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3 years ago

What is the area of a sector with a central angle of 131 degrees and a radius of 7.2 ft?

Mathematics

1 answer:

svetoff [14.1K]3 years ago

5 0

Answer:

162.78

Step-by-step explanation:

Use your π =3.14

3.14 times 7.2 times 7.2

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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

Where can we put parenthesis in 21 + 21 divided by 7 to make it equivalent to 6?

DiKsa [7]

(21+21)÷7

Step-by-step explanation:

21+21=42 42÷7=6 I'm not good at explaining lol

4 0

3 years ago

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Krystal bought a dishwasher from a rental center for $543.67. She makes 12 monthly payments of $48.62 with her credit card. The

Murljashka [212]

B.) $604.44 is your answer

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3 years ago

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What can you conclude about the population density from the table provided? Population Area (km²) Region A 20,178 521 Region B 1

Alika [10]

Answer:

A got it right

Step-by-step explanation:

got it right

6 0

2 years ago

-4 = x -1 can I see you work it out please?

kherson [118]

We need to get x alone, to do that we add 1 to both sides to cancel out the -1 on the right.
-4 = x -1
+1 +1
-3=x

This means x is equal to -3. Hope this helps!

4 0

3 years ago

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