Step-by-step explanation:
Recall that for a quadratic equation y = ax² + bx + c in the X-Y plane, the x-location of the vertex (i.e maximum or minimum point) is given by
x @vertex = -b/2a
in this case your quadratic equation is
h = 4 + 20t - 5t² (rearranging in the form y = ax² + bx + c )
h = - 5t² + 20t + 4
hence a= -5, b = 20 and c = 4
applying the formula for vertex
t @ vertex = -b /2a = -(20) / (2)(-5) = -20/-10 = 2
therefore t = 2
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⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛free points thanks
Assuming that the sides of the box are square (having 90° angles on all four corners), then it should be relatively easy for us to find the length of the box, given the perimeter and the length of one side.
We know the length of all sides combined is 42 inches, and that the length of one side is 9 inches. With a rectangular prism, the length of one side is the same as the length of the opposite side, so there are two sides that measure 9 inches.
All we need to do to find the measure of both the other sides' lengths is subtract the known lengths from the total length.
9 + 9 = 18
42 - 18 = 24
So the rest of the side lengths added together is 24 inches.
There are two sides left, so all we have to do is divide by 2 to find the length of the box.
24 / 2 = 12
The length of Kate's jewelry box is 12 inches.
Hope that helped =)
