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3 years ago

Which of the following are equivalent to 160%

Mathematics

1 answer:

vichka [17]3 years ago

3 0

18/10
9/5
Anything along those lines!

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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

2 years ago

Need help with compound fractions. Please answer both

Reika [66]

$\frac{8*( \frac{c}{c} )- \frac{3}{c} }{2*( \frac{7c}{7c})+ \frac{3}{7c} } \\ \\ \frac{ \frac{8c-3}{c} }{ \frac{14c+3}{7c} } \\ \\ \frac{8c-3}{c} * \frac{7c}{14c+3} \\ \\ = \frac{56c-21}{14c+3}$

Domain restrictions are what x values make the denominator zero.
a² + 5a - 36 = (a + 9)(a - 4)
a ≠ -9 ; a ≠ 4

6 0

2 years ago

Please help thank you.

Mnenie [13.5K]

Answer:

Option D

Step-by-step explanation:

Whenever we take a square root of a number the ± sign is with it like here in the question

$x^2=20\\\\Apply\ square\ root\ on\ both\ sides\\sqrt{x^2}=\sqrt{20} \\\\The\ square\ cancels\ out\ with\ the\ root\x=\sqrt{20}$

And then x = ±4.47 which means x has two values one is +4.47 and the other is -4.47 so Option D is our answer.

7 0

2 years ago

8. The measures of two angles in an isosceles triangle are shown in the diagram.

mote1985 [20]

Answer:

Step-by-step explanation:

Because 45 + 2x = 180 divide it by 2 gives 4

8 0

3 years ago

User: Translate the following words to algebra symbols, using "n" as the variable. Seven is two less than twice a number.

muminat

7 = 2n - 2

n= a number so twice a number is 2n and 7 is 2 less than twice this number.

7 0

2 years ago