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2 years ago

How many real solutions does this system of equations have? (x−3)^2+(y+1)^2=16x−7=0

Mathematics

2 answers:

Alinara [238K]2 years ago

6 0

Answer:

infinitely many

Step-by-step explanation:

Modeling with Systems assignment edge 2021:)

romanna [79]2 years ago

4 0

Answer:

Unsolvable

Step-by-step explanation:

This system right here has no solutions, maybe try something else if you were looking for a problem with multiple answers.

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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

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

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

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3 years ago

What is “One third of the opposite of a number is less than 12?”

nirvana33 [79]

Answer:

$\frac{1}{3}(-x)$ <12

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2 years ago

A sports club rewards teams based on overall points earned in a season. The data for points are shown in the table, where Low re

Kay [80]

The team that should be awarded for consistent performance should be Team M. This is because the standard deviation of the team's players' scores is the lowest. Standard deviation is a measure of how much the individual data points vary from the average value, and for a consistent performance, this variation will be low.

The team with the highest average is Team N. The average is the same as the mean, and this is the highest for Team N, with a value of 13.

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3 years ago

Let A = { 0 , 2 , 4 , 6 } , B = { 1 , 2 , 3 , 4 , 5 } , and C = { 1 , 3 , 5 , 7 } . Find { x ∣ x ∈ B or x ∈ C } .

EastWind [94]

Answer:

{1, 2, 3, 4, 5, 7}

Step-by-step explanation:

x in B or C is ...

B ∪ C = {1, 2, 3, 4, 5, 7}

5 0

3 years ago

The ratio of the ages of three children is 2:4:5. The sum of their ages is 33. What is the age of each child?

sdas [7]

We can represent this situation by the equation 2x+4x+5x=33.

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6:12:15.

Do these 3 ages add up to 33? 6 + 12 + 15 = 33? YES!

The children's ages are 6, 12 and 15 years respectively.

4 0

2 years ago

Read 2 more answers