Mathematics: ) An engineer deploys a set of sensors. Each sensor reports its location as a point in two-dimensional space. The points are (2, 7), (8, 2), (6, 11), (6, 5), and (11, 6). Use determinants to calculate the area of the polygon formed by the sensors.

) An engineer deploys a set of sensors. Each sensor

Ответ:

hungtistic

19.01.2022

Mathematics

The polygon area is $51.5 U^{2}$

Step-by-step explanation:

Points:

(2,7), (8,2), (6,11), (6,5), (11,6)

1. The area of the polygon could be calculate with the eqation:

$A=\frac{1}{2}\left[\begin{array}{ccc}x_{1} &y_{1}\\x_{2} &y_{2}\\x_{3} &y_{3}\\x_{4} &y_{4}\\x_{5} &y_{5}\end{array}\right]$

2. Replace the coordinates in equation for A:

$A=\frac{1}{2}\left[\begin{array}{ccc}2&7}\\8&2\\6&11\\6&5\\11&6\end{array}\right]$

3. Solve the determinant, and calculate A:

$A=\frac{1}{2}\left[\begin{array}{ccc}2&7}\\8&2\\6&11\\6&5\\11&6\end{array}\right]\\A=\frac{1}{2}[(6)(7)+(11)(11)+(8)(6)+(6)(2)]-[(2)(11)+(6)(6)+(11)(2)+(8)(5)]\\A=\frac{1}{2}[42+121+48+12]-[22+36+22+40]\\A=\frac{1}{2}[223]-[120]\\\\A=\frac{1}{2}[103]=51,5 U^{2}$

The polygon area is $51.5 U^{2}$

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Ответ:

Brandon4188

23.04.2022

Mathematics

4 T-shirts and 5 long sleeves shirts.

Step-by-step explanation:

T-shirt cost =$10

Long sleeve shirt cost = $15

Total number of shirts = 9

Total number of T-shirts = 4

Cost of 4 T-shirts = 4 × 10 =$ 40

Total number of long sleeve shirt = 5

Cost of 5 long sleeve shirt = 5 × 15 =$ 75

Verification:

75+40 = $115 proved!

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) An engineer deploys a set of sensors. Each sensor reports its location as a point in two-dimensional space. The points are (2, 7), (8, 2), (6, 11), (6, 5), and (11, 6). Use determinants to calculate the area of the polygon formed by the sensors.

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