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(9^6 * 7^-9)^-4.<br> Thanks!

Anuta_ua [19.1K]

Answer:

$\frac{7^{36}}{9^{24}}$

Step-by-step explanation:

Check the picture

7 0

1 year ago

The quantity, Q, of a drug in the blood stream begins with 250 mg and decays to one-fifth its value over every 90 minute period.

Mazyrski [523]

Answer:

$a=250 \, mg\\\\b=5\\\\T= 90'$

Step-by-step explanation:

We have that $Q(t) = a\cdot b^{-\frac{t}{T}} \\$

Where t is the time (in minutes) and for the sake of dimensional consistency, let's assume that T is also in minutes, b is an adimensional number, and a is in mg. So we will have Q in mg as a consequence.

We now want to find out what values these constants might take. Let's see what happens when $t=0$ , that is, just as we start. At that point, we have that the amount of drug in the bloodstream must be equal to 250mg, thus:

$Q(0)= a\cdot b ^{-\frac{0}{T} }=250\,mg\\Q(0)= a=250\,mg$

We have found the constant $a$ ! It is the initial amount of drug! we have made use of the fact that any number raised to the 0th power is equal to one.

Now, we know that every 90 minutes, the amount of drug decreases to one fifth of its former value. How do we put this in mathematical form? Like so:

$Q(t+90')=Q(t)/5$

That is, 90 minutes after time t the amount of drug will be one fifth of the amount of drug at time t. Let's expand the last equation:

$Q(t+90')=Q(t)/5\\\\a\cdot b^{-\frac{t+90'}{T} }=a\cdot b^{-\frac{t}{T} }/5\\\\ b^{-\frac{t+90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{t}{T} }b^{-\frac{90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{90'}{T} }=\frac{1}{5}$

Now the last expression isn't enough to determine both T and b, but that also means that we have some freedom in how we choose them. What seems most simple is to pick $T=90'$ and thus we will get:

$b^{-1 }=\frac{1}{5}\\\\\frac{1}{b}= \frac{1}{5}\\\\b=5$

And that is our final result.

3 0

3 years ago

X = –6 3x − 2y = –6 solve using substetution <br> NEED FAST

kondaur [170]

Answer:

(x = -6), (y = -6)

(-6,-6)

Step-by-step explanation:

X=-6

3x - 2y = -6

3(-6) - 2y = -6

-18 - 2y = -6

What you do to one side, you do to the other. And when you take it over to the other side, you'll have to turn -18 into a positive 18.

-2y = 18 - 6

-2y = 12

Divide both sides by -2

y = -6

7 0

3 years ago

10. When you add the same number to both sides of an inequality, is the inequality still true? Explain how you know your stateme

avanturin [10]

The inequality is still true! If you add a number, say 5 to both sides of the following inequality, does anything change?

3 < 6

3 + 5 < 6 + 5

8 < 11

The inequality is still true. We know the statement holds for subtracting the same number because, in a way, addition and subtraction are pretty much the same operation. If I subtract 5 from both sides, I can think of it like "I add negative 5 to both sides" or something along those lines. It's kind of backwards thinking.

6 0

3 years ago

The owner of a restaurant wants to collect data to find out the customers' opinions on the variety of appetizers offered on the

kirill115 [55]

I think the answer is D

6 0

3 years ago

I will give brainliest if you sub and stay subbed to JD Outdoors & Gaming​

I will give brainliest if you sub and stay subbed to JD Outdoors & Gaming