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Karolina [17]
3 years ago
11

A rectangle picture frame has a perimeter of 30 inches,the height of the frame is 8 inches , what is the width of the frame?

Mathematics
1 answer:
77julia77 [94]3 years ago
4 0
The answer is 7
hope this helps
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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
4(3-2x)=15 please helppp
mestny [16]

Answer:

x = -3/8

Step-by-step explanation:

4(3-2x)=15

Distribute

12 -8x = 15

Subtract 12 from each side

12-8x-12 = 15-12

-8x =3

Divide each side by -8

-8x/-8 = 3/-8

x = -3/8

7 0
2 years ago
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Find the area of the shaded region. (Plz show work)
Kamila [148]

Answer:

Area of shaded region ≈ 192.42

Step-by-step explanation:

21/2 = radius

radius = 10.5 m

A = πr squared

Area of shaded region≈346.36

10.5 - 3.5 = 7

Area of unshaded region ≈ 153.94

346.36 - 153.94 = 192.42

8 0
3 years ago
Look at pic 10 pts will mark brainilest WILL HELP OUT W 3 QUESTIONS
swat32

Answer:D

Step-by-step explanation:

I think that it is D since C is obviously dependant on everything else, B is also dependant on D, and since A is dependant on D.

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2 years ago
The fuel for a chainsaw is a mix of oil and gasoline.The label says to mix 6 ounces of oil and 16 ounces of gasoline. How much o
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I believe that choice A is the best answer out of those given above.
Hope this helps and please enjoy Brainly! -ZeusROX
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3 years ago
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