions

W = (19h^2)/703 and W = (25h^2)/703 on a coordinate plane.

First, let's solve for h in terms of W for both equations:

(19h^2)/703 = W
=> h^2 = (703W)/19
=> h = sqrt((703W)/19)

(25h^2)/703 = W
=> h^2 = (703W)/25
=> h = sqrt((703W)/25)

Now, let's plot these functions on the coordinate plane.

On the x-axis, we will plot h (height) and on the y-axis, we will plot W (weight).

For h = 0 to h = 80 (inclusive), plot points on the graph using the equations above. Connect the dots to obtain the graphs of the two functions.

Next, we need to shade the region between the two functions, as we are looking for weights that satisfy both inequalities.

Since we are interested in finding the range of healthy weights for a person who is 67 inches tall, we can substitute h = 67 into the inequalities:

W >= (19(67^2))/703
=> W >= 115.95

W <= (25(67^2))/703
=> W <= 149.91

Therefore, the range of healthy weights for a person 67 inches tall is 115.95 lbs to 149.91 lbs.