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4 years ago

WILL MARK BRAINLIEST!!!

Mathematics

1 answer:

lions [1.4K]4 years ago

8 0

Answer:

Step-by-step explanation: I did this test and got it right. I hope this helps!

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Given that y = (e^x)/x, x > 0, find the range of values of x where y is a decreasing

vodka [1.7K]

Answer:

The interval for which y is a decreasing function of x is:

$(0, 1)$

Or as an inequality:

$0$

Step-by-step explanation:

We are given the equation:

$\displaystyle y=\frac{e^x}{x}\, ,x>0$

And we want to find the range of values x for which y is a decreasing function of x.

y is decreasing whenever y' is negative. Find y' using the Quotient Rule:

$\displaystyle y'=\frac{(e^x)'(x)-e^x(x)'}{(x)^2}$

Differentiate:

$\displaystyle y'=\frac{xe^x-e^x}{x^2}$

y is decreasing whenever y' is negative. Thus:

$\displaystyle 0>\frac{xe^x-e^x}{x^2}$

Multiply both sides by x². This is always positive so we do not need to change the sign:

$xe^x-e^x$

Factor:

$e^x(x-1)$

eˣ is always positive. So:

$x-1$

Adding one to both sides produces:

$x$

Therefore, y is a decreasing function of x when x is less than one (and greater than 0).

In interval notation:

$(0, 1)$

Or as an inequality:

$0$

8 0

3 years ago

PLS PLS PLS IM BEGGING YOU, HELP ME, i’ve been trying so hard to solve this for hours and i still dont get it :( pls help me

OverLord2011 [107]

Answer:

m=79

t=54

Step-by-step explanation:

yes these are the answers

7 0

3 years ago

Read 2 more answers

Lucille has a collection of more than 500 songs on her phone that have a mean duration of 215 seconds and a standard deviation o

DochEvi [55]

Answer:

The mean of the sampling distribution is of 215 seconds and the standard deviation is 5.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .