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3 years ago

Please answer -w- i really need help lol online school is kinda hard.

Mathematics

1 answer:

Yuliya22 [10]3 years ago

8 0

Answer:

518.7

Step-by-step explanation:

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M is the centroid (center of gravity) of △ABC, line k goes thru M and intersects AB and AC . The distances of the vertices B and

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Step-by-step explanation:

The midpoint of BC will be a distance from line k that is the average of the distances of B and C: (17+13)/2 = 15. Call that midpoint P. We know distance MP is half of distance MA. This same relationship will hold with respect to the distances from P and A to any line through M. That is, the distance from line k (through M) is twice the distance from P to line k: 30 units.

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3 years ago

The table above gives values of the differentiable functions f and g, and f', the derivative of f, at selected values of x. If g

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Step-by-step explanation:

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2 years ago

If a/b = 4/3 and b/c = 2/3, what is a,b, and c?

kaheart [24]

Answer:

Step-by-step explanation:

$\frac{a}{b} = \frac{4}{3}$

$\frac{b}{c} = \frac{2}{3}$

to give b from both equation the same value

$\frac{a}{b} = \frac{4}{3} \times \frac{2}{2} = \frac{8}{6}$

$\frac{b}{c} = \frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$

a:b:c = 8:6:9

a = 8

b = 6

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3 years ago

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

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

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3 years ago

Two angles are supplementary. The first angle measures 40 degrees. What is the measurement of the second angle

Dmitrij [34]

Supplementary angles add up to 180º
If one is 40º, then the other is (180º-40º) = 140º

None of those choices describes a plane.
choice C is the only example of a plane.

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3 years ago

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