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2 years ago

5.

Mathematics

1 answer:

adelina 88 [10]2 years ago

4 0

Answer:

IHG= scalene

HJI= isosceles

KHI= scalene

HJK= equilateral

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F(x) = lnx/x

My name is Ann [436]

$f(x) = \frac{lnx}{x}$

(a) $f'(x) = \frac{d}{dx}[\frac{lnx}{x}]$
Using the quotient rule:
$f'(x) = \frac{\frac{1}{x} \cdot x - lnx}{x^{2}}$
$f'(x) = \frac{1 - lnx}{x^{2}}$

For maximum, f'(x) = 0;
$\frac{1 - lnx}{x} = 0$
$lnx = 1, x = e$

(b) <em>Deduce:
</em> $e^{x} \geq x^{e}, x > 0$
<em>
Soln:</em> Since x = e is the greatest value, then f(e) ≥ f(x) > f(0)
$\frac{ln(e)}{e} \geq \frac{lnx}{x}$
$\frac{1}{e} \geq \frac{lnx}{x}$ , since ln(e) is simply equal to 1

Now, since x > 0, then we don't have to worry about flipping the signs when multiplying by x.
$\frac{x}{e} \geq lnx$
$x \geq elnx$
$x \geq ln(x^{e})$

Taking the exponential to both sides will cancel with the natural logarithmic function in the right hand side to produce:
$e^{x} \geq e^{ln(x^{e}})$
$e^{x} \geq x^{e}$ , as required.

3 0

3 years ago

Write an equation of the line in slope intercept form that pass through the two

Ber [7]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -2}}\quad ,&{{ 15}})\quad 
% (c,d)
&({{ 9}}\quad ,&{{ -18}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-18-15}{9-(-2)}\implies \cfrac{-18-15}{9+2}
\\\\\\
\cfrac{-33}{11}\implies -3$

$\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-15=-3[x-(-2)]
\\\\\\
y-15=-3(x+2)\implies y-15=-3x-6\implies y=-3x+9$

8 0

3 years ago

Mr. Jimerson records the amount of snowfall that the local area recieves. 12am-1am: 0.3 inches | 1am-2am: 0.8 inches | 2am-3am:

MatroZZZ [7]

Answer:

5.781 inches.

Step-by-step explanation:

Since Mr. Jimerson records the amount of snowfall that the local area recieves, recording the following data: 12 am-1am: 0.3 inches | 1 am-2am: 0.8 inches | 2 am-3am: 1.36 inches | 3 am-4am: 2.019, if the total amount of snowfall at 7am is 7.8 inches, to determine how much snow fell between 4 am-7am the following calculation must be performed:

7.8 - 2.019 = X

5.781 = X

Therefore, since the amount of snow accumulated at 7 am was 7.8 inches, the snowfall between 4 and 7 am was 5.781 inches.

6 0

2 years ago

Hi. I have been doing really bad at math. I have a "tutor" and I study for hours yet I get F's on all my quizzes. I really need

Damm [24]

Answer:

just practice time and again practice might not make perfect but it surely makes better. relying when your teacher only might not help you must mostly rely on your hard work and also have people at your disposal to help you including the said teacher hope you'll improve

7 0

3 years ago

the point (-1,0.5) lies on the graph of f^-1(x)=2^x based on this information, which point lies on the graph of f(x)=log2x

Norma-Jean [14]

Answer:

(-1,0.5)...

the inverse "f^-1" of an exponential function is BY DEFINITION the "Log" function

Step-by-step explanation:

3 0

3 years ago