y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.

Mathematics

2 answers:

kirill115 [55]3 years ago

8 0

2 x-intercepts and the water is above 0 feet.

Lina20 [59]3 years ago

6 0

Answer: This parabola has 0.3875 x-intercepts,
representing the times when the dolphin's height above water is 
0 feet.

The x-intercept is the point where the graph crosses the x-axis, which is when the value is y=0.
The calculation for y=0 would be
Y = -16x2 + 32x - 10
0 = -16x2 + 32x - 10
-8x2 + 16x - 5=0

-b +-√(b^2-4ac) /2a=
-16 +-√(16^2-4(-8)(-5)) /2(-8) =
-16+- √(256-160/ -16 =
-16+- √(96/ -16 =
-16+- 9.8/ -16 =
x1= 0.3875
x2= -1.6125

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Answer:

Step-by-step explanation:

The right triangle on the right side of the figure has a height of 6 (two same sides lengths) and a base of 3.

x is the hypotenuse (side opposite of 90 degree angle).

We can use the pythagorean theorem to find x. The pythagorean theorem tells us to square each leg (height and base) of the triangle and add it. It should be equal to the hypotenuse square.

For this triangle it means, we square 6 and 3 and add it. It should be equal to x squared. Then we can solve. Shown below:

$6^2 + 3^2 = x^2\\36 + 9 = x^2\\45 = x^2\\x=\sqrt{45}$