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kiruha [24]
2 years ago
7

The surface area S of a right pyramid is given by S=1/2P1+B, where P is the perimeter of the base, 1 is the slant height, and B

is the area of the base. Solve for 1 ​
Mathematics
1 answer:
Nina [5.8K]2 years ago
8 0

Answer:

The general formula for the lateral surface area of a regular pyramid is L.S.A.=12pl where p represents the perimeter of the base and l the slant heigh

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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.

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2 years ago
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larisa [96]

Answer:CA, BC, BA

Step-by-step explanation:

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3 years ago
A scientist measured the growth rate of a bamboo plant at 6 inches in 12 hours. She compared the growth rate of a bamboo plant t
Arturiano [62]

Answer:

Answer Picture:

Step-by-step explanation:

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3 years ago
The graph shows the locations of a ball and a player seconds after the ball is thrown. What point could represent the player cat
svp [43]

Answer: The player is catching the ball at (4,25), therefore the second option is correct.

Explanation:

It the given graph x-axis represents the time (in seconds) after throw and y-axis represents the distance from goal (in yards).

In the graph violet and orange lines represents the distance of player and ball  respectively, from the goal at different point of time.

The player will catch the ball when the distance of player and ball from the goal is same on the single point of time.

The point of time where distance of player and ball from the goal is same, is the point of intersection of both lines.

From the graph it is clearly noticed that both lines  violet and orange insects at point (4,26), therefore player is catching the ball at (4,25), therefore the second option is correct.

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3 years ago
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Emily thinks the perfect tomato sauce has 888 cloves of garlic in every 500 mL . Raphael's tomato sauce has 12 cloves of garlic
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Answer:

Step-by-step explanation:

Choice A will be true, that is, Emily would fine the sauce too garlicky.

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