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Radda [10]
3 years ago
5

A box is to be constructed from a sheet of cardboard that is 10 cm by 60 cm by cutting out squares of length x by x from each co

rner and bending up the sides. What is the maximum volume this box could have?
Mathematics
1 answer:
Stells [14]3 years ago
6 0

Volume of a rectangular box = length x width x height<span>

From the problem statement,
length = 60 - 2x
width = 10 - 2x
height = x</span>

<span>
where x is the height of the box or the side of the equal squares from each corner and turning up the sides

V = (60-2x) (10-2x) (x)
V = (60 - 2x) (10x - 2x^2)
V = 600x - 120x^2 -20x^2 + 4x^3
V = 4x^3 - 100x^2 + 600x

To maximize the volume, we differentiate the expression of the volume and equate it to zero.

V = </span>4x^3 - 100x^2 + 600x<span>
dV/dx = 12x^2 - 200x + 600
12x^2 - 200x + 600 = 0</span>

<span>x^2 - 50/3x + 50 = 0

Solving for x,
x1 = 12.74 ;      Volume = -315.56  (cannot be negative)
x2 = 3.92 ;      Volume = 1056.31

So, the answer would be that the maximum volume would be 1056.31 cm^3.
</span><span>
</span>
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Consider the graph of the sixth-degree polynomial function f.
vekshin1

Answer:

b = 1, c = -1 and d = 4

Step-by-step explanation:

To solve this question the rule of multiplicity of a polynomial is to be followed.

If the multiplicity of a polynomial is even at a point, graph of the polynomial will touch the x-axis.

If the multiplicity of the polynomial is odd, graph will cross the x-axis at that point.

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Since, graph of the function 'f' crosses x-axis at x = 1 and x = 4, multiplicity will be odd and touches the x-axis at x = -1 multiplicity will be even.

So the function will be,

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3 years ago
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Help me please fast ​
Natalija [7]

Answer:

Step-by-step explanation:

\frac{5}{x-3}+\frac{2}{x+1}=3  \\\\\frac{5(x+1)+2(x-3)}{(x-3)(x+1)} =3\\\\5x+5+2x-6=3(x-3)(x+1)\\\\7x-1=3(x^2+x-3x-3)\\\\7x-1=3(x^2-2x-3)\\\\7x-1=3x^2-6x-9\\\\0=3x^2-6x-7x-9+1\\0=3x^2-13x-8

Hence proved!

3 0
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Rewrite the expression 2(x + 5) using the Distributive Property.​
ehidna [41]

Answer:

2x + 10

Step-by-step explanation:

To expand (using the distributive property) <u>multiply</u> the number outside the bracket i.e. in this case '2', with the <u>values inside the brackets</u>.

So multiply '2' and 'x' and '2' and 5' and add or subtract on basis of whether the second value is positive or negative.

So

2(x + 5)

= (2*x)+(2*5)

=2x+10

<em>extention note:</em> <u>be careful</u> when the symbol within the equation within the brackets is a subtraction because it implies that the second value would instead be a negative number and should be treated as such.

an example

2(x-5)

= (2*x)+(2*-5)

=2x -10

Anyhow, I hope this helped!

5 0
2 years ago
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