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2 years ago

Identify the constants from this expression. 5x - 7x + 5 - 12 + 4x - 3

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

5 0

Answer:

5, -12, -3

Step-by-step explanation:

A constant is a number by itself. Here, you can see that 5X is paired with a letter, that means that 5X is not a constant. So you could say that any whole number is a constant number and in this problem, 5, -12 and -3 are all the constant numbers in this expression.

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Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)

melamori03 [73]

Answer:

Step-by-step explanation:

Given that:

$f_x = \dfrac{x^2}{a^7-x^7}$

$= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}$

$= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}$

since $\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)$

Then, it implies that:

$\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n$

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$= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}$

$\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}$

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2 years ago

The sum of two numbers is 54. The large number is 18 more than the sampler number. What are the numbers ?

Karolina [17]

Answer: a=36; b=18

Step-by-step explanation:

1. You know that the sum of two numbers is 54, then, you have:

a+b=54

2. According to the problem, the larger number is 18 more than the sampler number, this can be expressed as following:

a=b+18

3. Then, you must substitute the second equation into the first equation and solve for b:

b+18+b=54

b=18

4. Then the value of a is:

a+18=55

a=36

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