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3 years ago

15

A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90 degrees.What depth will provid

e maximum cross-sectional area and hence allow the most water to flow?

1 answer:

fredd [130]3 years ago

7 0

Answer:

18 in^2

Step-by-step explanation:

<em>1 )The three sides of the gutter add up to 12</em>

2x+ y = 12

<em>2) Subtract 2x from both sides. </em>

y = 12 — 2x

<em>3 )Find the area of the rectangle in terms of x and simplify.</em>

Area = xy = x(12 — 2x) = -2x^2+12x = f(x)

<em>4 ) x=-b/2a</em>

<em>x co-ordinate of the vertex= -12/2(-2)=3</em>

<em>5 )Plug in 3 for x into they equation.</em>

y co-ordinate of the vertex= 12 — 2(3) = 6

<em>6 ) Plug in 3 for x and 6 for y. </em>

Area= xy = 3(6) = 18

RESULT

18 in^2

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Answer:

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We know that the arithmetic sequence formula is

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Now

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------------------------------------------

Similarly

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Substituting the given value we get

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-------------------------------------------------

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Substituting the given value we get

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-------------------------------------------------------------------------------------------

<u>B</u><u> $a_n=a_{(n-1)}-8$ with $a_1=10$ </u>

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

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-------------------------------------------------------------------------------------------

<u>C) $a_1=3, a_2=1$ </u>

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

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$a_{4}=a_{1}+(3)d$

Substituting the value we get

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----------------------------------------------------------------------------------

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Substituting the value we get

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