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3 years ago

(t^-4)^-9t^2 A)t^26 B)t^-26 C)t^38 D)t^-38

1 answer:

4 0

The relevant rules of exponents are
.. (t^a)^b = t^(a·b)
.. t^a·t^b = t^(a+b)

You have
.. (t^-4)^-9·t^2
.. = t^((-4)*(-9) +2)
.. = t^38 . . . . . . . . . . . selection C

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Find the 8th term of the geometric sequence 3, 12, 48,...

Sophie [7]

$\begin{gathered} \text{The first term is 3, the common ratio is 4} \\ \text{That means;} \\ a=3,r=4 \\ \text{The nth term is } \\ T_n=ar^{(n-1)} \\ 8th=3\times4^{(8-1)} \\ 8th=3\times4^7 \\ 8th=3\times16384 \\ 8th=49152 \end{gathered}$

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1 year ago

A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$

The rate is negative as it represents the amount of caffeine leaving the body at certain time.

3 0

3 years ago

Use the figure to find the measures of the numbered angles. Explin your reasoning.

Reika [66]

1)81° due to the fact that 99° and (1) are supplementary angles
2)99° due to the fact that (5) and (2) are adjacent angles that sum up to equal 180°
3)81° due to the fact that it is the corresponding angle to (5)
4)99° due to the fact that (4) and (2) are alternate interior angles which equal the same
5)81° due to the fact that (5) and (6) are adjacent angles which means they are supplementary angles that add to equal 180°
6)99° due to the fact that (6) and (2) are corresponding angles which equal the same value
7)81° due to the fact that (7) and (3) are corresponding angles with equal the same degree

7 0

3 years ago

Help.... Other question got deleted.

Helen [10]

-2/25 is the slope
x1=4
hope this helps!

7 0

3 years ago

Use the function notation to write a recursive formula to represent the sequence: 4, 8, 12, ...

melamori03 [73]

Answer:

The correct answer is f(n) = f(n − 1) + 4

Step-by-step explanation:

Let us consider the sequence: 4, 8, 12, …

Using f(n) = f(n − 1) + 4, we can easily get the sequence.

As the first term is 4 and next term is obtained by adding 4 to the first term.

i.e. 4+4 = 8

8+4 = 12

12+4 = 16 and so on.

Since the next term is obtained by adding 4 to the previous term.

So, f(n) = f(n-1) + 4 would be the correct recursive formula for the function of the sequence 4, 8, 12, ....

Verification:

f(n) = f(n-1) + 4

Putting n=2 in f(n) = f(n-1) + 4 to get the second term of the sequence.

f(2) = f(2-1) + 4

f(2) = f(1) + 4

f(2) = 4 + 4

f(2) = 8

Putting n=3 in f(n) = f(n-1) + 4 to get the third term of the sequence.

f(3) = f(3-1) + 4

f(3) = f(2) + 4

So, adding 4 in f(2)=8 would give us the next term i.e. 12

f(3) = 8 + 4

f(3) = 12

Keywords: recursive formula, sequence

Learn more about using recursive formula from brainly.com/question/1851471

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7 0

2 years ago