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3 years ago

1. Rewrite y = 3x in function notation. 3x = y f(x) = 3x f = 3x f(x) = y

Mathematics

2 answers:

Helen [10]3 years ago

4 0

3x = y is the answer

earnstyle [38]3 years ago

3 0

The answer is: f(x) = 3x

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Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

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3 years ago

42=Wf×64 (what fraction)

Dmitry [639]

So basically 42=x times 64 or 42=64x where you want x to be represented as a fraction so just don't simplify as much

42=64x
divide both sdies by 64
42/64=64/64x
42/64=1x
x=42/64
simplify
42/64=21/32

the answer is 21/32 in simplest form

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3 years ago

a collector has 80 jackeys and 125 shirts she wants to maintain ratio in her collection but she needs to sell some of her items

Irina18 [472]

Answer:

Step-by-step explanation:

Well, we need to simplify this. we have a ratio of 80:125.

As these numbers end in either 0 or 5, we know they are divisible by 5.

By dividing these by five, our ratio becomes 16:25.

As we have 16 jackets, we know we must need to sell 25 jackets to maintain the ratio.

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Calculate the area of quadrilateral ABCD state the units of your answer .

Zarrin [17]

Answer:158.76 cm^2

Step-by-step explanation:

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avanturin [10]

The answer is y=5+0
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