Write a rule for finding the value of any base with an exponet of 0

Select the correct answer. Convert (2, pi) to rectangular form.

mylen [45]

Answer:

B.

Step-by-step explanation:

Just took the test, is correct for Plato.

4 0

3 years ago

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t

BlackZzzverrR [31]

No idea what the previous part of the problem is, but you have

$f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n$
$f(x)=\displaystyle8\sum_{n\ge0}\left(-\dfrac14\right)^nx^{2n}$

which is valid for $\left|-\dfrac{x^2}4\right|$ , or $|x|$ . So the integral from 0 to 2 is

$\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx$
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\int_0^2x^{2n}\,\mathrm dx$

Note that since the power series only converges on the interval if $x$ is strictly less than 2, which means we have to treat this as an improper integral.

$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx$ [/tex]
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}$
$=\displaystyle8\sum_{n\ge0}\frac{(-1)^n}{2^{2n}(2n+1)}\lim_{t\to2^-}t^{2n+1}$
$=\displaystyle16\sum_{n\ge0}\frac{(-1)^n}{2n+1}$
$=16-\dfrac{16}3+\dfrac{16}5-\dfrac{16}7+\dfrac{16}9+\cdots$

6 0

3 years ago

7 times as much as the sum of 1/3 and 4/5

Vlada [557]

$7( \frac{1}{3} + \frac{4}{5} )$

$=7( \frac{1(5)}{3(5)} + \frac{4(3)}{5(3)} )$

$=7( \frac{5}{15} + \frac{12}{15} )$

$=7( \frac{17}{15})$

$=\frac{7}{1} ( \frac{17}{15})$

$=\frac{119}{15}$

$= 7\frac{14}{15}$ ≈ 7.93

4 0

3 years ago

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What is the quotient of b^3+4b^2-3b+126/b+7

stepladder [879]

The correct answer for the question that is being presented above is this one: "D. b² − 3b + 18 R252. T<span>he quotient of b^3+4b^2-3b+126/b+7. In order to get the answer, you have to start dividing b^3 by b. Then multiply the quotient to b + 7. Then after that, subtract. Do the same thing until you reached the end.</span>

7 0

3 years ago

A spherical exercise ball has a maximum diameter of 30 inches when filled with air. The ball was completely empty at the start,

Alex73 [517]

Answer:

A) A(t) = 4500*π - 1600*t

B) A(4) = 7730 in³

C) t = 8,8 sec

Step-by-step explanation:

The volume of the sphere is:

d max = 30 r max = 15 in

V(s) = (4/3)*π*r³ V(s) = (4/3)*π* (15)³

V(s) = 4500*π

A) Amount of air needed to fill the ball A(t)

A(t) = Total max. volume of the sphere - rate of flux of air * time

A(t) = 4500*π - 1600*t in³

B) After 4 minutes

A(4) = 4500*π - 6400

A(4) = 14130 - 6400

A(4) = 7730 in³

C) A(t) = 4500*π - 1600*t

when A(t) = 0 the ball got its maximum volume then:

4500*π - 1600*t = 0

t = 14130/1600

t = 8,8 sec

8 0

3 years ago