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2 years ago

Solve for y in terms of x

Mathematics

1 answer:

Alika [10]2 years ago

3 0

Answer:

(a) 3 - 2x - 2x² (b) -21

Step-by-step explanation:

given, y +2x² = 3 -2x

make y the subject:

y = 3 - 2x - 2x²

if y = f(x)

then

f(x) = 3 - 2x - 2x²

(b)<u> to find f(3) we need to replace x with 3:</u>

<u />

3 - 2(3) - 2*(3)²

-21

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2 years ago

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anyanavicka [17]

Answer:

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Step-by-step explanation:

The sum you are trying to understand is this.

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n}$

Remember that in general when you have a geometric series

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$\sum\limits_{n = 0}^{\infty} a*r^n = \frac{a}{1-r}$ and that equality is true as long as $|r| < 1$ .

Therefore here we have

$\sum\limits_{n=0}^{\infty} \frac{2}{3^n}\frac{(-1)^n}{5^n} = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{3*5} \big)^n = \sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n$ and $\big|\frac{-1}{15} \big| = \frac{1}{15} < 1$

Therefore we can use the formula and

$\sum\limits_{n=0}^{\infty} 2* \big(\frac{-1}{15} \big)^n = \frac{2}{1-(-1/15)} = \frac{2}{1+1/15} = 30/16 = 15/8$

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3 years ago

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