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4 years ago

Is 12/10 rational or irrational?

Mathematics

2 answers:

RSB [31]4 years ago

5 0

It is a rational number

Viefleur [7K]4 years ago

3 0

12/10 is a rational number

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Make a function table for each situation. The find the domain and range.

kupik [55]

For the first hour its 24, then 48, then 72, then 100!!!

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4 years ago

What is the area of B

german

If there is no more informations, then:

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3 years ago

Evaluate the limits<br><br>

julsineya [31]

$x > \ln(x)$ for all $x$ , so

$\displaystyle \lim_{x\to\infty} (\ln(x) - x) = - \lim_{x\to\infty} x = \boxed{-\infty}$

Similarly, $\displaystyle \lim_{x\to\infty} (x-e^x) = - \lim_{x\to\infty} e^x = \boxed{-\infty}$

We can of course see the limits are identical by replacing $x\mapsto e^x$ , so that

$\displaystyle \lim_{x\to\infty} (\ln(x) - x) = \lim_{x\to\infty} (\ln(e^x) - e^x) = \lim_{x\to\infty} (x - e^x)$

You can also rewrite the limands to accommodate the application of l'Hôpital's rule. For instance,

$\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\exp\left(\lim_{x\to\infty} (x - e^x)\right)\right) = \ln\left(\lim_{x\to\infty} e^{x-e^x}\right) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right)$

Using the rule, the limit here is

$\displaystyle \lim_{x\to\infty} \frac{(e^x)'}{\left(e^{e^x}\right)'} = \lim_{x\to\infty} \frac{e^x}{e^x e^{e^x}} = \lim_{x\to\infty} \frac1{e^{e^x}} = 0$

so the overall limit is

$\displaystyle \lim_{x\to\infty} (x - e^x) = \ln\left(\lim_{x\to\infty} \frac{e^x}{e^{e^x}}\right) = \ln(0) = \lim_{x\to0^+} \ln(x) = -\infty$

6 0

2 years ago

A hardware store has 200 paintbrushes. They order 9 boxes with 12 paintbrushes each. They sell 11 boxes that have 6 paintbrushes

grin007 [14]

Answer:

Step-by-step explanation:

The hardware store has 200 paintbrushes. They order 9 boxes with 12 paintbrushes each. This means that the total number of paintbrushes that was ordered is

12 × 9 = 108

Therefore, the total number of paintbrushes that the store has would be

200 + 108 = 308

They sell 11 boxes that have 6 paintbrushes each. This means that the total number of paintbrushes that they sold is

11 × 6 = 66

Therefore, the number of paintbrushes left would be

308 - 66 = 242

The manager's estimate is reasonable. They ordered about 120 paintbrushes and sold about 60 of them so they should have about 60 more paintbrushes than they started with.

4 0

4 years ago

A=2 pie r squared + 2 pie r h solve for h

Sindrei [870]

<span>A=2pie r^2 + 2pie rh so get h alone.
first take out the common factor of 2pie 2, so A=2pie r (r+h)
then divide by 2pie r, A/2pie r= r+h
then subtract r, so (A/2pie r) - r= h</span>

8 0

3 years ago