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Crazy boy [7]
3 years ago
15

7 = 3/9x solve for x

Mathematics
2 answers:
lisov135 [29]3 years ago
7 0

Answer:

x = 2.33333333

Step-by-step explanation:

7 = 3/9x

21 = 9x

21/9 = x

x = 2.33333333

noname [10]3 years ago
4 0

Answer:

x = 1/21

Step-by-step explanation:

7 = 3/9x

Multiply both sides by 9x

7 x 9x = 3/9x x 9x

9x cancels out on the right side

63x = 3

Divide both sides by 63 to isolate x

63x/63 = 3/63

x = 1/21

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use the general slicing method to find the volume of The solid whose base is the triangle with vertices (0 comma 0 )​, (15 comma
lyudmila [28]

Answer:

volume V of the solid

\boxed{V=\displaystyle\frac{125\pi}{12}}

Step-by-step explanation:

The situation is depicted in the picture attached

(see picture)

First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each

[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]

Now, we slice our solid into n slices.  

Each slice is a quarter of cylinder 5/n thick and has a radius of  

-k(5/n) + 5  for each k = 1,2,..., n (see picture)

So the volume of each slice is  

\displaystyle\frac{\pi(-k(5/n) + 5 )^2*(5/n)}{4}

for k=1,2,..., n

We then add up the volumes of all these slices

\displaystyle\frac{\pi(-(5/n) + 5 )^2*(5/n)}{4}+\displaystyle\frac{\pi(-2(5/n) + 5 )^2*(5/n)}{4}+...+\displaystyle\frac{\pi(-n(5/n) + 5 )^2*(5/n)}{4}

Notice that the last term of the sum vanishes. After making up the expression a little, we get

\displaystyle\frac{5\pi}{4n}\left[(-(5/n)+5)^2+(-2(5/n)+5)^2+...+(-(n-1)(5/n)+5)^2\right]=\\\\\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2

But

\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}(-k(5/n)+5)^2=\displaystyle\frac{5\pi}{4n}\displaystyle\sum_{k=1}^{n-1}((5/n)^2k^2-(50/n)k+25)=\\\\\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)

we also know that

\displaystyle\sum_{k=1}^{n-1}k^2=\displaystyle\frac{n(n-1)(2n-1)}{6}

and

\displaystyle\sum_{k=1}^{n-1}k=\displaystyle\frac{n(n-1)}{2}

so we have, after replacing and simplifying, the sum of the slices equals

\displaystyle\frac{5\pi}{4n}\left((5/n)^2\displaystyle\sum_{k=1}^{n-1}k^2-(50/n)\displaystyle\sum_{k=1}^{n-1}k+25(n-1)\right)=\\\\=\displaystyle\frac{5\pi}{4n}\left(\displaystyle\frac{25}{n^2}.\displaystyle\frac{n(n-1)(2n-1)}{6}-\displaystyle\frac{50}{n}.\displaystyle\frac{n(n-1)}{2}+25(n-1)\right)=\\\\=\displaystyle\frac{125\pi}{24}.\displaystyle\frac{n(n-1)(2n-1)}{n^3}

Now we take the limit when n tends to infinite (the slices get thinner and thinner)

\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}\displaystyle\frac{n(n-1)(2n-1)}{n^3}=\displaystyle\frac{125\pi}{24}\displaystyle\lim_{n \rightarrow \infty}(2-3/n+1/n^2)=\\\\=\displaystyle\frac{125\pi}{24}.2=\displaystyle\frac{125\pi}{12}

and the volume V of our solid is

\boxed{V=\displaystyle\frac{125\pi}{12}}

3 0
3 years ago
You mow your neighbor’a lawn in 5 hours and earn $45. what is your hourly wage
Talja [164]

$9.00 per hour. take 45 and divide by 5 you get 9.

6 0
3 years ago
Read 2 more answers
If the students finished their assignment at 1:30 and they had been working for an hour and 45 minutes, what time did they start
bekas [8.4K]

Answer:

11:15

Step-by-step explanation:

7 0
3 years ago
PLZ, HELP WILL GIVE 20 MORE POINTS FOR FREE!!!!!!
GrogVix [38]

Answer:

16x+12

Step-by-step explanation:

4 sides

2*(5x-2 )

10x-4

2(3x+8)

6x+16

10x-4+6x+16=16x+12

7 0
3 years ago
Read 2 more answers
A population of 60 rabbits increases by 25% each year for 8 years. Find the population the end of each year
MrRa [10]

Answer & Step-by-step explanation:

It increased by 10 each year

Year 1 of 8: 70

Year 2 of 8: 80

Year 3 of 8: 90

Year 4 of 8: 100

Year 5 of 8: 110

Year 6 of 8: 120

Year 7 of 8: 130

Year 8 of 8 (Final Year): 140

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<u><em>Hope this helps!!! :)</em></u>

3 0
3 years ago
Read 2 more answers
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