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3 years ago

. An elevator starts at the 6th floor. It goes up 7 floors twice, and then it goes

Mathematics

1 answer:

Anettt [7]3 years ago

4 0

Well let's see what floor each one lands on and figure out which one is higher.

Something to note:

down = subtracting

up = adding

if something says it's doing something more than once, add it the number of times it's doing that thing. (You can also multiply it by that number but the adding way is a bit easier to understand and explain)

Elevator 1:

6 + 7 + 7 - 10 = 10

Elevator 2:

20 - 5 - 5 - 5 + 12 = 17

Elevator 2 ends on a higher floor (reasoning above)

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Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note

Viktor [21]

a. Recall that

$\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C$

For $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

By integrating both sides, we get

$\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}$

If $x=0$ , then

$\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0$

so that

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

We can shift the index to simplify the sum slightly.

$\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n$

b. The power series for $x\ln(1-x)$ can be obtained simply by multiplying both sides of the series above by $x$ .

$\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n$

c. We have

$\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)$

$\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}$

4 0

3 years ago

How many cubic centimeters of water can this paper cone cup hold?

blagie [28]

48π cm^3

Step-by-step explanation:

The formula for the volume of a cone is...

$V=\frac{1}{3}\pi r^2h$

We can plug everything we know from the photo into the equation, but note that the picture gives us the diameter, which is 8, instead of the radius. The radius is half of the diameter, so the radius will be 4. Also we will be leaving pi as it is, instead of changing it to 3.14.

$V=\frac{1}{3}*(\pi *4*4*9)$