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SpyIntel [72]
3 years ago
13

Find the shaded area of the basketball court to the nearest foot.

Mathematics
1 answer:
Trava [24]3 years ago
5 0
So the image consists of 1 rectangle and half a circle.
Rectangle - 12*19 = 228Half a circle - \pi r^2 =  \pi 6^2 = 36 \pi /2 = 18 \pi
In the end there are 2 rectangles (2*228 = 456) and 1 full circle (18*2 = 36), which makes the shaded area 456ft and 36\pi
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Triangle ABC has AB=5, BC=7, and AC=9. D is on AC with BD=5. Find the length of DC
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Answer:

DC=\frac{8}{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

<em>In the right triangle ABM</em>

Applying the Pythagorean Theorem

BM^2=AB^2-AM^2

we have

AB=5\ units\\AM=x\ units

substitute

BM^2=5^2-x^2

BM^2=25-x^2 -----> equation A

<em>In the right triangle BMC</em>

Applying the Pythagorean Theorem

BM^2=BC^2-MC^2

we have

BC=7\ units\\MC=AC-AM=(9-x)\ units

substitute

BM^2=7^2-(9-x)^2

BM^2=49-(81-18x+x^2)  

BM^2=49-81+18x-x^2

BM^2=-x^2+18x-32 ----> equation B

equate equation A and equation B

-x^2+18x-32=25-x^2

solve for x

18x=25+32\\18x=57\\\\x=\frac{57}{18}

Simplify

x=\frac{19}{6}

<em>Find the length of DC</em>

DC=AC-2x

substitute the given values

DC=9-2(\frac{19}{6})

DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units

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