After plotting the quadrilateral in a Cartesian plane, you can see that it is not a particular quadrilateral. Hence, you need to divide it into two triangles. Let's take ABC and ADC.
The area of a triangle with vertices known is given by the matrix
M =
Area = 1/2· | det(M) |
= 1/2· | x₁·y₂ - x₂·y₁ + x₂·y₃ - x₃·y₂ + x₃·y₁ - x₁·y₃ |
= 1/2· | x₁·(y₂ - y₃) + x₂·(y₃ - y₁) + x₃·(y₁ - y₂) |
Therefore, the area of ABC will be:
A(ABC) = 1/2· | (-5)·(-5 - (-6)) + (-4)·(-6 - 7) + (-1)·(7 - (-5)) |
= 1/2· | -5·(1) - 4·(-13) - 1·(12) |
= 1/2 | 35 |
= 35/2
Similarly, the area of ADC will be:
A(ABC) = 1/2· | (-5)·(5 - (-6)) + (4)·(-6 - 7) + (-1)·(7 - 5) |
= 1/2· | -5·(11) + 4·(-13) - 1·(2) |
= 1/2 | -109 |
<span> = 109/2</span>
The total area of the quadrilateral will be the sum of the areas of the two triangles:
A(ABCD) = A(ABC) + A(ADC)
= 35/2 + 109/2
= 72
Answer:
26 ÷ r
Step-by-step explanation:
Is your expression.
Using the keywords divide you can identify the expression, its showing you divide 26 by r, r in this case is your unknown value(variable). This expression is showing what you divide. You can also consider this as 26/r
Answer:
Step-by-step explanation:
90(n-98)²=90(97-98)²=90(-1)²=90*1=90
n=97
Answer:
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Answer:
From the values obtained, we can see that after the initial 10mg/L values obtained in the first 1 and 2 minutes, the concentration has been dipping and it will continue to do so.
Step-by-step explanation:
The concentration monitored ar time, t > 0 is represented by :
C(t) = 30t / (t² + 2.)
At, t = 1
C(1) = 30(1) / (1 + 2) = 30/3 = 10
At t = 2
C(2) = 30(2) / (2² + 2) = 60/(4+2) = 60/6 = 10
At t = 3
C(3) = 30(3) / (3² + 2) = 90/ 11 = 8.18
At t = 4
C(4) = 30(4) / (4²+2) = 120/18 = 6.67
At t = 5
C(5) = 30(5) / (5²+2) = 150/ 27 = 5.55
At t = 10
C(10) = 30(10) / (10²+2) = 300/102 = 2.94
From the values obtained, we can see that after the initial 10mg/L values obtained in the first 1 and 2 minutes, the concentration has been dipping and it will continue to do so.