Question

Rui is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by: d(x)=\dfrac12x^2 -10xd(x)= 2 1 ​ x 2 −10xd, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 2, end fraction, x, squared, minus, 10, x How many seconds after diving will Rui reach his lowest altitude?

Answer 1

Rui will reach his lowest altitude in 10 seconds after diving.

Step-by-step explanation:

The altitude function d(x) is a quadratic function with a negative leading coefficient (½). This means it opens downwards, reaching its maximum (in this case, minimum altitude) at the vertex.

To find the time when Rui reaches his lowest altitude, we need to find the vertex of the parabola represented by d(x). The x-coordinate of the vertex is given by the formula:

x_vertex = -b / 2a

where a and b are the coefficients of the quadratic term (x^2) and the linear term (-10x) in d(x), respectively.

In this case, a = ½ and b = -10. Therefore:

x_vertex = -(-10) / (2 * ½) = 10

Therefore, Rui reaches his lowest altitude 10 seconds after diving, as indicated by the x-coordinate of the vertex.

Answer 2

Rui will reach his lowest altitude after 20seconds of diving

Step-by-step explanation:

Given the function that models the altitude of Rui at any time x expressed as:

d(x) = 1/2 x² - 10x

The height of rui at his lowest altitude will be zero. Substitute d(x) = 0 into the expression and get x

d(x) = 1/2 x² - 10x

0 = 1/2 x² - 10x

-1/2x² = 10x

1/2 x = 10

Multiply both sides by 2

x/2 × 2 = 10×2

x×1 =20

x = 20

Hence Rui will reach his lowest altitude after 20seconds of diving