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Sergio039 [100]
3 years ago
10

A water sprinkler has a range of 5 meters as shown. The jet of water from the sprinkler sweeps out at an angle of 85° as the noz

zle turns. Solve for the total area watered by the sprinkler. Use the value π = 3.14, and round your answer to one decimal place.
a. 15.6 Square Meters
b. 17.8 Square Meters
c. 18.5 Square Meters
d. 19.2 Square Meters

Mathematics
2 answers:
kipiarov [429]3 years ago
8 0

Answer:

C. 18.5 Square Meters

Hope it helps :)

telo118 [61]3 years ago
6 0
I found the image that accompanied this problem.
We need to solve for the area of the sector.

A = n/360 * π * r²
A = 85/360 * 3.14 * 5²
A = 0.2361 * 3.14 * 25
A = 18.5347 

Answer is C. 18.5 square meters.
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In the following picture, (QS) ̅ and (PR) ̅ are chords of the circle. Find the length of QS. (Remember to show formulas/equation
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<h3>Answer: QS is 37 units long</h3>

=========================================

Explanation:

PN = 24 and NR = 14 are pieces of the chord PR. The two pieces multiply to some value. At the same time, the other two pieces QN = 21 and NS = 2x-4 also multiply to that same value. In short, the chord pieces multiply to the same number. This is known as the intersecting chord theorem.

PN*NR = QN*NS

24*14 = 21*(2x-4)

336 = 42x-84

336+84 = 42x-84+84 .... add 84 to both sides

420 = 42x

42x = 420

42x/42 = 420/42 ...... divide both sides by 42

x = 10

We know that x = 10 so we can use it to find the length of NS

NS = 2x-4

NS = 2*10-4

NS = 20-4

NS = 16

Therefore,

QS = QN + NS

QS = 21 + 16

QS = 37

--------

note: as a check,

PN*NR = QN*NS

24*14 = 21*16

336 = 336

we get a true equation, so we have the proper values

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