Answer:
the maximum value is 7
The minimum value is 0
Step-by-step explanation:
Step One : Interpret the question
The above question can be written like
The Equation
The diagram of the triangular plate and the bounded lines is shown on the first uploaded image
From the diagram 
Partial differentiation of the equation w.r.x
Partial differentiation of the equation w.r.y
Looking at the diagram the maximum value is 7 i.e at (x , y) = (0,1)
The minimum value is 0 i.e (x , y) = (0,0)
The answer is: 3.91 inches .
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Note: Volume of cylinder: V = (base area) * (height);
in which: V = volume = 384 in.³ ;
h = height = 8 in. ;
Base area = area of the base (that is; "circle") = π r² ;
in which; "r" = radius;
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Solve for "r" :
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V = π r² * (8 in.) ;
384 in.³ = (8 in.) * (π r²) ;
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Divide EACH SIDE of the equation by "8" ;
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(384 in.³) / 8 = [ (8 in.) * (π r²) in.] / 8 ;
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to get:
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48 in.³ = (π r²) in.² * in. ;
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↔ (π r²) in.² * in. = 48 in.³ ;
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Rewrite this equation; using "3.14" as an approximation for: π ;
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(3.14 * r²) in.² * in. = 48 in.³
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Divide EACH SIDE of the equation by:
"[(3.14)*(in.²)*(in.)]" ; to isolate "r² " on one side of the equation;
(since we want to solve for "r") ;
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→ [(3.14 * r²) in.² * in.] / [(3.14)*(in.²)*(in.)] = 48 in.³ / [(3.14)*(in.²)*(in.)] ;
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→ to get: r² = 48/3.14 ;
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→ r² = 15.2866242038216561 ;
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To solve for "r" (the radius; take the "positive square root" of EACH side of the equation:
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→ +√(r²) = +√(15.2866242038216561)
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→ r = 3.9098112747064475286 ; round to 3.91 inches .
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The Y-intercept is a point where the line crosses the Y lines. That means it would be the point where X=0. Then to find the Y-intercept you only need to insert X=0 into the equation. The calculation would be:
<span> 4×+2y=12
4(0) + 2 Y= 12
2Y =12
Y=6</span>
Answer:
See the pictures attached
Step-by-step explanation:
All the explanation is given in the pictures
