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Answer:
- The shaded region is 9.83 cm²
Step-by-step explanation:
<em>Refer to attached diagram with added details.</em>
<h2>Given </h2>Circle O with:
- OA = OB = OD - radius
- OC = OD = 2 cm
- The area of segment ADB.
Since r = OC + CD, the radius is 4 cm.
Consider right triangles OAC or OBC:
- They have one leg of 2 cm and hypotenuse of 4 cm, so the hypotenuse is twice the short leg.
Recall the property of 30°x60°x90° triangle:
- a : b : c = 1 : √3 : 2, where a- short leg, b- long leg, c- hypotenuse.
It means OC: OA = 1 : 2, so angles AOC and BOC are both 60° as adjacent to short legs.
In order to find the shaded area we need to find the area of sector OADB and subtract the area of triangle OAB.
Area of <u>sector:</u>
- A = π(θ/360)r², where θ- central angle,
- A = π*((mAOC + mBOC)/360)*r²,
- A = π*((60 + 60)/360))(4²) = 16.76 cm².
Area of<u> triangle AO</u>B:
- A = (1/2)*OC*(AC + BC), AC = BC = OC√3 according to the property of 30x60x90 triangle.
- A = (1/2)(2*2√3)*2 = 4√3 = 6.93 cm²
The shaded area is:
- A = 16.76 - 6.93 = 9.83 cm²
Using a system of equation, we have that:
a)
- x, which is the cost of on-site service.
- y, which is the cost of at-store service.
- z, which is the cost of by-mail service.
b)
The system is:
c)
The cost of one on-site repair service is of $90.
Item a:
The variables are:
- x, which is the cost of on-site service.
- y, which is the cost of at-store service.
- z, which is the cost of by-mail service.
Item b:
On-site service costs <u>3 times as much as at-store service</u>, thus:
By mail service costs <u>$10 less than at-store</u> service, thus:
Last week, the shop completed <u>15 services on-site, 40 services at-store, and 5 services by mail for total sales of $3100</u>, thus:
The system is:
Item c:
- The cost of one on-site repair service is x.
- First, replacing the first two equations into the third, we find y, and then with it we find x.
Then
The cost of one on-site repair service is of $90.
A similar problem is given at brainly.com/question/24823220