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3 years ago

Would he earn more money with simple interest or with compound interest

Mathematics

1 answer:

zaharov [31]3 years ago

6 0

Answer:

The more often your interest compounds, the more interest you'll earn on your investment. It's easy to see that money grows more quickly when it's earning compound interest than when it's earning simple interest

Step-by-step explanation:

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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

3 years ago

Solve for x 3x - 2/ 3x + 1

givi [52]

Answer:

$7/3x+1$

Step-by-step explanation:

$3x - 2/ 3x + 1$

$=7/3x+1$

8 0

4 years ago

Read 2 more answers

Please help. Look at screenshot

Citrus2011 [14]

Answer:

Increasing:

x < 0

x > 2

Decreasing:

0 < x < 2

-1 < x < 2

x > 2

x < -1

Step-by-step explanation:

Function is increasing when it is going up as we go rightward

Function is decreasing when it is going down as we go rightward

We can see that as we move up (from negative infinity) until x = 0, the function is increasing. Also, as we go right from x = 2 towards positive infinity, the function is going up (increasing).

So,

Increasing:

x < 0

x > 2

The function is going down, or decreasing, at the in-between points of increasing, that is from 0 to 2, so that would be:

Decreasing:

0 < x < 2

When we want where the function is greater than 0, we basically want the intervals at which the function is ABOVE the x-axis [ f(x) > 0 ].

Looking at the graph, it is

from -1 to 2 (x axis)

and 2 to positive infinity

We can write:

-1 < x < 2

x > 2

Now we want when the function is less than 0, that is basically saying when the function is BELOW the x-axis.

This will be the other intervals than the ones we mentioned above in part (b).

Looking at the graph, we see that the graph is below the x-axis when it is less than -1, so we can write:

x < -1

4 0

4 years ago

8.4.9 On or off the line & Practice Problems

Andrews [41]

Answer:

Number of quarters → 15

Number of dimes → 2

Step-by-step explanation:

Let the number of dimes I have = y

And number of quarters = x

Since, I have amount in my pocket = $2

Therefore, 0.10y + 0.25x = 2

100(0.10y + 0.25x) = 100×2

25x + 10y = 200

5x + 2y = 40

2y = -5x + 40

y = -2.5x + 20 ---------(1)

Total number of coins in my pocket = 17

x + y = 17

y = -x + 17 ---------(2)

By using a graphing calculator we can graph these two lines (As attached)

Solution of the given system of equations will be the point of intersection of these lines.

Solution → (2, 15)

Number of quarters → 15

Number of dimes → 2

4 0

3 years ago

What is the next term ofthe sequence 5z, 8x, 11v,...?

nexus9112 [7]

Answer:

14t

Step-by-step explanation:

stuvwxyz

567891011121314

6 0

4 years ago