You see a firefighter aim a fire hose from 4 feet above the ground at a window that is 26 feet above the ground. The equation h=-0.01d^2+1.06d+4 models the path of the water when h equals height in feet. Estimate, to the nearest whole number, the possible horizontal distances (d) in feet between the firefighter and the building.

been out of school for a while and can remember how to do this. if cant give the answer, instructions on how to would be much appreciated.

26=-.01d^2+ 1.06d+ 4

.01d^2-1.06d -22=0
multiplying by 100
d^2-106d-2200=0

Now use the quadratic equation..

d=(106 +- sqrt (106^2+8800))/2

d= 53+- 1/2 sqrt (94)

You can work that out, normally the firefighter would work at the shorter distance, but both are possible.

To find the possible horizontal distances (d) between the firefighter and the building, we need to solve the equation h = -0.01d^2 + 1.06d + 4 for d.

Let's rearrange the equation to make it easier to work with:
0.01d^2 - 1.06d - 4 + h = 0

Since we need to estimate the values, we can use the quadratic formula to solve for d:

d = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 0.01, b = -1.06, and c = -4 + h. Substituting these values into the quadratic formula, we get:

d = (1.06 ± √(1.06^2 - 4 * 0.01 * (-4 + h))) / (2 * 0.01)

Now, we can plug in the values and estimate the range of possible values for d. Let's assume h is at its maximum value of 26 feet:

d = (1.06 ± √(1.06^2 - 4 * 0.01 * (-4 + 26))) / (2 * 0.01)

d = (1.06 ± √(1.06^2 - 4 * 0.01 * 22)) / (2 * 0.01)

Now, we can simplify and calculate the two possible values of d:

d = (1.06 ± √(1.1236 - 0.88)) / 0.02

d = (1.06 ± √(0.2436)) / 0.02

d ≈ (1.06 ± 0.493) / 0.02

Using the ± symbol, we get two possible values for d:

d ≈ (1.06 + 0.493) / 0.02 ≈ 77

d ≈ (1.06 - 0.493) / 0.02 ≈ 29

Therefore, the estimated possible horizontal distances (d) between the firefighter and the building are approximately 29 feet and 77 feet, rounded to the nearest whole number.

To estimate the possible horizontal distances (d) between the firefighter and the building, we need to solve the given quadratic equation: h = -0.01d^2 + 1.06d + 4.

Since the equation models the path of the water, we want to find the values of d for which h = 26. So we set h = 26 and solve for d.

-0.01d^2 + 1.06d + 4 = 26

Rearranging the equation, we have:

-0.01d^2 + 1.06d - 22 = 0

To solve this quadratic equation, we can use the quadratic formula:

d = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = -0.01, b = 1.06, and c = -22.

Plugging in the values, we get:

d = (-(1.06) ± √((1.06)^2 - 4(-0.01)(-22))) / 2(-0.01)

After evaluating the expression within the square root, we simplify further:

d = (-1.06 ± √(1.1236 - 0.88)) / -0.02

d = (-1.06 ± √(0.2436)) / -0.02

Now, calculate the square root:

d = (-1.06 ± 0.4935) / -0.02

Using the plus-minus symbol, we get two possible values of d:

d1 = (-1.06 + 0.4935) / -0.02 = 28.2765

d2 = (-1.06 - 0.4935) / -0.02 = 0.3315

Since we are looking for the horizontal distance, which is usually positive, we can discard the negative solution (d2 = 0.3315).

Therefore, to the nearest whole number, the possible horizontal distance between the firefighter and the building is approximately 28 feet.