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2 years ago

Can I get some help on these

Mathematics

1 answer:

Rainbow [258]2 years ago

4 0

Number 1.
2x to the second power minus 2x minus 4
Number 2.
2a to the second power minus 3b minus a plus b to the second power.

Hope it helped :)

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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) Deduce:
 $e^{x} \geq x^{e}, x > 0$

Soln: 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

HELPP PLEASE AND GET POINTS

MArishka [77]

Answer:

112

Step-by-step explanation:

cause if you calculated it it will be 112.2222 so the closest thing is 112

3 0

2 years ago

In the diagram, R, S, and T are all points of tangency. What is the perimeter of Triangle XYZ?

Molodets [167]

Answer:

54 cm

Step-by-step explanation:

Perimeter = TZ + TX + RX + RY + SY + SZ

TZ = 5 cm

TX = 13 cm

RY = 9 cm

RX = TX = 13 cm (tangents drawn from and external point)

SY = RY = 9 cm (tangents drawn from and external point)

SZ = TZ = 5 cm (tangents drawn from and external point)

Plug in the values:

Perimeter = 5 + 13 + 13 + 9 + 9 + 5 = 54 cm

7 0

2 years ago

if your cell phone bill was $67.82 and there's a 7.5% late fee how much will you pay for your phone bill

kotegsom [21]

$67.82 if you pay it on time.
$90.43 if you pay it late.

8 0

3 years ago

The city buses that run in your neighborhood stop every 12 minutes .The first bus arrives at 5:00 am for passengers.You get to t

Irina-Kira [14]

Answer:

Therefore you will have to wait 11 minutes.

Step-by-step explanation:

Find the number of minutes between 5:00am and 8:37am

60 mins in an hour.

8-5=3 hours

60x3=180+37=217 minutes

Divide 217 by 12 to see how many bus stops have already been made

217/12=18

18*12=216

217-216=1 minute

12-1=11 minutes

Hope this helps!

8 0

2 years ago