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3 years ago

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Lucy cuts 4 squares with side length x in. From the corners of a 6 in. By 9 in. Cardboard rectangle. She folds the remaining car

dboard to make a tray that is x in. High. Write and simplify a function for the volume V of the tray in terms of x.

2 answers:

Fittoniya [83]3 years ago

8 0

Answer:

4x³ - 30x² + 54x

Step-by-step explanation:

Length of the rectangular cardboard = 9 inches

Width of the rectangular cardboard = 6 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have

Length of the tray = length of cardboard - 2(side of square )

= 9 - 2x

Width of the tray = width of cardboard - 2( side of square)

= 6 - 2x

height of tray = sides of square

= x

volume of tray = Length × width × height

= (9 - 2x) (6 - 2x) (x)

Open the parenthesis

= (54 - 18x - 12x + 4x²)(x)

= 54x - 18x² - 12x² + 4x³

= 54x - 30x² +4x³

Re-arrange

4x³ - 30x² + 54x

Volume, V of the tray in terms of x = 4x³ - 30x² + 54x

Amanda [17]3 years ago

7 0

Answer:

4x^3-30x^2+54x

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Analysing the question one statement at a time.

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The sample space is:

$S = \{1,1,2,2,2,3\}$

And the probability of each is:

$P(1) = \frac{n(1)}{n(s)}$

$P(1) = \frac{2}{6}$

$P(1) = \frac{1}{3}$

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$P(2) = \frac{1}{2}$

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$P(3) = \frac{1}{6}$

P(Odd Number) is then calculated as:

$P(Odd\ Number) = P(1) + P(3)$

$P(Odd\ Number) = \frac{1}{3} + \frac{1}{6}$

Take LCM

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$P(Odd\ Number) = \frac{1}{2}$

After the face with 3 is loaded to be twice likely to come up.

The sample space becomes:

$S = \{1,1,2,2,2,3,3\}$

The probability of each is:

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$P(2) = \frac{n(2)}{n(s)}$

$P(2) = \frac{3}{7}$

$P(3) = \frac{n(3)}{n(s)}$

$P(3) = \frac{1}{7}$

$P(Odd\ Number) = P(1) + P(3)$

$P(Odd\ Number) = \frac{2}{7} + \frac{1}{7}$

Take LCM

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Comparing P(Odd Number) before and after

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$P(Odd\ Number) = \frac{3}{7}$ --- After

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timofeeve [1]

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