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mars1129 [50]
2 years ago
13

An open metal tank of square base has a volume of 123 m^3

Mathematics
1 answer:
snow_lady [41]2 years ago
3 0

Answer:

  a) h = 123/x^2

  b) S = x^2 +492/x

  c) x ≈ 6.27

  d) S'' = 6; area is a minimum (Y)

  e) Amin ≈ 117.78 m²

Step-by-step explanation:

a) The volume is given by ...

  V = Bh

where B is the area of the base, x^2, and h is the height. Filling in the given volume, and solving for the height, we get:

  123 = x^2·h

  h = 123/x^2

__

b) The surface area is the sum of the area of the base (x^2) and the lateral area, which is the product of the height and the perimeter of the base.

S=x^2+Ph=x^2+(4x)\dfrac{123}{x^2}\\\\S=x^2+\dfrac{492}{x}

__

c) The derivative of the area with respect to x is ...

S'=2x-\dfrac{492}{x^2}

When this is zero, area is at an extreme.

0=2x -\dfrac{492}{x^2}\\\\0=x^3-246\\\\x=\sqrt[3]{246}\approx 6.26583

__

d) The second derivative is ...

S''=2+\dfrac{2\cdot 492}{x^3}=2+\dfrac{2\cdot 492}{246}=6

This is positive, so the value of x found represents a minimum of the area function.

__

e) The minimum area is ...

S=x^2+\dfrac{2\cdot 246}{x}=(246^{\frac{1}{3}})^2+2\dfrac{246}{246^{\frac{1}{3}}}=3\cdot 246^{\frac{2}{3}}\approx 117.78

The minimum area of metal used is about 117.78 m².

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There are two non congruent triangles where B=55 degrees a=15 and b=13. Find the measures of the angles of the triangle with the
liq [111]

Answer:

The side c needs to be 12.85 for the triangle to have greatest perimeter

Step-by-step explanation:

We are given;

b = 13

a = 15

Angle at b: B = 55°

Let's find side c.

Using the law of cosines,we have;

b² = a² + c² - 2ac•cos(B)

13² = 15² + c² - 2•15•c•cos(55)

169 = 225 + c² - 30c•cos(55)

c² - 30c•cos(55) + 225 - 169 = 0

c² - 30c•cos(55) + 56 = 0

c² - 30c•(0.5736) + 56 = 0

c² - 30c•(0.5736) + 56 = 0

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Using quadratic formula;

c = [-(-17.208) ± √((-17.208)² - (4•1•56)]/2(1)

c = [17.208 ± √(296.115 - 224)]/2

c = 8.604 ± 4.246

To have the greater perimeter, we need the larger value of c, thus we will use the positive sign and ignore the negative one ;

Thus,

c = 8.604 + 4.246 = 12.85

5 0
3 years ago
Please help!!!!!! i need to know what the answer is and how to do it.
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Answer:

Step-by-step explanation:

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6 0
2 years ago
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Answer:

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Step-by-step explanation:

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