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DENIUS [597]
3 years ago
9

Please help me with the question for the surface area of a cylinder !!

Mathematics
1 answer:
Snowcat [4.5K]3 years ago
4 0
Formula is 2\pir^2+2\pirh

2 x 3.14 x 4 x 4 = 100.48

2 x 3.14 x 4 x 5 = 125.6

Total: 226.08, aka answer choice D
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The sum of the squares of two numbers is 8 . The product of the two numbers is 4 . Find the numbers.
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Hello there.

First, assume the numbers x,~y such that they satisties both affirmations:

  • The sum of the squares of two numbers is 8.
  • The product of the two numbers is 4.

With these informations, we can set the following equations:

\begin{center}\align x^2+y^2=8\\ x\cdot y=4\\\end{center}

Multiply both sides of the second equation by a factor of 2:

2\cdot x\cdot y = 2\cdot 4\\\\\\ 2xy=8~~~~~(2)^{\ast}

Make (1)-(2)^{\ast}

x^2+y^2-2xy=8-8\\\\\\ x^2-2xy+y^2=0

We can rewrite the expression on the left hand side using the binomial expansion in reverse: (a-b)^2=a^2-2ab+b^2, such that:

(x-y)^2=0

The square of a number is equal to 0 if and only if such number is equal to 0, thus:

x-y=0\\\\\\ x=y~~~~~~(3)

Substituting that information from (3) in (2), we get:

x\cdot x = 4\\\\\\ x^2=4

Calculate the square root on both sides of the equation:

\sqrt{x^2}=\sqrt{4}\\\\\\ |x|=2\\\\\\ x=\pm~2

Once again with the information in (3), we have that:

y=\pm~2

The set of solutions of that satisfies both affirmations is:

S=\{(x,~y)\in\mathbb{R}^2~|~(x,~y)=(-2,\,-2),~(2,~2)\}

This is the set we were looking for.

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8540.0 is standard notation

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Why’d you put the answer?
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Answer:

Step-by-step explanation:

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