A swimmer takes a running jump off a pier. The path of the swimmer can be modeled by the equation h=-0.1d^2+0.1d+3, where h is the height (in feet) and d is the horizontal distance (in feet). How far from the pier does the swimmer enter the water?

6 feet from the pier

Step-by-step explanation:

The path of the swimmer can be modeled by the equation

where h is the height (in feet) and d is the horizontal distance (in feet).

Find d, when h is equal to 0 (when the swimmer enters the water):

The distance cannot be negative, so

feet

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).