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Firlakuza [10]
3 years ago
10

I WILL MARK BRAINLIEST :) Determine which segment is shortest in the diagram.

Mathematics
2 answers:
erastovalidia [21]3 years ago
8 0

Answer:

C.

Step-by-step explanation:

Nana76 [90]3 years ago
7 0

Answer:

C. Segment AC

Step-by-step explanation:

I am going to figure all the angles first. Triangles always add up to 180 degrees so I am going to use that.

50 + 49 = 99

180 - 99 = 81

<C = 81°

99 + 37 = 136

180 - 136 = 44

<A = 44°

The shortest segment is always going to be opposite the smallest angle. The smallest angle is 37°. Therefore, Segment AC is the shortest.

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3 years ago
A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a
kkurt [141]

Answer:

b=h=\sqrt{6} m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box=2b^2+4bh

2b^2+4bh=36

b^2+2bh=18

2bh=18-b^2

h=\frac{18-b^2}{2b}

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Substitute the values

V=b^2\times \frac{18-b^2}{2b}

V=\frac{1}{2}(18b-b^3)

Differentiate w. r.t b

\frac{dV}{db}=\frac{1}{2}(18-3b^2)

\frac{dV}{db}=0

\frac{1}{2}(18-3b^2)=0

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b^2=6

b=\pm \sqrt{6}

b=\sqrt{6}

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

\frac{d^2V}{db^2}=-3b

At  b=\sqrt{6}

\frac{d^2V}{db^2}=-3\sqrt{6}

Hence, the volume of box is maximum at b=\sqrt{6}.

h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}

h=\frac{18-6}{2\sqrt{6}}

h=\frac{12}{2\sqrt{6}}

h=\sqrt{6}

b=h=\sqrt{6} m

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3 years ago
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