4 years ago

This is the equation: g(r)=25-3r g(4)=

Mathematics

1 answer:

ANTONII [103]4 years ago

3 0

Equation: g(4)=25-3(4), answer: g(4)=13

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Step-by-step explanation:

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3 years ago

The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

$S_n=\displaystyle1+\frac13+\frac1{3^2}+\cdots+\frac1{3^n}$

Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

So we have

$\displaystyle\sum_{n=1}^\infty30\left(\frac13\right)^{n-1}=30\cdot\frac32=45$

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3 years ago

Find the inverse of the function y = x^2 + 12x

PilotLPTM [1.2K]

Answer:

y=x\\

x=y^{2} + 12y\\

y^{2} + 12y -x = 0\\

Delta = (12^{2}) - 4.1.(-x) = 144 +4X = 36.(4+x)

\sqrt{Delta} = 6 . \sqrt{(4+x)} \\

y' = \frac{-12 + 6.(\sqrt{(4+x)}}{2} = -6 + 3.\sqrt{(4+x)}\\

y" = -6 - 3.\sqrt{(4+x)}\\\\

y' = 3.\sqrt{(4+x)} - 6\\

y''= -3.\sqrt{(4+x)} - 6\\

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3 years ago

Put back into factored form: 144t - 36 Put back into factored form: 8x-12

erastovalidia [21]

Answer:

Step-by-step explanation:

In both cases we have a two-term expression. In each case, determine what the greatest common factor is and then use it to factor the expression:

144t - 36 = 36(4t - 1)

8x - 12 = 4(2x - 3)

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4 years ago

DEFG is a rhombus with m∠EFG=28. What is m∠FGE? 76 152 14

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14 adverage between numbers but i might be wrong

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3 years ago