3x + 4y + 3z = 5
2x + 2y + 3z = 5
5x + 6y + 7z = 7
<=> 3( 3x + 4y + 3z) = 5.3
6( 2x + 2y + 3z) = 5.6
2( 5x + 6y + 7z ) = 7.2
<=> 9x + 12y + 9z = 15 (1)
12x + 12y + 18z=30 (2)
10x + 12y + 14z = 14 (3)
<=> 3x +9z =15 [ (2) - (1) ]
2x + 4z = 16. [ (2) - (1) ]
<=> 2(3x +9z) = 15.2
3(2x + 4z) = 16.3
<=> 6x+ 18z = 30
6x + 12z = 48
<=> 6z = - 18 => z = -3 and 6x + 18z = 30 so x = [30 - 18.(-3) ] : 6 = 14
We have 2x + 2y + 3z =5 => 2.14 + 2y + 3.(-3) = 5 ==> y = -7
The answer is x = 14, y = -7, z = -3
Answer: -5/12
Step-by-step explanation:
Answer:
Step-by-step explanation:
The area of the base is given by the formula ...
A = πr²
so the radius is ...
r = √(A/π) = √(1386/(22/7)) = √441 = 21 . . . units
__
The volume is given by ...
V = (1/3)Bh
where B is the area of the base, and h is the height (equal to the radius). Filling in the numbers, we have ...
V = (1/3)(1386)(21) = 9702 . . . . cubic units
Answer:
43.8°
Step-by-step explanation:
Applying,
Cosine rule,
From the diagram attached,
x² = y²+z²-2yxcos∅.................... Equation 1
where ∅ = ∠YXZ
Given: x = 8.7 m, y = 10.4 m, z = 12.4 m
Substitute these values into equation 1
8.7² = 10.4²+12.4²-[2×10.4×12.4cos∅]
75.69 = (108.16+153.76)-(257.92cos∅)
75.69 = 261.92-257.92cos∅
collect like terms
257.92cos∅ = 261.92-75.69
257.92cos∅ = 186.23
Divide both sides by the coefficient of cos∅
cos∅ = 186.23/257.92
cos∅ = 0.722
Find the cos⁻¹ of both side.
∅ = cos⁻¹(0.7220)
∅ = 43.78°
∅ = 43.8°
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