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Lena [83]
3 years ago
6

Please help!!! 15 points problem below

Mathematics
1 answer:
MissTica3 years ago
5 0

We are given height function of the bridge

h(x) =-0.5(x-4)^2 +2.

Where height is the height of the bridge in feet and x is the distance between two bases.

We have height =0 on the base of the bridge. In order to find the both bases, we need to plug h(x) as 0 and solve for x.

-0.5(x-4)^2 +2 = 0

\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}

-0.5\left(x-4\right)^2+2-2=0-2

-0.5\left(x-4\right)^2=-2

\mathrm{Multiply\:both\:sides\:by\:}10

-0.5\left(x-4\right)^2\cdot \:10=-2\cdot \:10

-5\left(x-4\right)^2=-20

\mathrm{Divide\:both\:sides\:by\:}-5

\frac{-5\left(x-4\right)^2}{-5}=\frac{-20}{-5}

\left(x-4\right)^2=4

Taking square root on both sides, we get

x-4=\sqrt{4}

\:x-4=\sqrt{4} \ and \ x-4=-\sqrt{4}

x-4=2 \\x-4=-2

x=6,\:x=2

We got horizontal distances 2 feet and 6 feet.

Therefore, correct option is D.

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