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anyanavicka [17]

3 years ago

6

MOVIE PREVIEWS: There are eight previews before a movie. Seventy-five percent of the previews are for comedies. How many preview

s are for comedies?

2 answers:

Vedmedyk [2.9K]3 years ago

8 0

Answer:

It’s 6

Step-by-step explanation:

Step2247 [10]3 years ago

5 0

The answer is 6 Comedies!

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The graph of a quadratic function f(x) intersects the x-axis At -3 and 5. Create a function that would produce these results.

FinnZ [79.3K]

Answer:

f(x) = x² - 2x - 15

Step-by-step explanation:

∵ The function intersect x-axis at -3 and 5

∴ f(x) = 0 at x = -3 , 5

∵ The form of the quadratic equation is ⇒ ax² + -b/a x + c/a = 0

ax² - b/a x + c/a = 0

Where the sum of its roots is b/a and their multiplication is c/a

∵ a = 1

∵ -3 , 5 are the roots of the quadratic equation

∴ b = -3 + 5 = 2

∴ c = -3 × 5 = -15

∴ f(x) = x² - 2x - 15

6 0

4 years ago

najib brought a handheld game console for $289 after a 15% discount how much was the discount......................... PLS I NEE

sdas [7]

15% of 289 is 43.35 so just subtract 43.35 for 289 which is then $245.64 which is the discounted price

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3 years ago

When the exponent blank is applied to a nonzero base, the result is always 1

Anestetic [448]

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3 years ago

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SOLVE. integration of (1+v^2) /(1-v^3)

s2008m [1.1K]

$\displaystyle\int\frac{1+v^2}{1-v^3}\,\mathrm dv$

$1-v^3=(1-v)(1+v+v^2)$
$\implies\dfrac{1+v^2}{1-v^3}=\dfrac a{1-v}+\dfrac{b_0+b_1v}{1+v+v^2}$
$\implies\dfrac{1+v^2}{1-v^3}=\dfrac{a(1+v+v^2)+(b_0+b_1v)(1-v)}{1-v^3}$
$\implies 1+v^2=(a+b_0)+(a-b_0+b_1)v+(a-b_1)v^2$
$\implies\begin{cases}a+b_0=1\\a-b_0+b_1=0\\a-b_1=1\end{cases}\implies a=\dfrac23,b_0=\dfrac13,b_1=-\dfrac13$

So,

$\displaystyle\int\frac{1+v^2}{1-v^3}\,\mathrm dv=\dfrac23\int\frac{\mathrm dv}{1-v}+\dfrac13\int\frac{1-v}{1+v+v^2}\,\mathrm dv$

The first integral is easy. For the second, since the derivative of the denominator is $(1+v+v^2)=1+2v$ , we can add and subtract $3v$ to get

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

and for the first term employ a substitution. For the remaining term, we can complete the square in the denominator, then use a trigonometric substitution:

$\displaystyle\int\frac{1+2v}{1+v+v^2}\,\mathrm dv=\int\frac{\mathrm dt}t$

where $t=1+v+v^2\implies\mathrm dt=(1+2v)\,\mathrm dv$ , and

$\displaystyle\int\frac{3v}{1+v+v^2}\,\mathrm dv=3\int\frac v{\left(v+\frac12\right)^2+\frac34}\,\mathrm dv$

Then taking $v+\dfrac12=\dfrac{\sqrt3}2\tan s\implies \mathrm dv=\dfrac{\sqrt3}2\sec^2s\,\mathrm ds$ gives

$\displaystyle3\int\frac v{\left(v+\frac12\right)^2+\frac34}\,\mathrm dv=3\int\frac{\frac{\sqrt3}2\tan s-\frac12}{\left(\frac{\sqrt3}2\tan s\right)^2+\frac34}\left(\frac{\sqrt3}2\sec^2s\right)\,\mathrm ds$
$=\displaystyle\sqrt3\int(\sqrt3\tan s-1)\,\mathrm ds$
$=\displaystyle3\int\tan s\,\mathrm ds-\sqrt3\int\mathrm ds$

Now we're ready to wrap up.

$\displaystyle\int\frac{1+v^2}{1-v^3}\,\mathrm dv=\dfrac23\int\frac{\mathrm dv}{1-v}+\dfrac13\int\frac{1-v}{1+v+v^2}\,\mathrm dv$
$=\displaystyle-\frac23\ln|1-v|+\frac13\left(\int\frac{1+2v}{1+v+v^2}\,\mathrm dv-\int\frac{3v}{1+v+v^2}\,\mathrm dv\right)$
$=\displaystyle-\frac23\ln|1-v|+\frac13\int\frac{\mathrm dt}t-\frac13\left(3\int\tan s\,\mathrm ds-\sqrt3\int\mathrm ds\right)$
$=\displaystyle-\frac23\ln|1-v|+\frac13\ln|t|-\int\tan s\,\mathrm ds+\frac1{\sqrt3}\int\mathrm ds$
$=\displaystyle-\frac23\ln|1-v|+\frac13\ln|1+v+v^2|+\ln|\cos s|+\frac s{\sqrt3}+C$
$=\displaystyle-\frac23\ln|1-v|+\frac13\ln|1+v+v^2|+\ln\left|\frac{\sqrt3}{2\sqrt{1+v+v^2}}\right|+\frac1{\sqrt3}\tan^{-1}\frac{2v+1}{\sqrt3}+C$

This can be simplified a bit using some properties of logarithms to obtain

$=\displaystyle-\frac23\ln|1-v|+\frac13\ln(1+v+v^2)+\left(\ln\frac{\sqrt3}2-\frac12\ln(1+v+v^2)\right)+\frac1{\sqrt3}\tan^{-1}\frac{2v+1}{\sqrt3}+C$
$=\displaystyle-\frac23\ln|1-v|-\frac16\ln(1+v+v^2)+\frac1{\sqrt3}\tan^{-1}\frac{2v+1}{\sqrt3}+C$

6 0

3 years ago

Can someone help me with my assignments I need help with my ela assignments I’ll pay u 30$ if they are right

erastova [34]

Answer:

what are the questions? As long as it's not an essay I can try

Step-by-step explanation:

5 0

3 years ago

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