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weeeeeb [17]
2 years ago
9

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 6 cubi

c centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to three decimal places.) A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. An industrial tank of this shape must have a volume of 4480 cubic feet. The hemispherical ends cost twice as much per square foot of surface area as the sides. Find the dimensions that will minimize the cost. (Round your answers to three decimal places.)

Mathematics
1 answer:
lawyer [7]2 years ago
4 0

Answer:

1. The answer of the radius of the cylinder is 1.127cm to produce the minimum surface area

2. The radius of the industrial tank is 1.465ft and the height is 662.396 ft

Step-by-step explanation:

<u>The first step</u> is to draw the shape and to determine the total surface area and the total volume of the shape. This is done by adding the total surface area of two hemispheres and the surface area of the cylinder and for the volume this is done by adding the volume of two hemispheres and the volume of the cylinder.

<u>The second step</u> is to make the total volume of the shape the constraint equation and the total surface area of the shape becomes the optimisation equation. From the constraint equation solve for h and make it in terms of r (you should advisable use V as a constant and finally substituting at the end). Thereafter, input the value of h in the optimisation equation and differentiate the equation with respect to r. Finally equate the equation to zero.

Third step involves solving for r

Now, for the second question, one has to double the total surface area of the hemispheres to provide the cost equation (this is done to take into account the higher costs of the hemispherical ends. Solve in the same way as the first and you will get the answer.

[KINDLY NOTE I TRIED TYPING THE SOLUTION BUT IT TOOK SO LONG THAT I GOT LOGGED OUT SO FIND ATTACHED PICTURES OF THE SOLUTION, if you follow the steps, it would serve as a guide]

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marin [14]

Answer:

4

Step-by-step explanation:

3x² + 2x - 4

3(-2)² + 2(-2) - 4

3(4) - 4 - 4

12 - 4 - 4

12 - 8

= 4

4 0
3 years ago
I need to use the Pythagorean Theorem to find X. I don’t know how to do that!!
frutty [35]

Answer:

17) x=8

18) x=\sqrt{189} or x= 3\sqrt{21}

Step-by-step explanation:

So the rule is a^{2} +b^{2} =c^{2}, "c" being the hypothenuse, or the long line that is opposite to the right angle.

17) We know that both values of x are equal to each other, which makes everything 10x easier!

                                               x^{2} +x^{2} =(8\sqrt{2})  ^{2}

(by the way we know the x values are our a and b values because they are legs! the way I like to remember the legs is that they are connected to the right angle box, and therefore support the hypothenuse)

<em>simplify</em> (╥︣﹏╥)    

                                                2x^2=8^2(\sqrt{2} )^{2}  

                                                  2x^2=64(2)

                                                   2x^2=128    

                                                  x^{2}= 128/2  

                                                     x^{2} =64

                                                        x=8      

18) Just pretend that the flipped triangle doesn't exist. It's parallel to the other triangle with values on it, and basically servers no purpose other than being parallel to the sister triangle :)

Anyways, since we know the hypothenuse (15) but we don't know one of our leg values (x), we're going to change our equation a bit!

                                                    c^{2} - b^{2} = a^{2}

It doesn't matter if you put the one leg value in a or b, just as long as you stick to that same equation you started with the entire time!

                                                   15^{2} -6^{2} =x^{2}

                                                   225-36=x^{2}  

                                                     x^{2} =189

                                               x=\sqrt{189}=3\sqrt{21}

        The more you do these, the easier they'll get, so don't worry!

                           

4 0
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solong [7]
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3 years ago
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7 0
3 years ago
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Eddi Din [679]

Answer:

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Step-by-step explanation:x_{3}

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8y+5=6

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8y=6-5

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8y=1

divide both sides

y=\frac{1}{8} or y=0.125

4 0
3 years ago
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