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Drupady [299]
3 years ago
5

An open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the

sides. If x represents the side length of the squares, which of the following is a function giving the volume of the box of terms x

Mathematics
1 answer:
natka813 [3]3 years ago
6 0

Please find the attachment.

Let x represent the side length of the squares.

We have been given that an open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. We are asked to find the volume of the box.

The side of box will be 8-x-x=8-2x and 10-x-x=10-2x.

The height of the box will be x.

The volume of box will be area of base times height.

\text{Volume of box}=(8-2x)(10-2x)\cdot x

Now we will use FOIL to simplify our expression.

\text{Volume of box}=(80-16x-20x+4x^2)\cdot x

\text{Volume of box}=(80-36x+4x^2)\cdot x

Now we will distribute x.

\text{Volume of box}=80x-36x^2+4x^3

V(x)=80x-36x^2+4x^3

Therefore, the volume of the box would be V(x)=80x-36x^2+4x^3.

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hram777 [196]

Answer:

Step-by-step explanation:

xy = 300

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y = 50 - x                        substitute into xy = 300

x(50 - x) = 300               Remove the brackets.

50x - x^2 = 300             Bring the left to the right.

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This is a quadratic. It will have 2 solutions.

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Put these into the quadratic equation.

It turns out that x has two values -- both plus

x1 = 42.03

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y = 7,97

(42.03 , 7.97)

====================

x2 + y2 = 50

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6 0
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<u>Answer:</u>

Factor over complex numbers of 2 x^{4}+36 x^{2}+162 is 2(x+3 i)^{2}(x-3 i)^{2}

<u>Solution:  </u>

From question given that

2 x^{4}+36 x^{2}+162  → (1)

On substituting x^{2}=y in equation (1),

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Taking 2 as a common in above expression,

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Rewrite the above expression,

=2\left[y^{2}+2(y)(9)+9^{2}\right]

=2(y+9)^{2}  \left[\text { Using }(a+b)^{2}=a^{2}+2 a b+b^{2}\right]

=2\left(x^{2}+9\right)^{2} \left[\text { since } y=x^{2}\right]

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Hence Factor over complex numbers of 2 x^{4}+36 x^{2}+162 is 2(x+3 i)^{2}(x-3 i)^{2}

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