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3 years ago

Graph the point (-2,-3) on the coordinate plane

Mathematics

2 answers:

atroni [7]3 years ago

3 0

Answer:

The point will come in III quadrant

Step-by-step explanation:

The graph is as follows:

Fynjy0 [20]3 years ago

3 0

Just put a dot there

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Which plane is parallel to plane CIJ??

tekilochka [14]

Answer:

Step-by-step explanation:

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3 years ago

what key feature(s) can be easily identified from standard form? Explain how each key feature is related to the rollercoaster. U

raketka [301]

Answer:

Step-by-step explanation:

Key features

when t = 0

the initial height is 143/3 = 47⅔ ft

initial velocity is -310/3 = -103⅓ ft/s (downward)

initial acceleration is 2(64) = 128 ft/s² (upward)

I would not like to ride this roller coaster!

that's about four times the acceleration of gravity, and it only increases as the car gets to the bottom of the curve at t = 1 s

For part 3

I'm not sure what they mean by "not realistic"

while the initial acceleration is high. the acceleration at t = 1 is zero except that in 'reality' the car would have to be going through a curve to change direction from down to up. That would create very high centripetal acceleration and therefore centripetal forces.

5 0

2 years ago

(a) Suppose anxn has finite radius of convergence R and an ≥ 0 for all n. Show that if the series converges at R, then it also c

valina [46]

Answer:

a) See the proof below.

b) $\sum \frac{(-x)^n}{n}$

Step-by-step explanation:

Part a

For this case we assume that we have the following series $\sum a)n x^n$ and this series has a finite radius of convergence $R$ and we assume that $a_n \geq 0$ for all n, this information is given by the problem.

We assume that the series converges at the point $x= R$ since w eknwo that converges, and since converges we can conclude that:

$\sum a)n R^n < \infty$

For this case we need to show that converges also for $x=-R$

So we need to proof that $\sum a_n (-R)^n < \infty$

We can do some algebra and we can rewrite the following expression like this:

$\sum a_n (-R)^n = \sum (-1)^n a)n R^n$ and we see that the last series is alternating.

Since we know that $\sum a_n x^n$ converges then the sequence { $a_n R^n$ } must be positive and we need to have $lim_{n\to \infty} a^n R^n = 0$

And then by the alternating series test we can conclude that $\sum a_n (-R)^n$ also converges. And then we conclude that the power series $a_n x^n$ converges for $x=-R$ ,and that complete the proof.

Part b

For this case we need to provide a series whose interval of convergence is exactly (-1,1]

And the best function for this $\frac{(-x)^n}{n}$

Because the series $\sum \frac{(-x)^n}{n}$ converges to $-ln(1+x)$ when $|x|$ using the root test.

But by the properties of the natural log the series diverges at $x=-1$ because $\sum \frac{1}{n} =\infty$ and for $x=1$ we know that converges since $\sum \frac{-1}{n}$ is an alternating series that converges because the expression tends to 0.