Answer:
Find the minimum and maximum values of the objective function subject to the given constrants. Objective function: C= 2x + 3y
Constraints:
x>0
y>0
Comment: These two conditions tell you the answers are in the 1st Quadrant.
-----------------------------
x +y < 9
Graph the boundary line: y = -x+9
Solutions points are below the boundary line and in the 1st Quadrant.
The correct answer is: [D]: " 576π cm³ " .
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Explanation:
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Use the formula for the volume, "V", of a cylinder, to find the volume of the given cylinder:
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V = π r² h ;
in which:
V = volume (for which we shall solve).
π = π ; All the answer choices given are in terms of 'π' ;
r = radius = 6 cm (given);
h = height = 16 cm (given);
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Plug in these values into the formula to solve for the volume, "V" :
V = π r² h
= π * (6 cm)² * (16 cm) ;
= π * (6²) * (cm²) * (16 cm) ;
= π * (6*6) * 16 * cm³ ;
= π * (36) * 16 * cm³ ;
= π * (36 * 16) * cm³
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V = 576 π cm³ ; which is: Answer choice: [D]: " 576π cm³ " .
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To get the sphere, you have to do r^3 x pi x 4/3, and since the radius is 12, 12^3 x 3.14 x 4/3 = 7234.56. Rounded to the tenth would be 7234.6.
Answer:
i. 
+ 26x + 144 - 299 = 0
ii. x = 5
Step-by-step explanation:
The area of the figure = 299 cm²
The figure has a shape of a rectangle, so that;
Area of rectangle = length x width
length of the figure = 18 + x
width of the figure = 8 + x
Area of the figure = (18 + x) x (8 + x)
299 = (18 + x) x (8 + x)
299 = + 26x + 144
+ 26x + 144 - 299 = 0
+ 26x - 155 = 0
applying the trigonometric formula;
x = (-b ± 
) ÷ 2a
= (-26 ± 
) ÷ 2
= (-26 ± 
) ÷ 2
= (-26 ± 
) ÷ 2
= (-26 ± 36) ÷ 2
x = (-26 + 36) ÷ 2 OR x = (-26 -36) ÷ 2
= 10 ÷ 2 OR -62 ÷ 2
= 5 OR -31
Thus, x = 5
