Work out the following questions

Mathematics

1 answer:

Basile [38]3 years ago

6 0

Answer: The first one is 2 2/3 and the second one is 10 1/2

Step-by-step explanation: So 2/3 divided by 1/4. First you would do keep, change, flip. Then that would give you 2/3 times 4/1. 2/3 times 4/1 would be 8/3 which can be simplified to 2 2/3. The second one 7 divided by 2/3. Again do keep, change, flip. 7 times 3/2. This would give you 21/2 when you simplify you get 10 1/2.

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You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in

NARA [144]

Let x = length and y = width

You would have 2 lengths, so 2x and 3 widths, so 3y

Those need to equal total length of fence:

2x + 3y = 1200

The 3 widths would equal total fence minus the 2 lengths:

3Y = 1200-2x

Solve for y: y = 400 -2/3x

Area = length x width = xy. Replace y :

Area = x(400-2/3x) = 400x-2/3x^2

Differentiate:

400-4x/3 =0

4x/3 = 400

4x = 1200

X = 300

Y = 400-2/3(300) = 200

The dimension would be 300 ft x 200 ft

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$\bf \textit{difference of squares}
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(a-b)(a+b) = a^2-b^2\qquad \qquad 
a^2-b^2 = (a-b)(a+b)
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\textit{also recall that }i^2=-1\\\\
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x=-1-4i\implies &x+1+4i=0
\end{cases}
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(x+1-4i)(x+1+4i)=\stackrel{y}{0}
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