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4 years ago

_+_+_= 30 You can only use 1,3,5,7,9,11,13,15 No zeros, no decimals, no tricks.

Mathematics

2 answers:

butalik [34]4 years ago

7 0

There is no solution to this equation using normal methods.

4vir4ik [10]4 years ago

5 0

I am not sure that you can. You can not add 3 odd numbers and get an even number.

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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

Graph the system of equations.

Y_Kistochka [10]

Answer:

Step-by-step explanation:

I cannot use the line tool for you, but I can rewrite the equations

y = -x + 4 is good enough

Two points for this graph:

x = 0 -> y = 4 gives the point (0, 4)

x = 1 -> y = 3 gives the point (1, 3)

18x + 6y = -6

6y = -18x - 6

y = -3x - 2

Two ponts for this graph:

x = 0 -> y = -2 gives the point (0, -2)

x = 1 -> y = -5 gives the point (1, -5 )

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3 years ago

What’s the product (5r+2)(3r-4)

Marrrta [24]

$(5r+2)(3r-4) =15r^2-20r+6r-8=15r^2-14r-8$

3 0

3 years ago

Read 2 more answers

If f(x) = 5x, what is f–1(x)?

Verdich [7]

We are given f(x) = 5x
and we are to find inverse of f(x).

Step 1:
Replace f(x) by y.
So,

y = 5x

Step 2:
Isolate x
So,

x = y/5

Step 3:
Replace x by f'(y)
So,

f'(y) = y/5

Step 4:
Replace all occurrences of y by x.
So,

f'(x) = x/5

Therefore, the inverse of f(x) = 5x is f'(x) = x/5

7 0

4 years ago

The sale price S (in dollars) of an item is given by the formula S=L−rL, where L is the list price (in dollars) and r is the dis

ser-zykov [4K]

The sale price S (in dollars) of an item is given by the formula

S=L−rL , where L is the list price (in dollars) and r is the discount rate.

Since, S = L -rL

rL = L -S

r = $\frac{L-S}{L}$