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3 years ago

The vertices of a triangle are P(−3, −4), Q(3, 4), and R(−6, −3). Name the vertices of Rx = 0 (PQR).

1 answer:

6 0

The correct answer is A) P'(3, −4), Q'(−3, 4), R'(6, −3)

Rx = 0 indicates a reflection over the y-axis.

The rule for such a transformation is:
(x, y) --> (-x, y)
which means that the x-coordinate changes sign and the y-coordinate stays the same.

Therefore:
P(-3, -4) --> P'(3, -4)
Q(3, 4) --> Q'(-3, 4)
R(-6, -3) --> R'(6, -3)

These points are those in option A).

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3 years ago

Micah made a scale model of the Empire State building.The building has an actual height of 381 meters. Micah’s model used a scal

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Answer:

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3 years ago

At work, Elon takes a break 1/5 of each hour he works. He also takes a lunch break for 1/2 of an hour each day he works. Elo

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Answer:

$h=50\ hours$

Step-by-step explanation:

Let

h -----> the number of hours, Elon works during one 5-day work week

we know that

$12\frac{1}{2}\ h=\frac{12*2+1}{2}=\frac{25}{2}\ h$

Elon’s break time must be equal to 1/2 of an hour multiplied by 5 days plus 1/5 multiplied by the total hours h

$\frac{25}{2}=5(\frac{1}{2})+\frac{1}{5}h$

Solve for h

Multiply by 10 both sides to remove the fraction

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3 years ago

Which statement about the cylinder are true? Select two options

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Answer:

$\ur \: answer)$

Step-by-step explanation:

<h2>THE RÅDIÜS ØF THE CYLINDER IS</h2><h2> $\frac{1}{2} x \: units$ </h2>

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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

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

3 0

3 years ago