Mathematics: If the diameter of a large trampoline is 26 ft., then the radius must be A. 81.64ft B. 52ft C. 40.82ft D. 13ft

If the diameter of a large trampoline is 26 ft.,

Ответ:

ktenz

19.03.2022

a=-0.35747

Step-by-step explanation:

We know that all the vertices of the isosceles trapezoid lie on the parabola, and the points A and D lie along the x-axis, i.e at y=0

Therefore points A and D are located where

a(x+1)(x-5)=0

A=x=-1

D=x=5

Now we need to find the coordinates of point C; we already have its y-coordinate (it's y=2 ), and looking at the figure attached we see that the x-coordinate of point C is $\frac{2}{tan(60^o)}$ farthar from the coordinate of point C; thus

$C_x=\frac{2}{tan(60^o)}-1=0.1547$

Therefore the coordinates of C are C=(0.1547,2)

Now this point C lies on the parabola, and therefore must satisfy the equation y=a(x+1)(x-5):

2=a(0.1547+1)(0.5147-5)

$\therefore a=\frac{2}{(0.1547+1)(0.5147-5)} =-0.35747\\\\\boxed{a=-0.35747}$

An isosceles trapezoid abcd with height 2 units has all its vertices on the parabola y=a(x+1)(x−5).

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If the diameter of a large trampoline is 26 ft., then the radius must be A. 81.64ft
B. 52ft
C. 40.82ft
D. 13ft

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