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2 years ago

12

Type the correct answer in each box. Consider the sum of cubes identity: a3 + b3 = (a + b)(a2 − ab + b2). For the polynomial 8x3

+ 27, a = and b = .

1 answer:

zhuklara [117]2 years ago

4 0

Answer:

a = 2x, b = 3.

Step-by-step explanation:

8x^3+27 = (2x)^3 + 3^3

a = 2x and b = 3.

We can cube root 8x^3 getting 2x and cube root 27 getting 3.

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Let: u, v, w \varepsilon R3<br><br> Prove: (u x v) * [(v x w) x (w x u)] = [u * (v x w)]2

sweet [91]

Recall that for 3 vectors $a,b,c$ , all in $\mathbb R^3$ , the vector triple product

$a\times(b\times c)=(a\cdot c)b-(a\cdot b)c$

So

$(v\times w)\times(w\times u)=((v\times w)\cdot u)w-((v\times w)\cdot w)u$

Also recall the scalar triple product,

$a\cdot(b\times c)$

which gives the signed volume of the parallelipiped generated by the three vectors $a,b,c$ . When either $a=b$ or $a=c$ , the parallelipepid is degenerate and has 0 volume, so

$(v\times w)\cdot w=0$

and the above reduces to

$(v\times w)\times(w\times u)=((v\times w)\cdot u)w$

so that

$(u\times v)\cdot[(v\times w)\times(w\times u)]=(u\times v)\cdot((v\times w)\cdot u)w$

The scalar triple product has the following property:

$a\cdot(b\times c)=b\cdot(c\times a)=c\cdot(a\times b)$

Since $(v\times w)\cdot u$ is a scalar, we can factor it out to get

$((v\times w)\cdot u)((u\times v)\cdot w)$

and by the property above we have

$(u\times v)\cdot w=u\cdot(v\times w)$

and so we end up with

$[u\cdot(v\times w)]^2$

as required.

4 0

2 years ago

Expand.<br> Your answer should be a polynomial in standard form.<br> (3c + 2)(c^2-6c-4)

evablogger [386]

Answer:

After expanding the polynomial $(3c + 2)(c^2-6c-4)$ we get $3c^3-16c^2-24c-8$

Step-by-step explanation:

We need to expand the polynomial $(3c + 2)(c^2-6c-4)$

Multiply the terms:

$(3c + 2)(c^2-6c-4)\\=3c(c^2-6c-4)+2(c^2-6c-4)\\=3c^3-18c^2-12c+2c^2-12c-8\\=3c^3-18c^2+2c^2-12c-12c-8\\=3c^3-16c^2-24c-8$

So, after expanding the polynomial $(3c + 2)(c^2-6c-4)$ we get $3c^3-16c^2-24c-8$

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2 years ago

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Volgvan

Ur answer is : h(d) = 2d + 3

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IceJOKER [234]

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