paolaviviana

paolaviviana

16.03.2022 •

Mathematics

Explain how soil contributes to biodiversity, fighting diseases and agriculture

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Ответ:

aaqa3735

29.01.2020

a) 0 seconds.

b) The stunt diver is in the air for 2.81 seconds.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Height of the diver after t seconds:

h(t) = -4.9t^2 + 12t + 5

a) How long is the stunt diver above 15 m?

Quadratic equation with a < 0 , so the parabola is concave down, and it will be above 15m between the two roots that we found for h(t) = 15 . So

h(t) = -4.9t^2 + 12t + 5

15 = -4.9t^2 + 12t + 5

-4.9t^2 + 12t - 10 = 0

Quadratic equation with a = -4.9, b = 12, c = -10 . Then

$\Delta = 12^{2} - 4(-4.9)(-10) = -52$

Negative $\Delta$ , which means that the stunt diver is never above 15m, so 0 seconds.

b) How long is the stunt diver in the air?

We have to find how long it takes for the diver to hit the ground, that is, t for which h(t) = 0 . So

h(t) = -4.9t^2 + 12t + 5

0 = -4.9t^2 + 12t + 5

-4.9t^2 + 12t + 5 = 0

Quadratic equation with a = -4.9, b = 12, c = 5 . Then

$\Delta = 12^{2} - 4(-4.9)(5) = 242$

$x_{1} = \frac{-12 + \sqrt{242}}{2*(-4.9)} = -0.36$

$x_{2} = \frac{-12 - \sqrt{242}}{2*(4.9)} = 2.81$

Time is a positive measure, so we take 2.81.

The stunt diver is in the air for 2.81 seconds.

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