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igomit [66]
3 years ago
13

What is the solution of the set?

Mathematics
1 answer:
ziro4ka [17]3 years ago
3 0
x^2=16-4x\ \ \ |+4x\\\\x^2+4x=16\ \ \ \ |+2^2\\\\\underbrace{x^2+2\cdot x\cdot2+2^2}_{(a+b)^2=a^2+2ab+b^2}=16+2^2\\\\(x+2)^2=20\iff x+2=\pm\sqrt{20}\\\\x+2=-\sqrt{4\cdot5}\ \vee\ x+2=\sqrt{4\cdot5}\ \ \ |-2\\\\x=-2-2\sqrt5\ \vee\ x=-2+2\sqrt5

Answer: D.
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ElenaW [278]

Given:

A prism with height 5 cm and equilateral triangular base with side 2 cm.

To find:

The total surface area of the prism.

Solution:

Area of an equilateral triangle is:

A_1=\dfrac{\sqrt{3}}{4}a^2

Where, a is the side length.

Putting a=2, we get

A_1=\dfrac{\sqrt{3}}{4}(2)^2

A_1=\dfrac{\sqrt{3}}{4}(4)

A_1=\sqrt{3}

A_1\approx \sqrt{3}

The base and top of the prism are congruent so their area must be equal.

The lateral surface area of the prism is:

LA=Ph

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Therefore, the total surface area is 33.46 cm².

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