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4 years ago

I don’t understand the problem please help

Mathematics

1 answer:

balu736 [363]4 years ago

3 0

Answer:

See below

Step-by-step explanation:

So basically the product is the result of mulyplying ---> factor × factor = product. You need to replace the values given so basically

8 ×2/5(0.40) =3.2 which is between 0 and 8, making the first statement true. Hopefully, this gives you an idea on how to answer the rest!!

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Consider the function g(x) = (x-e)^3e^-(x-e). Find all critical points and points of inflection (x, g(x)) of the function g.

Elden [556K]

Answer:

The answer is " $cirtical\ points \ (x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})$ "

Step-by-step explanation:

Given:

$g(x) = (x-e)^3e^{-(x-e)}$

Find critical points:

$g(x) = (x-e)^3e^{(e-x)}$

differentiate the value with respect of x:

$\to g'(x)= (x-e)^3 \frac{d}{dx}e^{e-r} +e^{e-r} \frac{d}{dx}(x-e)^3=(x-e)^2 e^{(e-x)} [-x+e+3]$

critical points $g'(x)=0$

$\to (x-e)^2 e^{(e-x)} [e+3-x]=0\\\\\to e^{(e-x)}\neq 0 \\\\\to (x-e)^2=0\\\\ \to [e+3-x]=0\\\\\to x=e\\\\\to x=e+3\\\\\to x= e,e+3$

So,

The critical points of $(x,g(x))\equiv (e,0),(e+3,\frac{27}{e^3})$

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3 years ago

Given that y varies directly with x, and y = 15 when x = 8 , what is the proportionality constant, k? Round your answer to the h

aniked [119]

The proportionality constant "k" is 1.88

<h3><u>Solution:</u></h3>

Given that y varies directly with x

y = 15 when x = 8

To find: proportionality constant "k"

Direct variation means that increase/decrease in one quantity also causes increase/decrease in other quantity.

⇒ y varies directly with x

This means,

$y \propto x$

Can also be written as:

y = kx

Where "k" is the proportionality constant

Substituting the given values of "x" and "y"

15 = k(8)

$k = \frac{15}{8}$

k = 1.875

On rounding to nearest hundredths place we get 1.88

Thus the proportionality constant is 1.88

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