Log (z ^ 3)/(x ^ 4 * y ^ 5) with steps please

Neptune has 8 known moons. This is 2 more than 1/3 of the number of known moons on Saturn. How many moons is Saturn known to hav

horrorfan [7]

If Neptune has 8 and is 2 more than 1/3 the number of Saturn's moons, you would subtract 2 from 8 to get 6, then multiply that by 3 to get 18.

5 0

3 years ago

Learning Theory In a typing class,the averege number N of words per minutes typed after t weeks of lessons can be modeled by N =

Jet001 [13]

Answer:

a) $N(t=10) = \frac{95}{1+8.5 e^{-0.12(10)}}= \frac{95}{1+ 8.5 e^{-1.2}} = 26.684$

b) $N(t=20) = \frac{95}{1+8.5 e^{-0.12(20)}}= \frac{95}{1+ 8.5 e^{-2.4}} = 53.639$

c) $70 =\frac{95}{1+8.5 e^{-0.12t}}$

$1+ 8.5 e^{-0.12t} = \frac{95}{70}= \frac{19}{14}$

$8.5 e^{-0.12t} = \frac{19}{14}-1= \frac{5}{14}$

$e^{-0.12t} = \frac{\frac{5}{14}}{8.5}= \frac{5}{119}$

$ln e^{-0.12t} = ln (\frac{5}{119})$

$-0.12 t = ln(\frac{5}{119})$

$t = \frac{ln(\frac{5}{119})}{-0.12} = 26.414 weeks$

d) If we find the limit when t tend to infinity for the function we have this:

$lim_{t \to \infty} \frac{95}{1+8.5 e^{-0.12t}} = 95$

So then the number of words per minute have a limit and is 95 as t increases without bound.

Step-by-step explanation:

For this case we have the following expression for the average number of words per minutes typed adter t weeks:

$N(t) = \frac{95}{1+8.5 e^{-0.12t}}$

Part a

For this case we just need to replace the value of t=10 in order to see what we got:

$N(t=10) = \frac{95}{1+8.5 e^{-0.12(10)}}= \frac{95}{1+ 8.5 e^{-1.2}} = 26.684$

So the number of words per minute typed after 10 weeks are approximately 27.

Part b

For this case we just need to replace the value of t=20 in order to see what we got:

$N(t=20) = \frac{95}{1+8.5 e^{-0.12(20)}}= \frac{95}{1+ 8.5 e^{-2.4}} = 53.639$

So the number of words per minute typed after 20 weeks are approximately 54.

Part c

For this case we want to solve the following equation:

$70 =\frac{95}{1+8.5 e^{-0.12t}}$

And we can rewrite this expression like this:

$1+ 8.5 e^{-0.12t} = \frac{95}{70}= \frac{19}{14}$

$8.5 e^{-0.12t} = \frac{19}{14}-1= \frac{5}{14}$

Now we can divide both sides by 8.5 and we got:

$e^{-0.12t} = \frac{\frac{5}{14}}{8.5}= \frac{5}{119}$

Now we can apply natural log on both sides and we got:

$ln e^{-0.12t} = ln (\frac{5}{119})$

$-0.12 t = ln(\frac{5}{119})$

And then if we solve for t we got:

$t = \frac{ln(\frac{5}{119})}{-0.12} = 26.414 weeks$

And we can see this on the plot 1 attached.

Part d

If we find the limit when t tend to infinity for the function we have this:

$lim_{t \to \infty} \frac{95}{1+8.5 e^{-0.12t}} = 95$

So then the number of words per minute have a limit and is 95 as t increases without bound.

8 0

3 years ago

Can you simplify 5/11?

boyakko [2]

No

decimal form <span>0.45454545</span>

8 0

3 years ago

Members of the high school baseball team need to purchase cleats before the season starts. The pitcher paid $70 for his, but the

prohojiy [21]

Answer:

The pitcher paid $70.

The second baseman paid $63.

$70 -$63 = $7

Step-by-step explanation:

6 0

3 years ago

Points J and K are midpoints of the sides of triangle FGH. What is the value of y?

sashaice [31]

The answer

the complement of the question is

What is the value of y?

2
5
7
<span>8
</span>
According to the image, HKJ and FGH are similar, we can apply the theorem of thales
since GK and GF are parallels, so

HK / HF = HJ / HG = KJ / GF and as we see on the figure, HK = HF /2, this implies 2HK =HF

HK / 2HK = KJ / GF it is equivalent to 1/2 = 2y+5 / 5y +3

likewise, equivalent to 5y +3 = 4y +10, 5y-4y = 10-3, and y = 7

so the answer is 7

7 0

3 years ago

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