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3 years ago

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Philll weights 120 lb Kim weighs 75% as phill eathan weigh 90% as much as Kim. And Amy weighs 2/3 as much as earthen what is the

average weight of them?

1 answer:

Serjik [45]3 years ago

3 0

Answer:

Step-by-step explanation:

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Let $m$ be the number of integers $n$, $1 \le n \le 2005$, such that the polynomial $x^{2n} + 1 + (x + 1)^{2n}$ is divisible by

Kisachek [45]

$x^2+x+1=\dfrac{x^3-1}{x-1}$

so we know $x^2+x+1$ has roots equal to the cube roots of 1, not including $x=1$ itself, which are

$\omega=e^{2i\pi/3}\text{ and }\omega^2=e^{4i\pi/3}$

Any polynomial of the form $p_n(x)=x^{2n}+1+(x+1)^{2n}$ is divisible by $x^2+x+1$ if both $p(\omega)=0$ and $p(\omega^2)=0$ (this is the polynomial remainder theorem).

This means

$p(\omega)=\omega^{2n}+1+(1+\omega)^{2n}=0$

But since $\omega$ is a root to $x^2+x+1$ , it follows that

$\omega^2+\omega+1=0\implies1+\omega=-\omega^2$

$\implies\omega^{2n}+1+(-\omega^2)^{2n}=0$

$\implies\omega^{4n}+\omega^{2n}+1=0$

and since $\omega^3=1$ , we have $\omega^{4n}=\omega^{3n}\omega^n=\omega^n$ so that

$\implies\omega^{2n}+\omega^n+1=0$

From here, notice that if $n=3k$ for some integer $k$ , then

$\omega^{2(3k)}+\omega^{3k}+1=1+1+1=3\neq0$

$\omega^{4(3k)}+\omega^{2(3k)}+1=1+1+1=3\neq0$

which is to say, $p(x)$ is divisible by $x^2+x+1$ for all $n$ in the given range that are *not* multiples of 3, i.e. the integers $3k-2$ and $3k-1$ for $k\ge1$ .

Since 2005 = 668*3 + 1, it follows that there are $m=668 + 669 = 1337$ integers $n$ such that $x^2+x+1\mid p(x)$ .

Finally, $m\equiv\boxed{337}\pmod{1000}$ .

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4 years ago

Roger has a traditional health insurance plan with $1000 deductible and 80/20 coinsurance, and $3000 out of pocket max. if roger

Angelina_Jolie [31]

Medical bill = $9,875
Deductible = $1,000

Amount Roger will pay =1000 + (9875-1000)*20/100 = 1000+1775 = $2,775

3 0

3 years ago

Read 2 more answers

Solve for angle p and q

kicyunya [14]

no es la pele jiii ya no bemoa quedate en casa

4 0

3 years ago

A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.

mr Goodwill [35]

9514 1404 393

Answer:

3362 ft²

Step-by-step explanation:

As we saw in brainly.com/question/22284853, the long side of the area will be half the length of the fence: 82 feet. The remaining two sides will be 41 feet each, so the largest area that can be enclosed is ...

A = LW

A = (82 ft)(41 ft) = 3362 ft²

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3 years ago

Write the expression as a product of polynomials:

Sonja [21]

(b+c)(x+3)
I hope this is true

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4 years ago