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saveliy_v [14]
3 years ago
15

18x^2+69x+60 Factor the expression

Mathematics
1 answer:
Kipish [7]3 years ago
6 0
3(3x+4)(2x+5)

Because you factor out the 3 and then factor 6x^2+23x+20
That becomes (6x^2+8x)+(15x+20)
Factor out a two from the left and five from the right.
That makes 2x(3x+4) + 5(3x+4)
That becomes (3x+4)(2x+5)
Then put the three back in front.
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Alexus [3.1K]

Answer:

Max\ Area = \frac{x^2}{16}

Step-by-step explanation:

Given

P = x ---- the perimeter of fencing

Required

The maximum area

Let

L \to Length

W \to Width

So, we have:

P = 2(L + W)

This gives:

2(L + W) = x

Divide by 2

L + W = \frac{x}{2}

Make L the subject

L = \frac{x}{2} - W

The area (A) of the fence is:

A = L * W

Substitute L = \frac{x}{2} - W

A = (\frac{x}{2} - W) * W

Open bracket

A = \frac{x}{2}W - W^2

Differentiate with respect to W

A' = \frac{x}{2} - 2W

Set to 0

\frac{x}{2} - 2W = 0

Solve for 2W

2W = \frac{x}{2}

Solve for W

W = \frac{x}{4}

Recall that:

L = \frac{x}{2} - W

L = \frac{x}{2} - \frac{x}{4}

L = \frac{2x- x}{4}

L = \frac{x}{4}

So, the maximum area is:

A = L * W

A = \frac{x}{4}*\frac{x}{4}

Max\ Area = \frac{x^2}{16}

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