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3 years ago

What is the value of -3|15 - s| + 2s^3 when s = -3?

Mathematics

1 answer:

Scilla [17]3 years ago

3 0

-3|15 - s| + 2s^3
=-3|15 - (-3)| + 2(-3)^3
= -3|18| -54
= -54 - 54
= -108

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Fine the smallest positive integer n so that

Marizza181 [45]

Answer:

n = 9

Step-by-step explanation:

Let's first prove that for any constants k > 0, $n\geq 1$

$\lim_{x\to \infty}\frac{\log x^k}{x^n}=0$

The derivative

$(\log (x^k))'=\frac{kx^{k-1}}{x^k}=\frac{k}{x}$

and the derivative $(x^n)' = nx^{n-1}$

Now, applying L'Hôpital's rule we find that

$\lim_{x\to \infty}\frac{\log x^k}{x}=\lim_{x\to \infty}\frac{k}{nx^n}=0$

Now, let f be the function

$f(x)=x^8log(x^3)+x^6log(x^5)$

It is easy to see that f(x) is $O(x^n)$ only if $n\geq 9$

If $n\geq 9$

$\frac{f(x)}{x^n}=\frac{x^8log(x^3)+x^6log(x^5)}{x^n}=\frac{log(x^3)}{x^{n-8}}+\frac{log(x^5)}{x^{n-6}}$

but both n-8 and n-6 are greater than one, so

$\lim_{x \to \infty}\frac{f(x)}{x^n}=0$

and f is $O(x^n)$

On the other hand, if $n \leq 8$ then

$\frac{f(x)}{x^n}=x^{8-n}log(x^3)+x^{6-n}log(x^5)$

but 8-n is greater or equal than one, so

$\lim_{x \to \infty}\frac{f(x)}{x^n}=\infty$

and so f(x) in not $O(x^n)$

3 0

3 years ago

Recall that a conflict of interest scenario was presented to a sample of 200 marketing researchers and that 109 of these researc

Tju [1.3M]

Answer: Null hypothesis: $p\leq0.50$

Alternative hypothesis: $p>0.50$

Step-by-step explanation:

A null hypothesis is a type of hypothesis that states that there is no difference between a particular parameter of a population whereas an alternative hypothesis states that there is a difference.

Given: p = Proportion of all marketing researchers who disapprove of the actions taken in the conflict of interest scenario.

n= 200

Sample proportion = $\hat{p}=\dfrac{109}{200}=0.545$

Claim : p>0.50

Null hypothesis: $p\leq0.50$

Alternative hypothesis: $p>0.50$

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3 years ago

Apply the distributive property to factor out the greatest common factor. 6+30

marissa [1.9K]

The greatest common factor between 6 and 30 would be 6, but I need to see the problem on the original piece of paper of a picture to understand the distributive property part of your question.

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4 years ago

Read 2 more answers

What is x ^ 7 times x ^ -2?

gtnhenbr [62]

The answer to that question is going to be 44 because x ^ 7 times 46 x ^ - 2 is 44 that's the answer

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4 years ago

A ferris wheel can accommodate 55 people in Twenty minutes. How many people can ride the ferris wheel in 3 hours? What was the r

DerKrebs [107]

1 hour = 60 minutes.

60 minutes / 20 minutes = 3.

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165 people x 3 hours = 495 people. (Total people in 3 hours)

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