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2 years ago

√(25 - 10 √(3) + 3) (not as a decimal)

Mathematics

1 answer:

nikitadnepr [17]2 years ago

6 0

Answer:

$\huge\boxed{\sqrt{25-10\sqrt3+3}=5-\sqrt3}$

Step-by-step explanation:

$\sqrt{25-10\sqrt3+3}=(*)\\\\25=5^2\\3=(\sqrt3)^2\\10\sqrt3=(2)(5)(\sqrt3)\\\\(*)=\sqrt{5^2-(2)(5)(\sqrt3)+(\sqrt3)^2}\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=\sqrt{(5-\sqrt3)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|5-\sqrt3|=5-\sqrt3\\\\^{\text{because}\ 5>\sqrt3\to5-\sqrt3>0}$

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2 years ago

An animal shelter has 9 puppies. If the puppies are 36% of the total dog and cat population, how many dogs and cats are in the a

Luda [366]

Answer:

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As per the statement:

An animal shelter has 9 puppies.

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3 years ago

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

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Answer:

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Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, of the box with a square base are described below:

$A_{s} = l^{2}+h\cdot l$ (1)

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Where:

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$h$ - Height of the box, in centimeters.

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Then, we find the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find the critical value of the side length of the base is:

$30000-3\cdot l^{2} = 0$

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Then, we evaluate this result in the expression of the second derivative:

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2 years ago

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3 years ago

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Shtirlitz [24]

Answer:

Step-by-step explanation:

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3 years ago