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3 years ago

X*2-6x-8 Find the vertex Find the X intercept Find the y intercept Graph

1 answer:

3 0

X^2 -6x -8 is a parabola in ax^2 + bx + c form
The axis of symmetry is -b/2a = 3
The vertex is (3,f(3)) = (3,-17)
The x-intercept is f(x)= 0 where x=-1.123, 7.123
Graphing: it opens upwards

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ch4aika [34]

What is the question here?

4 0

3 years ago

Find the radius of convergence, then determine the interval of convergence

galben [10]

The radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series. This can be obtained by using ratio test.

<h3>Find the radius of convergence R and the interval of convergence:</h3>

Ratio test is the test that is used to find the convergence of the given power series.

First aₙ is noted and then aₙ₊₁ is noted.

For ∑ aₙ, aₙ and aₙ₊₁ is noted.

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = β

If β < 1, then the series converges

If β > 1, then the series diverges

If β = 1, then the series inconclusive

Here $a_{k}$ = $\frac{(x+2)^{k}}{\sqrt{k} }$ and $a_{k+1}$ = $\frac{(x+2)^{k+1}}{\sqrt{k+1} }$

Now limit is taken,

$\lim_{n \to \infty} |\frac{a_{n+1}}{a_{n} }|$ = $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }/\frac{(x+2)^{k} }{\sqrt{k} }|$

= $\lim_{n \to \infty} |\frac{(x+2)^{k+1} }{\sqrt{k+1} }\frac{\sqrt{k} }{(x+2)^{k}}|$

= $\lim_{n \to \infty} |{(x+2) } }{\sqrt{\frac{k}{k+1} } }}|$

= $|{x+2 }|\lim_{n \to \infty}}{\sqrt{\frac{k}{k+1} } }}$

= $|{x+2 }|$ < 1

- 1 < ${x+2 }$ < 1

- 1 - 2 < x < 1 - 2

- 3 < x < - 1

We get that,

interval of convergence = (-3, -1)

radius of convergence R = 1

Hence the radius of convergence R is 1 and the interval of convergence is (-3, -1) for the given power series.

Learn more about radius of convergence here:

brainly.com/question/14394994

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5 0

1 year ago

Read 2 more answers

Choose all of the transformations that are rigid motions.

kkurt [141]

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, dilation and rotation.

Rigid transformations are transformation that produces an image with the same size, shape and angle as the original object. Rigid transformations are translation, rotation and reflection.

Dilation is not a rigid transformation.

All the transformations attached are rigid transformations.

7 0

3 years ago

What is 6/7-2/3 equal to

Ann [662]

6/7-2/3

Make sure they have the same denominators which means looking for the GCF

So the GCF is 21 in this case

6/7= 18/21

2/3= 14/21

18/21 - 14/21= 4/21

The answer is 4/21

8 0

3 years ago

Read 2 more answers

What is the circumference of a circle if the diameter is 12 in

Delvig [45]

Answer:
______________________________________________________
The circumference (in terms of "π") is: " 12π in. " .
__________________________________________________________
The circumference (using "3.14" as an approximation for "π") is: " 37.7 in. " .
__________________________________________________________

Circumference, "C" = π* d ; (d = diameter = 12 in.);

C = π* d = π * 12 in. = " 12π in. " (in terms of "π").

Or, using the approximation, "π ≈ 3.14" ;

C = 3.14 * (12 in.) = 37.68 inches ; round to: " 37.7 in. " .
______________________________________________

6 0

3 years ago