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3 years ago

How to round .9999 to the nearest hundred?

Mathematics

1 answer:

sesenic [268]3 years ago

3 0

Since .9999 is less than 100, the nearest hundred is 0.

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Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 +

timama [110]

Looks like your function is

$f(x)=\dfrac x{6x^2+1}$

Rewrite it as

$f(x)=\dfrac x{1-(-6x^2)}$

Recall that for $|x|$ , we have

$\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n$

If we replace $x$ with $-6x^2$ , we get

$f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}$

By the ratio test, the series converges if

$\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2$

Solving for $x$ gives the interval of convergence,

$|x|^2$

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

3 0

3 years ago

Please help!! thank you.

Zina [86]

(A) Product of $-2x^{3}+x-5$ and $x^{3}-3x-4$ is:

$(-2x^{3}+x-5)(x^{3}-3x-4)$

$=-2x^{3}(x^{3}-3x-4)+x(x^{3}-3x-4)-5(x^{3}-3x-4)$

$=(-2x^{3})(x^{3})+(-2x^{3})(-3x)+(-2x^{3})(-4)+x(x^{3})+(x)(-3x)+(x)(-4)+(-5)(x^{3})+(-5)(-3x)+(-5)(-4)$

$=-2x^{6}+6x^{4}+8x^{3}+x^{4}-3x^{2}-4x-5x^{3}+15x+20$

$=-2x^{6}+6x^{4}+x^{4}+ 8x^{3}-5x^{3}-3x^{2}-4x+15x+20$

$=-2x^{6}+7x^{4}+3x^{3}-3x^{2}+11x+20$

(B) Yes.

Product of $-2x^{3}+x-5$ and $x^{3}-3x-4$ = Product of $x^{3}-3x-4$ and $-2x^{3}+x-5$ because multiplication is commutative.

Commutative Property of multiplication says that a.b = b.a.

Thus, multiplication is same irrespective of the order of two numbers.

5 0

3 years ago

PLEASE HELP URGENT‼️‼️

Dima020 [189]

Part A

(3x)^2*x^4

(3x)*(3x)*x^4 .... expand out (3x)^2

(3*3)*(x*x*x^4)

9x^6

Answer: 9x^6

============================================

Part B

It appears that Tonya forgot to square the 3 term and had this as her steps

(3x)^2*x^4

3x^2*x^4

3x^(2*4)

3x^8

Which is incorrect as the answer in part A indicates.

Not only is the '3' part wrong, but also the exponent of 8. Instead of multiplying the exponents, she should have added them.

The rule is a^b*a^c = a^(b+c). In this case, a = x, b = 2 and c = 4.

So x^2*x^4 = x^(2+4) = x^6

3 0

3 years ago

What is the measure in degrees for the central angle of a circle whose radius is 9 cm and intercepted arc length is 7.2 cm?

Marina CMI [18]

Answer:

Therefore the measure of the central angle is 45.86°.

Step-by-step explanation:

Given:

Radius = 9 cm

arc length = 7.2 cm

pi = 3.14

To Find:

Central angle = θ =?

Solution:

If the θ measured in degree then the arc length is given as

$\textrm{arc lenght}=\dfrac{\theta}{360\°}\times 2\pi r$

Where r = radius, θ = Central angle

On substituting the values we get

$7.2=\dfrac{\theta}{360}\times 2\times 3.14\times 9\\\\\theta=\dfrac{2592}{56.52}=45.8598=45.86\\\therefore \theta=45.86\°$

Therefore the measure of the central angle is 45.86°.

4 0

3 years ago

O perimetro de um quadrado de area 100 cm2 é??

Murljashka [212]

Answer:

sorry. I don't speak your language

8 0

2 years ago