A dolphin jumping out of the water follows a path described by
h = − (x2 − 10x + 16), where h is the vertical height, in metres, and x metres is the horizontal distance travelled.
a) How far horizontally does the dolphin travel out of the water?
Oh, we're talking about a jumping dolphin now? That's quite a leap in conversation! Anyway, let's get to the question.
To find out how far horizontally the dolphin travels out of the water, we need to look for the values of x where h equals zero. Why? Well, when h is zero, it means the dolphin is at ground level, or the water in this case.
So, let's set h = 0 and solve for x:
0 = -(x^2 - 10x + 16)
Now, we can factor this equation:
0 = -((x - 2)(x - 8))
We can see that the equation would be equal to zero if either (x - 2) = 0 or (x - 8) = 0.
So, the dolphin travels horizontally when x = 2 or x = 8.
Therefore, the dolphin travels 2 meters and 8 meters horizontally out of the water.
Hope that answers your question, and I hope the dolphin remembered to bring a towel!
To find out how far horizontally the dolphin travels out of the water, we need to determine the horizontal distance at which the dolphin reaches a vertical height of zero.
Given the equation for the path of the dolphin:
h = -(x^2 - 10x + 16)
To find the horizontal distance at which the dolphin reaches a height of zero (h=0), we can set the equation equal to zero and solve for x:
0 = -(x^2 - 10x + 16)
Let's solve for x by factoring the equation:
0 = -(x-2)(x-8)
Setting each factor equal to zero:
x-2 = 0 or x-8 = 0
Solving for x:
x = 2 or x = 8
Therefore, the dolphin travels horizontally for a distance of 2 meters and 8 meters out of the water.
To find how far horizontally the dolphin travels out of the water, we need to determine the value(s) of 'x' when the dolphin reaches its maximum height or when it returns to the water level (h = 0).
Step 1: Set the equation equal to zero:
0 = -(x^2 - 10x + 16)
Step 2: Solve the quadratic equation:
x^2 - 10x + 16 = 0
We can solve this equation by factoring or by using the quadratic formula.
Factoring method:
(x - 2)(x - 8) = 0
From this equation, we can determine that either (x - 2) = 0 or (x - 8) = 0.
So, x = 2 or x = 8.
Step 3: Determine the horizontal distance travelled by the dolphin.
The dolphin will travel out of the water from x = 2 meters to x = 8 meters horizontally. Therefore, the dolphin travels a distance of 8 - 2 = 6 meters horizontally out of the water.
h(x) = 0 when x = 2 or 8
so the dolphin is in the air for 6 meters