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3 years ago

Simplify the rational expression 6x-24/16-x^2

Mathematics

2 answers:

Setler [38]3 years ago

6 0

I haven't learned this yet sorry

8_murik_8 [283]3 years ago

5 0

The answer would be -x^2 + 6x - 3/2

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Find the product (4x-3) (3x+8)

m_a_m_a [10]

Hi there!

Assuming "Find the product" means multiplying (4x-3) by (3x+8) and factor to it's simplest form the answer would be:

12x²+23x-24

The way you solve this is by using the distributive property of multiplication as shown below:

Start by multiplying -3 from (4x-3) by everything in (3x+8)

3x*(-3) = -9x

8*(-3) = -24

Once you've done that you then multiply everything 4x

4x*8 = 32x

4x*3x = 12x²

(Note: when multiplying two of the same variables like x it means you are multiplying x by itself which is the same as x²)

When you put all of this together it looks like this

12x²+32x-9x-24

from there we combine like terms

32x-9x = 23x

to get

12x²+23x-24

I hope this helps!

God bless,

ASIAX

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3 years ago

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4 years ago

A bin is constructed from sheet metal with a square base and 4 equal rectangular sides. if the bin is constructed from 48 square

kondaur [170]

This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

V = length x width x height

That is:

$V = xxy = x^{2}y$

We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:

Surface area of the square base = $x^{2}$

Surface area of the rectangular sides = $4xy$

Therefore, the total area of the cube is:

$A = 48 ft^{2} = x^{2} + 4xy$

Isolating the variable y in terms of x:

$y = \frac{48- x^{2} }{4x}$

Substituting this value in V:

$V = x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}$

Getting the derivative and finding the maxima. This happens when the derivative is equal to zero:

$\frac{dv}{dx} = 48-3x^{2} =0$

Solving for x:

$x = \sqrt{\frac{48}{3}} = \sqrt{16} = 4$

Solving for y:

$y = \frac{48- 4^{2} }{(4)(4)} = 2$

Then, <span>the dimensions of the largest volume of such a bin is:
</span>
Length = 4 ft
Width = 4 ft
Height = 2 ft

And its volume is:

$V = (4^{2} )(2) = 32 ft^{3}$

8 0

3 years ago