Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), x seconds after diving, is modeled by g(x)=(1)/(20)x(x-100) What is the lowest altitude Guillermo will reach? meters relative to sea level

Question

Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level),  x seconds after diving, is modeled by  g(x)=(1)/(20)x(x-100) What is the lowest altitude Guillermo will reach? meters relative to sea level

Bytelearn · Accepted Answer

Find Minimum Value: To find the lowest altitude Guillermo will reach, we need to find the minimum value of the function g(x)=(1/20)x(x-100). This is a quadratic function, which is parabolic in shape and opens upwards since the coefficient of x^2 is positive. The minimum value of the function occurs at the vertex of the parabola.Calculate Vertex: The vertex of a parabola given by the function f(x) = ax^2 + bx + c is at the point (h, k), where h = -b/(2a). In the case of g(x), we can rewrite the function in the form of ax^2 + bx + c to find a and b. g(x) = (1/20)x(x-100) = (1/20)x^2 - (1/20)*100x = (1/20)x^2 - 5x. Here, a = 1/20 and b = -5.Find x-coordinate: Now we calculate the x-coordinate of the vertex using the formula h = -b/(2a). h = -(-5)/(2*(1/20)) = 5/(1/10) = 5*10 = 50.Find y-coordinate: The x-coordinate of the vertex is 50. To find the y-coordinate, which is the minimum altitude, we substitute x = 50 into the function g(x). g(50) = (1/20)*50*(50-100) = (1/20)*50*(-50) = -125.Final Altitude: The lowest altitude Guillermo will reach is -125 meters relative to sea level.

Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), $x$ seconds after diving, is modeled by $\newline$ $g(x)=\frac{1}{20}x(x-100)$ $\newline$ What is the lowest altitude Guillermo will reach? meters relative to sea level

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Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), xxx seconds after diving, is modeled by\newlineg(x)=120x(x−100)g(x)=\frac{1}{20}x(x-100)g(x)=201​x(x−100)\newlineWhat is the lowest altitude Guillermo will reach? meters relative to sea level

Guillermo is a professional deep water free diver. His altitude (in meters relative to sea level), $x$ seconds after diving, is modeled by $\newline$ $g(x)=\frac{1}{20}x(x-100)$ $\newline$ What is the lowest altitude Guillermo will reach? meters relative to sea level