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soldier1979 [14.2K]

3 years ago

15

On New years Eve, the temperature fell by 24 degrees in a span of 6 hours. By how many degrees did the temperature fall every ho

ur?

1 answer:

DochEvi [55]3 years ago

3 0

Answer:

4

Step-by-step explanation:

24/6

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

4 years ago

Read 2 more answers

Please help <br> Algebra 1<br> Look at the photo below...

I am Lyosha [343]

horizontal line: x=9

vertical line: y=3

You can plug it into the application demos to see it visually just put y=3 on one line and x=9 on the other

7 0

3 years ago

PLLLEEEAASSEE HELP ME<br><br> explain how you got the answer

valkas [14]

For # 1, the answer will be 1 because of the exponential rule $a^{0} = 1$ .

#2, the answer is going to be $x^{4}$ because of the exponential rule $a^{-b} = \frac{1}{a ^{b} }$ .

#3. I'm not sure that this could be simplified any further.

#4 To get the answer to this question, we must apply the distributive property, along with the exponential rule $a ^{m} × a ^{n} = a ^{m+n}$ . When we apply these properties, we'll get $- \frac{3}{x^4}$

For the other questions, they all apply the Laws of Exponents.

5 0

3 years ago

Help pleasseeeeeeeeee 6. If Ai charges $3.25 per serving of ice cream, how much will she make if she sells it to 12

Ivenika [448]

Answer:

40.62

Step-by-step explanation:

that's the answer I got

6 0

2 years ago

Determine if line AB is tangent to the circle. Type

adoni [48]

Answer:

If AB is a tangent to the circle, the triangle ABO is right angled, as the angle where a tangent meets the circumference is always 90 degrees.

We also know that Pythogoras' theorem only holds for right angled triangles.

The hypotenuse is 12 + 8 as 12 is the radius so is 20.

16^2+12^2 = 256 + 144 = 400 = 20^2 so AB must be tangent.

6 0

3 years ago