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Vera_Pavlovna [14]

3 years ago

13

For each algebraic equation, select the property that could be used to solve it: 1. x-3=-5 2. 6x=72 3. x/5=3

1 answer:

kykrilka [37]3 years ago

5 0

X - 3 = -5........addition property....because u add -3 to both sides

6x = 72.....either division property...because u divide both sides by 6.
or multiplication property...because u multiply both sides by 1/6

x/5 = 3.....multiplication property....because u multiply both sides by 5

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Identify all factors of the expression 12x^2-14x-6

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A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

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Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

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Substitute the values

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$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

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$\implies 18-3b^2=0$

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$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

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