The area of the sector is 472.6 ft²
<h3>Area of a Sector</h3>
For finding the area of the sector, you need apply the formula:
, where:
r= radius
α= central angle
The question gives:
r= radius= 19 ft
α= central angle = 150°
Thus, the area of the sector will be:

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Answer:
x = -0.6
y = 2.2
z = 2
Step-by-step explanation:
2x + y - 2z = -3
x + 3y - z = 4
3x + 4y - z = 5
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
2 1 -2 -3
1 3 -1 4
3 4 -1 5
R1 / 2 → R1 (divide the 1 row by 2)
1 0.5 -1 -1.5
1 3 -1 4
3 4 -1 5
R2 - 1 R1 → R2 (multiply 1 row by 1 and subtract it from 2 row); R3 - 3 R1 → R3 (multiply 1 row by 3 and subtract it from 3 row)
1 0.5 -1 -1.5
0 2.5 0 5.5
0 2.5 2 9.5
R2 / 2.5 → R2 (divide the 2 row by 2.5)
1 0.5 -1 -1.5
0 1 0 2.2
0 2.5 2 9.5
R1 - 0.5 R2 → R1 (multiply 2 row by 0.5 and subtract it from 1 row); R3 - 2.5 R2 → R3 (multiply 2 row by 2.5 and subtract it from 3 row)
1 0 -1 -2.6
0 1 0 2.2
0 0 2 4
R3 / 2 → R3 (divide the 3 row by 2)
1 0 -1 -2.6
0 1 0 2.2
0 0 1 2
R1 + 1 R3 → R1 (multiply 3 row by 1 and add it to 1 row)
1 0 0 -0.6
0 1 0 2.2
0 0 1 2
x = -0.6
y = 2.2
z = 2
It would be 0.2222 so it's your answer
Answer: 41 vans will be needed.
Step-by-step explanation:
There are a total of 492 campers. We know that each van can hold a total of 12 passengers.
So, simply divide 492 by 12 to get the total amount of vans needed.
492/12 = 41 vans.
A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]
B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)
<h3>A. How to determine the mid point</h3>
- Coordinate of C = (4, 5)
- Coordinate of D = (p, q)
- Mid point =?
Mid point = (X , Y)
X = (x₁ + x₂) / 2
X = (4 + p) / 2
Y = (y₁ + y₂) / 2
Y = (5 + q) / 2
Thus,
Mid point = (X , Y)
Mid point = [(4 + p) / 2 , (5 + q) / 2]
<h3>B. How to determine the coordinates of D</h3>
- Mid point = (7, 1)
- Coordinates of D =?
Mid point = (7, 1) = (X , Y)
X = (4 + p) / 2
7 = (4 + p) / 2
Cross multiply
7 × 2 = 4 + p
14 = 4 + p
Collect like terms
p = 14 - 4
p = 10
Y = (5 + q) / 2
1 = (5 + q) / 2
Cross multiply
1 × 2 = 5 + q
2 = 5 + q
Collect like terms
q = 2 - 5
q = -3
Coordinates of D = (p, q)
Coordinates of D = (10 , -3)
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