The base of a rectangle lies on the x-axis, while the upper two vertices lie on the parabola y = 13 − x2. Suppose that the coordinates of the upper right vertex of the rectangle are (x, y). Express the area of the rectangle as a function of x.

Respuesta :

Answer:

Area of Rectangle = [tex]26x - 2x^3[/tex]

Step-by-step explanation:

Rectangle two vertices lie on x axis ; two vertices lie on parabola [tex]y = 13 - x^2[/tex].

Supposing coordinates of upper right vertex of rectangle are P = [tex]x , y[/tex]

Due to parabola symmetry, width of rectangle is twice the distance  horizontal (X) axis distance between Y axis & point P.

Width of rectangle = [tex]2x[/tex]

Length of rectangle = [tex]y[/tex]  ; [tex]y = 13 - x^2[/tex]

Area of Rectangle = Length x Width

= [tex]2x (y)[/tex]

= [tex]2x (13 - x^2)[/tex]

= [tex]26x - 2x^3[/tex]

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