The safety inspector notes that ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so ray can include it in his coaster plan. f(x)=4x^2+5x+2

vertex: (-5/8, 7/16)axis of symmetry: x = -5/8

Step-by-step explanation:

For quadratic ax²+bx+c, the axis of symmetry is located at x=-b/(2a).

Here, we have a=4, b=5, so the axis of symmetry is ...

... x = -5/(2·4) = -5/8

The vertex y-value will be f(-5/8).

... f(-5/8) = (4·(-5/8) +5)·(-5/8) +2 = (5/2)·(-5/8) +2 = -25/16 +32/16

... f(-5/8) = 7/16

The axis of symmetry is x = -5/8; the vertex is (-5/8, 7/16).

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )