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Ivenika [448]
3 years ago
11

Use the Rational Root Theorem to list all possible rational roots for the equation.

Mathematics
2 answers:
Anna71 [15]3 years ago
8 0
Q^n + k^(n-1).... + P = 0
Like: 3x^3+9x-6=0

All rational roots will be rational factors of P/Q such that:

Q = 3 Factors: 1,3
P = -6 Factors: [+/-] 1,2,3,6

Possible Rational Roots: [1/1,1/3,2/1,2/3,3/1,3/3,6/1,6/3] = [+/-] 1,1/3,2,2/3,3,6

Now you just test them in the equation itself and where the input makes the function equal 0, you have a root.

For this polynomial, no roots are rational, so when you test it you'll find that it must only contain irrational roots and may only be solved by other means.
Mariana [72]3 years ago
6 0

\bf \stackrel{q}{3}x^3+9x-\stackrel{p}{6}~\hspace{5em}\stackrel{\textit{factors of \boxed{p}}}{3,2,1,6}\qquad \stackrel{\textit{factors of \boxed{q}}}{3,1}\qquad \qquad \pm\cfrac{p}{q} \\\\\\ \textit{therefore, using the \underline{rational root test}}


\bf \begin{cases} \pm \cfrac{3}{3}\implies &\pm 1\\\\ \pm \cfrac{3}{1}\implies &\pm 3\\\\ \end{cases}\quad \begin{cases} \pm \cfrac{2}{3}\\\\ \pm \cfrac{2}{1}\implies \pm 2 \end{cases}\quad \begin{cases} \pm \cfrac{1}{3}\\\\ \pm \cfrac{1}{1}\implies \pm 1 \end{cases}\quad \begin{cases} \pm \cfrac{6}{3}\implies &\pm 2\\\\ \pm \cfrac{6}{1}\implies &\pm 6 \end{cases}

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Eva is going to the amusement park, where she has to pay a set price of admission and another price for tickets to go on each of
lyudmila [28]

Answer:

B. The change in the total amount if money for every one additional ride she goes on

Step-by-step explanation:

Given,

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y = total amount of money Eva will spend

x = number of rides Eva rides on

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3 years ago
Find the average value of f(x+y)=sin(x+y) over
Troyanec [42]

For each given region D, the average value of f over D is the integral of f over D divided by the area of D. In both cases, D is a rectangle so the area is trivial.

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\displaystyle\int_0^{5\pi/3}\int_0^{\pi/3}\sin(x+y)\,\mathrm dx\,\mathrm dy

\displaystyle=\int_0^{5\pi/3}\left(\cos y-\cos\left(y+\dfrac\pi3\right)\right)\,\mathrm dy

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b. The area of D is \dfrac{2\pi}3\cdot\dfrac{7\pi}6=\dfrac{7\pi^2}9. The integral of f is

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=\sin\dfrac{7\pi}6-\sin\left(\dfrac{7\pi}6+\dfrac{2\pi}3\right) - \sin0+\sin\dfrac{2\pi}3=\dfrac{\sqrt3}2

The average vale of f over this region is then \dfrac{\frac{\sqrt3}2}{\frac{7\pi^2}9}=\dfrac{9\sqrt3}{14\pi^2}.

4 0
2 years ago
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Answer:

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Only 8 is left as an even number. So 8 would be at the one's place.

In the ten-thousand places, arrange the three digits 3,9 and 5 in the middle.

So there are 3*2=6 ways to arrange the  middle three digits in the ten-thousand places.  

23958, 23598, 25938, 25398, 29358, 29538....

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3 years ago
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