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love history [14]
2 years ago
9

Find the volume of the cone. Round your answer to the nearest hundredth.

Mathematics
1 answer:
noname [10]2 years ago
7 0

Answer:

can we get the figure plz

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Calculus hw, need help asap with steps.
nikdorinn [45]

Answers are in bold

S1 = 1

S2 = 0.5

S3 = 0.6667

S4 = 0.625

S5 = 0.6333

=========================================================

Explanation:

Let f(n) = \frac{(-1)^{n+1}}{n!}

The summation given to us represents the following

\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=\sum_{n=1}^{\infty} f(n)\\\\\\\displaystyle \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!}=f(1) + f(2)+f(3)+\ldots\\\\

There are infinitely many terms to be added.

-------------------

The partial sums only care about adding a finite amount of terms.

The partial sum S_1 is the sum of the first term and nothing else. Technically it's not really a sum because it doesn't have any other thing to add to. So we simply say S_1 = f(1) = 1

I'm skipping the steps to compute f(1) since you already have done so.

-------------------

The second partial sum is when things get a bit more interesting.

We add the first two terms.

S_2 = f(1)+f(2)\\\\S_2 = 1+(-\frac{1}{2})\\\\S_2 = \frac{1}{2}\\\\S_2 = 0.5\\\\\\

The scratch work for computing f(2) is shown in the diagram below.

-------------------

We do the same type of steps for the third partial sum.

S_3 = f(1)+f(2)+f(3)\\\\S_3 = 1+(-\frac{1}{2})+\frac{1}{6}\\\\S_3 = \frac{2}{3}\\\\S_3 \approx 0.6667\\\\\\

The scratch work for computing f(3) is shown in the diagram below.

-------------------

Now add the first four terms to get the fourth partial sum.

S_4 = f(1)+f(2)+f(3)+f(4)\\\\S_4 = 1+(-\frac{1}{2})+\frac{1}{6}-\frac{1}{24}\\\\S_4 = \frac{5}{8}\\\\S_4 \approx 0.625\\\\\\

As before, the scratch work for f(4) is shown below.

I'm sure you can notice by now, but the partial sums are recursive. Each new partial sum builds upon what is already added up so far.

This means something like S_3 = S_2 + f(3) and S_4 = S_3 + f(4)

In general, S_{n+1} = S_{n} + f(n+1) so you don't have to add up all the first n terms. Simply add the last term to the previous partial sum.

-------------------

Let's use that recursive trick to find S_5

S_5 = [f(1)+f(2)+f(3)+f(4)]+f(5)\\\\S_5 = S_4 + f(5)\\\\S_5 = \frac{5}{8} + \frac{1}{120}\\\\S_5 = \frac{19}{30}\\\\S_5 \approx 0.6333

The scratch work for f(5) is shown below.

7 0
2 years ago
Solve the formula for h: A=1/2bh+3
olga55 [171]

cross multiply the equation to give you

1= a(2bh+3)

divide both sides by a(2b+3)

answer is 1/2ab+3 = h


5 0
3 years ago
Read 2 more answers
Mitzi has 79 coins she divides the coins equally among herself and her 3 brothers Mitzi will keep any coins left over how many c
Elanso [62]

Answer:

19

Step-by-step explanation:

79÷4=19R3

       ≈ 19

7 0
2 years ago
Please help..Thanks:)
finlep [7]
From top to bottom: 16, 5, 28. Please give me 'brainliest answer?
8 0
3 years ago
Read 2 more answers
Solve 2x – 11 = k for x.
Flura [38]

Answer:

First, you add 11 to the other side of the equals sign. So it would be 2x=k+11. Now, you divide 2 from x and do the same on the other side of the equals sign. so x=  k+11

                ----------

                     2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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